1,1,241,0,0.188120," ","integrate((d*x^2+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"1/4*sqrt(2)*((a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*d)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*d)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
2,1,241,0,0.172360," ","integrate((-d*x^2+c)/(b*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + \left(a b^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{b}}\right)}{8 \, a b^{3}}"," ",0,"1/4*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^2*c - (a*b^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/b)^(1/4))/(a/b)^(1/4))/(a*b^3) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*d)*log(x^2 + sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3) - 1/8*sqrt(2)*((a*b^3)^(1/4)*b^2*c + (a*b^3)^(3/4)*d)*log(x^2 - sqrt(2)*x*(a/b)^(1/4) + sqrt(a/b))/(a*b^3)","A",0
3,1,230,0,0.181776," ","integrate((d*x^2+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(b^{2} c + \sqrt{-a b} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b d\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b d\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}}"," ",0,"-1/4*sqrt(2)*(b^2*c + sqrt(-a*b)*b*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c - sqrt(-a*b)*b*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c - sqrt(-a*b)*b*d)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c - sqrt(-a*b)*b*d)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4)","B",0
4,1,228,0,0.324862," ","integrate((-d*x^2+c)/(-b*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(b^{2} c - \sqrt{-a b} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + \sqrt{-a b} b d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(-\frac{a}{b}\right)^{\frac{1}{4}}\right)}}{2 \, \left(-\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, \left(-a b^{3}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(b^{2} c + \sqrt{-a b} b d\right)} \log\left(x^{2} + \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b^{2} c + \sqrt{-a b} b d\right)} \log\left(x^{2} - \sqrt{2} x \left(-\frac{a}{b}\right)^{\frac{1}{4}} + \sqrt{-\frac{a}{b}}\right)}{8 \, \left(-a b^{3}\right)^{\frac{3}{4}}}"," ",0,"-1/4*sqrt(2)*(b^2*c - sqrt(-a*b)*b*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/4*sqrt(2)*(b^2*c + sqrt(-a*b)*b*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(-a/b)^(1/4))/(-a/b)^(1/4))/(-a*b^3)^(3/4) - 1/8*sqrt(2)*(b^2*c + sqrt(-a*b)*b*d)*log(x^2 + sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4) + 1/8*sqrt(2)*(b^2*c + sqrt(-a*b)*b*d)*log(x^2 - sqrt(2)*x*(-a/b)^(1/4) + sqrt(-a/b))/(-a*b^3)^(3/4)","B",0
5,1,52,0,0.200724," ","integrate((3*x^2+2)/(9*x^4+4),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{9}{8} \, \sqrt{2} \left(\frac{4}{9}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{4}{9}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{9}{8} \, \sqrt{2} \left(\frac{4}{9}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{4}{9}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/6*sqrt(3)*arctan(9/8*sqrt(2)*(4/9)^(3/4)*(2*x + sqrt(2)*(4/9)^(1/4))) + 1/6*sqrt(3)*arctan(9/8*sqrt(2)*(4/9)^(3/4)*(2*x - sqrt(2)*(4/9)^(1/4)))","A",0
6,1,40,0,0.170190," ","integrate((-3*x^2+2)/(9*x^4+4),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(x^{2} + \sqrt{2} \left(\frac{4}{9}\right)^{\frac{1}{4}} x + \frac{2}{3}\right) - \frac{1}{12} \, \sqrt{3} \log\left(x^{2} - \sqrt{2} \left(\frac{4}{9}\right)^{\frac{1}{4}} x + \frac{2}{3}\right)"," ",0,"1/12*sqrt(3)*log(x^2 + sqrt(2)*(4/9)^(1/4)*x + 2/3) - 1/12*sqrt(3)*log(x^2 - sqrt(2)*(4/9)^(1/4)*x + 2/3)","A",0
7,1,29,0,0.158669," ","integrate((3*x^2+2)/(-9*x^4+4),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} \log\left({\left| x + \frac{1}{3} \, \sqrt{6} \right|}\right) - \frac{1}{12} \, \sqrt{6} \log\left({\left| x - \frac{1}{3} \, \sqrt{6} \right|}\right)"," ",0,"1/12*sqrt(6)*log(abs(x + 1/3*sqrt(6))) - 1/12*sqrt(6)*log(abs(x - 1/3*sqrt(6)))","B",0
8,1,12,0,0.159360," ","integrate((-3*x^2+2)/(-9*x^4+4),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x\right)"," ",0,"1/6*sqrt(6)*arctan(1/2*sqrt(6)*x)","A",0
9,-2,0,0,0.000000," ","integrate((b*x^2+a^(1/2)*b^(1/2))/(b*x^4+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
10,-2,0,0,0.000000," ","integrate((-b*x^2+a^(1/2)*b^(1/2))/(b*x^4+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
11,1,222,0,0.170611," ","integrate((e*x^2+d)/(e^2*x^4+d^2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + 2 \, x\right)} e^{\frac{1}{2}}}{2 \, {\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-6\right)}}{4 \, d^{2}} + \frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} - 2 \, x\right)} e^{\frac{1}{2}}}{2 \, {\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-6\right)}}{4 \, d^{2}} + \frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} - {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left(\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} x e^{\left(-\frac{1}{2}\right)} + x^{2} + \sqrt{d^{2}} e^{\left(-1\right)}\right)}{8 \, d^{2}} - \frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} - {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left(-\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} x e^{\left(-\frac{1}{2}\right)} + x^{2} + \sqrt{d^{2}} e^{\left(-1\right)}\right)}{8 \, d^{2}}"," ",0,"1/4*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) + (d^2)^(3/4)*e^(11/2))*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2)^(1/4)*e^(-1/2) + 2*x)*e^(1/2)/(d^2)^(1/4))*e^(-6)/d^2 + 1/4*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) + (d^2)^(3/4)*e^(11/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2)^(1/4)*e^(-1/2) - 2*x)*e^(1/2)/(d^2)^(1/4))*e^(-6)/d^2 + 1/8*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) - (d^2)^(3/4)*e^(11/2))*e^(-6)*log(sqrt(2)*(d^2)^(1/4)*x*e^(-1/2) + x^2 + sqrt(d^2)*e^(-1))/d^2 - 1/8*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) - (d^2)^(3/4)*e^(11/2))*e^(-6)*log(-sqrt(2)*(d^2)^(1/4)*x*e^(-1/2) + x^2 + sqrt(d^2)*e^(-1))/d^2","B",0
12,1,222,0,0.223747," ","integrate((-e*x^2+d)/(e^2*x^4+d^2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} - {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + 2 \, x\right)} e^{\frac{1}{2}}}{2 \, {\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-6\right)}}{4 \, d^{2}} + \frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} - {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} - 2 \, x\right)} e^{\frac{1}{2}}}{2 \, {\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-6\right)}}{4 \, d^{2}} + \frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left(\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} x e^{\left(-\frac{1}{2}\right)} + x^{2} + \sqrt{d^{2}} e^{\left(-1\right)}\right)}{8 \, d^{2}} - \frac{\sqrt{2} {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left(-\sqrt{2} {\left(d^{2}\right)}^{\frac{1}{4}} x e^{\left(-\frac{1}{2}\right)} + x^{2} + \sqrt{d^{2}} e^{\left(-1\right)}\right)}{8 \, d^{2}}"," ",0,"1/4*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) - (d^2)^(3/4)*e^(11/2))*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2)^(1/4)*e^(-1/2) + 2*x)*e^(1/2)/(d^2)^(1/4))*e^(-6)/d^2 + 1/4*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) - (d^2)^(3/4)*e^(11/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2)^(1/4)*e^(-1/2) - 2*x)*e^(1/2)/(d^2)^(1/4))*e^(-6)/d^2 + 1/8*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) + (d^2)^(3/4)*e^(11/2))*e^(-6)*log(sqrt(2)*(d^2)^(1/4)*x*e^(-1/2) + x^2 + sqrt(d^2)*e^(-1))/d^2 - 1/8*sqrt(2)*((d^2)^(1/4)*d*e^(11/2) + (d^2)^(3/4)*e^(11/2))*e^(-6)*log(-sqrt(2)*(d^2)^(1/4)*x*e^(-1/2) + x^2 + sqrt(d^2)*e^(-1))/d^2","B",0
13,1,19,0,0.159426," ","integrate((2*x^2+5)/(x^4-1),x, algorithm=""giac"")","-\frac{3}{2} \, \arctan\left(x\right) - \frac{7}{4} \, \log\left({\left| x + 1 \right|}\right) + \frac{7}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-3/2*arctan(x) - 7/4*log(abs(x + 1)) + 7/4*log(abs(x - 1))","B",0
14,0,0,0,0.000000," ","integrate((b*x^2+1)/(-b^2*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{b x^{2} + 1}{\sqrt{-b^{2} x^{4} + 1}}\,{d x}"," ",0,"integrate((b*x^2 + 1)/sqrt(-b^2*x^4 + 1), x)","F",0
15,0,0,0,0.000000," ","integrate((-b*x^2+1)/(-b^2*x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{b x^{2} - 1}{\sqrt{-b^{2} x^{4} + 1}}\,{d x}"," ",0,"integrate(-(b*x^2 - 1)/sqrt(-b^2*x^4 + 1), x)","F",0
16,0,0,0,0.000000," ","integrate((b*x^2+1)/(b^2*x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{b x^{2} + 1}{\sqrt{b^{2} x^{4} - 1}}\,{d x}"," ",0,"integrate((b*x^2 + 1)/sqrt(b^2*x^4 - 1), x)","F",0
17,0,0,0,0.000000," ","integrate((-b*x^2+1)/(b^2*x^4-1)^(1/2),x, algorithm=""giac"")","\int -\frac{b x^{2} - 1}{\sqrt{b^{2} x^{4} - 1}}\,{d x}"," ",0,"integrate(-(b*x^2 - 1)/sqrt(b^2*x^4 - 1), x)","F",0
18,0,0,0,0.000000," ","integrate((-b*x^2+1)/(b^2*x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{b x^{2} - 1}{\sqrt{b^{2} x^{4} + 1}}\,{d x}"," ",0,"integrate(-(b*x^2 - 1)/sqrt(b^2*x^4 + 1), x)","F",0
19,0,0,0,0.000000," ","integrate((b*x^2+1)/(b^2*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{b x^{2} + 1}{\sqrt{b^{2} x^{4} + 1}}\,{d x}"," ",0,"integrate((b*x^2 + 1)/sqrt(b^2*x^4 + 1), x)","F",0
20,0,0,0,0.000000," ","integrate((-b*x^2+1)/(-b^2*x^4-1)^(1/2),x, algorithm=""giac"")","\int -\frac{b x^{2} - 1}{\sqrt{-b^{2} x^{4} - 1}}\,{d x}"," ",0,"integrate(-(b*x^2 - 1)/sqrt(-b^2*x^4 - 1), x)","F",0
21,0,0,0,0.000000," ","integrate((b*x^2+1)/(-b^2*x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{b x^{2} + 1}{\sqrt{-b^{2} x^{4} - 1}}\,{d x}"," ",0,"integrate((b*x^2 + 1)/sqrt(-b^2*x^4 - 1), x)","F",0
22,0,0,0,0.000000," ","integrate((c^2*x^2+1)^(1/2)/(-c^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c^{2} x^{2} + 1}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 + 1)/sqrt(-c^2*x^2 + 1), x)","F",0
23,0,0,0,0.000000," ","integrate((c^2*x^2+1)/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{c^{2} x^{2} + 1}{\sqrt{-c^{4} x^{4} + 1}}\,{d x}"," ",0,"integrate((c^2*x^2 + 1)/sqrt(-c^4*x^4 + 1), x)","F",0
24,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(c^2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/sqrt(c^2*x^2 + 1), x)","F",0
25,0,0,0,0.000000," ","integrate((-c^2*x^2+1)/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{c^{2} x^{2} - 1}{\sqrt{-c^{4} x^{4} + 1}}\,{d x}"," ",0,"integrate(-(c^2*x^2 - 1)/sqrt(-c^4*x^4 + 1), x)","F",0
26,1,1642,0,1.118873," ","integrate((e*x^2+d)/(e^2*x^4+b*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} - 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} + 16 \, b^{2} d^{2} e^{4} - 2 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} - 2 \, b^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} - 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} + 2 \, b^{3} e^{4} + 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{b + \sqrt{-4 \, d^{2} e^{2} + b^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} + 8 \, b d^{3} e^{6} - 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} + 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} - 16 \, b^{2} d^{2} e^{4} - 2 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} + 2 \, b^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} + 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} - 2 \, b^{3} e^{4} - 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{b - \sqrt{-4 \, d^{2} e^{2} + b^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} + 8 \, b d^{3} e^{6} - 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 - 32*d^4*e^6 + 8*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 + 16*b^2*d^2*e^4 - 2*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 - 2*b^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 - 8*b*d^2*e^6 + sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 + 2*b^3*e^4 + 8*(4*d^2*e^2 - b^2)*d^2*e^4 - 2*(4*d^2*e^2 - b^2)*b^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 + 2*(4*d^2*e^2 - b^2)*b*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(b + sqrt(-4*d^2*e^2 + b^2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 + 8*b*d^3*e^6 - 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6) + 1/4*(16*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 + 32*d^4*e^6 + 8*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 - 16*b^2*d^2*e^4 - 2*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 + 2*b^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 + 8*b*d^2*e^6 + sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 - 2*b^3*e^4 - 8*(4*d^2*e^2 - b^2)*d^2*e^4 + 2*(4*d^2*e^2 - b^2)*b^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 - 2*(4*d^2*e^2 - b^2)*b*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(b - sqrt(-4*d^2*e^2 + b^2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 + 8*b*d^3*e^6 - 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6)","B",0
27,1,1642,0,1.087122," ","integrate((e*x^2+d)/(e^2*x^4+f*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} - 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} + 16 \, d^{2} f^{2} e^{4} - 2 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} - 2 \, f^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} - 8 \, d^{2} f e^{6} + 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} + 2 \, f^{3} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{f + \sqrt{-4 \, d^{2} e^{2} + f^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} + 8 \, d^{3} f e^{6} - 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} + 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} - 16 \, d^{2} f^{2} e^{4} - 2 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} + 2 \, f^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} + 8 \, d^{2} f e^{6} - 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} - 2 \, f^{3} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{f - \sqrt{-4 \, d^{2} e^{2} + f^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} + 8 \, d^{3} f e^{6} - 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 - 32*d^4*e^6 + 8*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 + 16*d^2*f^2*e^4 - 2*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 - 2*f^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 - 8*d^2*f*e^6 + 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 + 2*f^3*e^4 - 2*(4*d^2*e^2 - f^2)*f^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 + 2*(4*d^2*e^2 - f^2)*f*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(f + sqrt(-4*d^2*e^2 + f^2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 + 8*d^3*f*e^6 - 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6) + 1/4*(16*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 + 32*d^4*e^6 + 8*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 - 16*d^2*f^2*e^4 - 2*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 + 2*f^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 + 8*d^2*f*e^6 - 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 - 2*f^3*e^4 + 2*(4*d^2*e^2 - f^2)*f^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 - 2*(4*d^2*e^2 - f^2)*f*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(f - sqrt(-4*d^2*e^2 + f^2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 + 8*d^3*f*e^6 - 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6)","B",0
28,1,1676,0,1.122128," ","integrate((e*x^2+d)/(e^2*x^4-b*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} + 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} - 16 \, b^{2} d^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} + 2 \, b^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} - 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} + 2 \, b^{3} e^{4} - 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(b + \sqrt{-4 \, d^{2} e^{2} + b^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} - 8 \, b d^{3} e^{6} + 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} - 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} + 16 \, b^{2} d^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} - 2 \, b^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} + 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} - 2 \, b^{3} e^{4} + 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(b - \sqrt{-4 \, d^{2} e^{2} + b^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} - 8 \, b d^{3} e^{6} + 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 + 32*d^4*e^6 - 8*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 - 16*b^2*d^2*e^4 + 2*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 + 2*b^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 - 8*b*d^2*e^6 + sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 + 2*b^3*e^4 - 8*(4*d^2*e^2 - b^2)*d^2*e^4 + 2*(4*d^2*e^2 - b^2)*b^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 + 2*(4*d^2*e^2 - b^2)*b*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(b + sqrt(-4*d^2*e^2 + b^2))*e^(-2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 - 8*b*d^3*e^6 + 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6) + 1/4*(16*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 - 32*d^4*e^6 - 8*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 + 16*b^2*d^2*e^4 + 2*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 - 2*b^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 + 8*b*d^2*e^6 + sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 - 2*b^3*e^4 + 8*(4*d^2*e^2 - b^2)*d^2*e^4 - 2*(4*d^2*e^2 - b^2)*b^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 - 2*(4*d^2*e^2 - b^2)*b*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(b - sqrt(-4*d^2*e^2 + b^2))*e^(-2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 - 8*b*d^3*e^6 + 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6)","B",0
29,1,1676,0,1.139258," ","integrate((e*x^2+d)/(e^2*x^4-f*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} + 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} - 16 \, d^{2} f^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} + 2 \, f^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} - 8 \, d^{2} f e^{6} - 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} + 2 \, f^{3} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(f + \sqrt{-4 \, d^{2} e^{2} + f^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} - 8 \, d^{3} f e^{6} + 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} - 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} + 16 \, d^{2} f^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} - 2 \, f^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} + 8 \, d^{2} f e^{6} + 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} - 2 \, f^{3} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(f - \sqrt{-4 \, d^{2} e^{2} + f^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} - 8 \, d^{3} f e^{6} + 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 + 32*d^4*e^6 - 8*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 - 16*d^2*f^2*e^4 + 2*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 + 2*f^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 - 8*d^2*f*e^6 - 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 + 2*f^3*e^4 + 2*(4*d^2*e^2 - f^2)*f^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 + 2*(4*d^2*e^2 - f^2)*f*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(f + sqrt(-4*d^2*e^2 + f^2))*e^(-2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 - 8*d^3*f*e^6 + 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6) + 1/4*(16*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 - 32*d^4*e^6 - 8*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 + 16*d^2*f^2*e^4 + 2*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 - 2*f^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 + 8*d^2*f*e^6 + 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 - 2*f^3*e^4 - 2*(4*d^2*e^2 - f^2)*f^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 - 2*(4*d^2*e^2 - f^2)*f*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(f - sqrt(-4*d^2*e^2 + f^2))*e^(-2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 - 8*d^3*f*e^6 + 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6)","B",0
30,1,1642,0,1.162610," ","integrate((-e*x^2+d)/(e^2*x^4+b*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} - 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} + 16 \, b^{2} d^{2} e^{4} - 2 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} - 2 \, b^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} - 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} + 2 \, b^{3} e^{4} + 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{b + \sqrt{-4 \, d^{2} e^{2} + b^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} + 8 \, b d^{3} e^{6} - 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} + 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} - 16 \, b^{2} d^{2} e^{4} - 2 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} + 2 \, b^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} + 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} - 2 \, b^{3} e^{4} - 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{b - \sqrt{-4 \, d^{2} e^{2} + b^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} + 8 \, b d^{3} e^{6} - 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 - 32*d^4*e^6 + 8*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 + 16*b^2*d^2*e^4 - 2*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 - 2*b^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 - 8*b*d^2*e^6 + sqrt(2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 + 2*b^3*e^4 + 8*(4*d^2*e^2 - b^2)*d^2*e^4 - 2*(4*d^2*e^2 - b^2)*b^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 + 2*(4*d^2*e^2 - b^2)*b*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(b + sqrt(-4*d^2*e^2 + b^2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 + 8*b*d^3*e^6 - 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6) + 1/4*(16*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 + 32*d^4*e^6 + 8*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 - 16*b^2*d^2*e^4 - 2*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 + 2*b^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 + 8*b*d^2*e^6 + sqrt(2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 - 2*b^3*e^4 - 8*(4*d^2*e^2 - b^2)*d^2*e^4 + 2*(4*d^2*e^2 - b^2)*b^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 - 2*(4*d^2*e^2 - b^2)*b*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(b - sqrt(-4*d^2*e^2 + b^2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 + 8*b*d^3*e^6 - 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6)","B",0
31,1,1642,0,1.253655," ","integrate((-e*x^2+d)/(e^2*x^4+f*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} - 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} + 16 \, d^{2} f^{2} e^{4} - 2 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} - 2 \, f^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} - 8 \, d^{2} f e^{6} + 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} + 2 \, f^{3} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{f + \sqrt{-4 \, d^{2} e^{2} + f^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} + 8 \, d^{3} f e^{6} - 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} + 32 \, d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} - 16 \, d^{2} f^{2} e^{4} - 2 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} + 2 \, f^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} + 8 \, d^{2} f e^{6} - 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} - 2 \, f^{3} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{f - \sqrt{-4 \, d^{2} e^{2} + f^{2}}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} + 8 \, d^{3} f e^{6} - 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 - 32*d^4*e^6 + 8*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 + 16*d^2*f^2*e^4 - 2*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 - 2*f^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 - 8*d^2*f*e^6 + 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 + 2*f^3*e^4 - 2*(4*d^2*e^2 - f^2)*f^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 + 2*(4*d^2*e^2 - f^2)*f*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(f + sqrt(-4*d^2*e^2 + f^2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 + 8*d^3*f*e^6 - 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6) + 1/4*(16*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 + 32*d^4*e^6 + 8*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 - 16*d^2*f^2*e^4 - 2*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 + 2*f^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 + 8*d^2*f*e^6 - 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 - 2*f^3*e^4 + 2*(4*d^2*e^2 - f^2)*f^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 - 2*(4*d^2*e^2 - f^2)*f*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x*e/sqrt(f - sqrt(-4*d^2*e^2 + f^2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 + 8*d^3*f*e^6 - 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6)","B",0
32,1,1676,0,1.126776," ","integrate((-e*x^2+d)/(e^2*x^4-b*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} + 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} - 16 \, b^{2} d^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} + 2 \, b^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} - 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} + 2 \, b^{3} e^{4} - 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} - \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(b + \sqrt{-4 \, d^{2} e^{2} + b^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} - 8 \, b d^{3} e^{6} + 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{2} + \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{4} - 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d^{2} e^{4} + 16 \, b^{2} d^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} e^{2} - 2 \, b^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{2} e^{6} + 8 \, b d^{2} e^{6} + \sqrt{2} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} e^{4} - 2 \, b^{3} e^{4} + 8 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d^{2} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} b e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b^{2} d - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} b d e^{2} - 8 \, d^{3} e^{6} + 2 \, b^{2} d e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + b^{2}} \sqrt{-b e^{2} + \sqrt{-4 \, d^{2} e^{2} + b^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - b^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(b - \sqrt{-4 \, d^{2} e^{2} + b^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, b^{2} d^{3} e^{4} + b^{4} d e^{2} - 8 \, b d^{3} e^{6} + 2 \, b^{3} d e^{4} - 4 \, d^{3} e^{8} + b^{2} d e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 + 32*d^4*e^6 - 8*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 - 16*b^2*d^2*e^4 + 2*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 + 2*b^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 - 8*b*d^2*e^6 + sqrt(2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 + 2*b^3*e^4 - 8*(4*d^2*e^2 - b^2)*d^2*e^4 + 2*(4*d^2*e^2 - b^2)*b^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 + 2*(4*d^2*e^2 - b^2)*b*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 - sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(b + sqrt(-4*d^2*e^2 + b^2))*e^(-2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 - 8*b*d^3*e^6 + 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6) + 1/4*(16*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^2 + sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^4 - 32*d^4*e^6 - 8*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d^2*e^4 + 16*b^2*d^2*e^4 + 2*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3*e^2 - 2*b^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^2 - 4*sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^2*e^6 + 8*b*d^2*e^6 + sqrt(2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*e^4 - 2*b^3*e^4 + 8*(4*d^2*e^2 - b^2)*d^2*e^4 - 2*(4*d^2*e^2 - b^2)*b^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*e^4 - 2*(4*d^2*e^2 - b^2)*b*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b^2*d - 2*sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*b*d*e^2 - 8*d^3*e^6 + 2*b^2*d*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + b^2)*sqrt(-b*e^2 + sqrt(-4*d^2*e^2 + b^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - b^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(b - sqrt(-4*d^2*e^2 + b^2))*e^(-2)))/(16*d^5*e^6 - 8*b^2*d^3*e^4 + b^4*d*e^2 - 8*b*d^3*e^6 + 2*b^3*d*e^4 - 4*d^3*e^8 + b^2*d*e^6)","B",0
33,1,1676,0,1.080571," ","integrate((-e*x^2+d)/(e^2*x^4-f*x^2+d^2),x, algorithm=""giac"")","\frac{{\left(16 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} + 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} + 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} - 16 \, d^{2} f^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} + 2 \, f^{4} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} - 8 \, d^{2} f e^{6} - 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} + 2 \, f^{3} e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} - 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} - \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(f + \sqrt{-4 \, d^{2} e^{2} + f^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} - 8 \, d^{3} f e^{6} + 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}} + \frac{{\left(16 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{4} e^{4} - 8 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{2} + \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{4} - 32 \, d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} f e^{4} + 16 \, d^{2} f^{2} e^{4} + 2 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} e^{2} - 2 \, f^{4} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{3} + 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{2} - 4 \, \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{2} e^{6} + 8 \, d^{2} f e^{6} + 8 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d^{2} e^{4} + \sqrt{2} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f^{2} e^{4} - 2 \, f^{3} e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f^{2} e^{2} + \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} f e^{4} - 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} f e^{4} + 2 \, {\left(4 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d^{3} e^{2} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f^{2} - 2 \, \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d f e^{2} - 8 \, d^{3} e^{6} + 2 \, d f^{2} e^{4} - \sqrt{2} \sqrt{-4 \, d^{2} e^{2} + f^{2}} \sqrt{-f e^{2} + \sqrt{-4 \, d^{2} e^{2} + f^{2}} e^{2}} d e^{4} + 2 \, {\left(4 \, d^{2} e^{2} - f^{2}\right)} d e^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{-{\left(f - \sqrt{-4 \, d^{2} e^{2} + f^{2}}\right)} e^{\left(-2\right)}}}\right)}{4 \, {\left(16 \, d^{5} e^{6} - 8 \, d^{3} f^{2} e^{4} + d f^{4} e^{2} - 8 \, d^{3} f e^{6} + 2 \, d f^{3} e^{4} - 4 \, d^{3} e^{8} + d f^{2} e^{6}\right)}}"," ",0,"1/4*(16*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 + 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 + 32*d^4*e^6 - 8*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 - 16*d^2*f^2*e^4 + 2*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 + 2*f^4*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 - 8*d^2*f*e^6 - 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 + 2*f^3*e^4 + 2*(4*d^2*e^2 - f^2)*f^2*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 + 2*(4*d^2*e^2 - f^2)*f*e^4 - 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 - sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(f + sqrt(-4*d^2*e^2 + f^2))*e^(-2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 - 8*d^3*f*e^6 + 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6) + 1/4*(16*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^4*e^4 - 8*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f^2*e^2 - 4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^2 + sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^4 - 32*d^4*e^6 - 8*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*f*e^4 + 16*d^2*f^2*e^4 + 2*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3*e^2 - 2*f^4*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^3 + 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^2 - 4*sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^2*e^6 + 8*d^2*f*e^6 + 8*(4*d^2*e^2 - f^2)*d^2*e^4 + sqrt(2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f^2*e^4 - 2*f^3*e^4 - 2*(4*d^2*e^2 - f^2)*f^2*e^2 + sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*f*e^4 - 2*(4*d^2*e^2 - f^2)*f*e^4 + 2*(4*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d^3*e^2 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f^2 - 2*sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*f*e^2 - 8*d^3*e^6 + 2*d*f^2*e^4 - sqrt(2)*sqrt(-4*d^2*e^2 + f^2)*sqrt(-f*e^2 + sqrt(-4*d^2*e^2 + f^2)*e^2)*d*e^4 + 2*(4*d^2*e^2 - f^2)*d*e^4)*e)*arctan(2*sqrt(1/2)*x/sqrt(-(f - sqrt(-4*d^2*e^2 + f^2))*e^(-2)))/(16*d^5*e^6 - 8*d^3*f^2*e^4 + d*f^4*e^2 - 8*d^3*f*e^6 + 2*d*f^3*e^4 - 4*d^3*e^8 + d*f^2*e^6)","B",0
34,1,2202,0,1.372052," ","integrate((-e*x^2+d)/(c*d^2/e^2+b*x^2+c*x^4),x, algorithm=""giac"")","-\frac{{\left(32 \, c^{5} d^{4} e^{4} - 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 16 \, b^{2} c^{3} d^{2} e^{6} + 8 \, b c^{4} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} - 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} + 4 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 2 \, b^{4} c e^{8} - 2 \, b^{3} c^{2} e^{8} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} + 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b c^{2} e^{4} + 2 \, {\left(8 \, c^{5} d^{3} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} - 2 \, b^{2} c^{3} d e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{2} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{2} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d e^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{-4 \, c^{2} d^{2} e^{\left(-2\right)} + b^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{2} - 8 \, b^{2} c^{3} d^{3} e^{4} + 8 \, b c^{4} d^{3} e^{4} - 4 \, c^{5} d^{3} e^{4} + b^{4} c d e^{6} - 2 \, b^{3} c^{2} d e^{6} + b^{2} c^{3} d e^{6}\right)} {\left| c \right|}} + \frac{{\left(32 \, c^{5} d^{4} e^{4} + 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 16 \, b^{2} c^{3} d^{2} e^{6} + 8 \, b c^{4} d^{2} e^{6} - 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} + 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 2 \, b^{4} c e^{8} - 2 \, b^{3} c^{2} e^{8} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} - 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b c^{2} e^{4} + 2 \, {\left(8 \, c^{5} d^{3} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} - 2 \, b^{2} c^{3} d e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{2} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{2} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d e^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{-4 \, c^{2} d^{2} e^{\left(-2\right)} + b^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{2} - 8 \, b^{2} c^{3} d^{3} e^{4} + 8 \, b c^{4} d^{3} e^{4} - 4 \, c^{5} d^{3} e^{4} + b^{4} c d e^{6} - 2 \, b^{3} c^{2} d e^{6} + b^{2} c^{3} d e^{6}\right)} {\left| c \right|}}"," ",0,"-1/4*(32*c^5*d^4*e^4 - 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 16*b^2*c^3*d^2*e^6 + 8*b*c^4*d^2*e^6 + 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 - 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 + 4*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 8*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d^2*e^2 + 2*b^4*c*e^8 - 2*b^3*c^2*e^8 - sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^4*e^6 + 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*c*e^6 - sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*e^4 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*e^4 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*e^4 + 2*(4*c^2*d^2*e^2 - b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*b*c^2*e^4 + 2*(8*c^5*d^3*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d^3 - 2*b^2*c^3*d*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*d*e^2 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d*e^2 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d*e^2 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d*e^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(-4*c^2*d^2*e^(-2) + b^2))/c))/((16*c^5*d^5*e^2 - 8*b^2*c^3*d^3*e^4 + 8*b*c^4*d^3*e^4 - 4*c^5*d^3*e^4 + b^4*c*d*e^6 - 2*b^3*c^2*d*e^6 + b^2*c^3*d*e^6)*abs(c)) + 1/4*(32*c^5*d^4*e^4 + 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 16*b^2*c^3*d^2*e^6 + 8*b*c^4*d^2*e^6 - 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 + 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 - 4*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 8*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d^2*e^2 + 2*b^4*c*e^8 - 2*b^3*c^2*e^8 + sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^4*e^6 - 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*c*e^6 + sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*e^4 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*e^4 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*e^4 + 2*(4*c^2*d^2*e^2 - b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*b*c^2*e^4 + 2*(8*c^5*d^3*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d^3 - 2*b^2*c^3*d*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*d*e^2 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d*e^2 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d*e^2 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d*e^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(-4*c^2*d^2*e^(-2) + b^2))/c))/((16*c^5*d^5*e^2 - 8*b^2*c^3*d^3*e^4 + 8*b*c^4*d^3*e^4 - 4*c^5*d^3*e^4 + b^4*c*d*e^6 - 2*b^3*c^2*d*e^6 + b^2*c^3*d*e^6)*abs(c))","B",0
35,1,2202,0,1.402306," ","integrate((e*x^2+d)/(c*d^2/e^2+b*x^2+c*x^4),x, algorithm=""giac"")","-\frac{{\left(32 \, c^{5} d^{4} e^{4} - 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 16 \, b^{2} c^{3} d^{2} e^{6} + 8 \, b c^{4} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} - 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} + 4 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 2 \, b^{4} c e^{8} - 2 \, b^{3} c^{2} e^{8} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} + 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b c^{2} e^{4} - 2 \, {\left(8 \, c^{5} d^{3} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} - 2 \, b^{2} c^{3} d e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{2} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{2} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d e^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{-4 \, c^{2} d^{2} e^{\left(-2\right)} + b^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{2} - 8 \, b^{2} c^{3} d^{3} e^{4} + 8 \, b c^{4} d^{3} e^{4} - 4 \, c^{5} d^{3} e^{4} + b^{4} c d e^{6} - 2 \, b^{3} c^{2} d e^{6} + b^{2} c^{3} d e^{6}\right)} {\left| c \right|}} + \frac{{\left(32 \, c^{5} d^{4} e^{4} + 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 16 \, b^{2} c^{3} d^{2} e^{6} + 8 \, b c^{4} d^{2} e^{6} - 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} + 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 2 \, b^{4} c e^{8} - 2 \, b^{3} c^{2} e^{8} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} - 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b c^{2} e^{4} - 2 \, {\left(8 \, c^{5} d^{3} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} - 2 \, b^{2} c^{3} d e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{2} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{2} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d e^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{-4 \, c^{2} d^{2} e^{\left(-2\right)} + b^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{2} - 8 \, b^{2} c^{3} d^{3} e^{4} + 8 \, b c^{4} d^{3} e^{4} - 4 \, c^{5} d^{3} e^{4} + b^{4} c d e^{6} - 2 \, b^{3} c^{2} d e^{6} + b^{2} c^{3} d e^{6}\right)} {\left| c \right|}}"," ",0,"-1/4*(32*c^5*d^4*e^4 - 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 16*b^2*c^3*d^2*e^6 + 8*b*c^4*d^2*e^6 + 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 - 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 + 4*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 8*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d^2*e^2 + 2*b^4*c*e^8 - 2*b^3*c^2*e^8 - sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^4*e^6 + 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*c*e^6 - sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*e^4 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*e^4 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*e^4 + 2*(4*c^2*d^2*e^2 - b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*b*c^2*e^4 - 2*(8*c^5*d^3*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d^3 - 2*b^2*c^3*d*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*d*e^2 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d*e^2 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d*e^2 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d*e^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(-4*c^2*d^2*e^(-2) + b^2))/c))/((16*c^5*d^5*e^2 - 8*b^2*c^3*d^3*e^4 + 8*b*c^4*d^3*e^4 - 4*c^5*d^3*e^4 + b^4*c*d*e^6 - 2*b^3*c^2*d*e^6 + b^2*c^3*d*e^6)*abs(c)) + 1/4*(32*c^5*d^4*e^4 + 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 16*b^2*c^3*d^2*e^6 + 8*b*c^4*d^2*e^6 - 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 + 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 - 4*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 8*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d^2*e^2 + 2*b^4*c*e^8 - 2*b^3*c^2*e^8 + sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^4*e^6 - 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*c*e^6 + sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*e^4 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*e^4 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*e^4 + 2*(4*c^2*d^2*e^2 - b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*b*c^2*e^4 - 2*(8*c^5*d^3*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d^3 - 2*b^2*c^3*d*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*d*e^2 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d*e^2 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d*e^2 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d*e^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(-4*c^2*d^2*e^(-2) + b^2))/c))/((16*c^5*d^5*e^2 - 8*b^2*c^3*d^3*e^4 + 8*b*c^4*d^3*e^4 - 4*c^5*d^3*e^4 + b^4*c*d*e^6 - 2*b^3*c^2*d*e^6 + b^2*c^3*d*e^6)*abs(c))","B",0
36,1,2202,0,1.350089," ","integrate((e*x^2+d)/(b*x^2+c*(d^2/e^2+x^4)),x, algorithm=""giac"")","-\frac{{\left(32 \, c^{5} d^{4} e^{4} - 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 16 \, b^{2} c^{3} d^{2} e^{6} + 8 \, b c^{4} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} - 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} + 4 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 2 \, b^{4} c e^{8} - 2 \, b^{3} c^{2} e^{8} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} + 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b c^{2} e^{4} - 2 \, {\left(8 \, c^{5} d^{3} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} - 2 \, b^{2} c^{3} d e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{2} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{2} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d e^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{-4 \, c^{2} d^{2} e^{\left(-2\right)} + b^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{2} - 8 \, b^{2} c^{3} d^{3} e^{4} + 8 \, b c^{4} d^{3} e^{4} - 4 \, c^{5} d^{3} e^{4} + b^{4} c d e^{6} - 2 \, b^{3} c^{2} d e^{6} + b^{2} c^{3} d e^{6}\right)} {\left| c \right|}} + \frac{{\left(32 \, c^{5} d^{4} e^{4} + 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 16 \, b^{2} c^{3} d^{2} e^{6} + 8 \, b c^{4} d^{2} e^{6} - 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} + 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 2 \, b^{4} c e^{8} - 2 \, b^{3} c^{2} e^{8} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} - 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} b c^{2} e^{4} - 2 \, {\left(8 \, c^{5} d^{3} e^{4} - 4 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} - 2 \, b^{2} c^{3} d e^{6} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{2} - 2 \, \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{2} + \sqrt{2} \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{-4 \, c^{2} d^{2} e^{2} + b^{2} e^{4}} c e^{2}} c^{3} d e^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - b^{2} e^{4}\right)} c^{3} d e^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{-4 \, c^{2} d^{2} e^{\left(-2\right)} + b^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{2} - 8 \, b^{2} c^{3} d^{3} e^{4} + 8 \, b c^{4} d^{3} e^{4} - 4 \, c^{5} d^{3} e^{4} + b^{4} c d e^{6} - 2 \, b^{3} c^{2} d e^{6} + b^{2} c^{3} d e^{6}\right)} {\left| c \right|}}"," ",0,"-1/4*(32*c^5*d^4*e^4 - 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 16*b^2*c^3*d^2*e^6 + 8*b*c^4*d^2*e^6 + 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 - 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 + 4*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 8*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d^2*e^2 + 2*b^4*c*e^8 - 2*b^3*c^2*e^8 - sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^4*e^6 + 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*c*e^6 - sqrt(2)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*e^4 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*e^4 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*e^4 + 2*(4*c^2*d^2*e^2 - b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*b*c^2*e^4 - 2*(8*c^5*d^3*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d^3 - 2*b^2*c^3*d*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*d*e^2 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d*e^2 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d*e^2 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d*e^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(-4*c^2*d^2*e^(-2) + b^2))/c))/((16*c^5*d^5*e^2 - 8*b^2*c^3*d^3*e^4 + 8*b*c^4*d^3*e^4 - 4*c^5*d^3*e^4 + b^4*c*d*e^6 - 2*b^3*c^2*d*e^6 + b^2*c^3*d*e^6)*abs(c)) + 1/4*(32*c^5*d^4*e^4 + 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 16*b^2*c^3*d^2*e^6 + 8*b*c^4*d^2*e^6 - 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 + 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 - 4*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 8*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d^2*e^2 + 2*b^4*c*e^8 - 2*b^3*c^2*e^8 + sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^4*e^6 - 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*c*e^6 + sqrt(2)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^3*e^4 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*e^4 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*e^4 + 2*(4*c^2*d^2*e^2 - b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*b*c^2*e^4 - 2*(8*c^5*d^3*e^4 - 4*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d^3 - 2*b^2*c^3*d*e^6 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b^2*c*d*e^2 - 2*sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*b*c^2*d*e^2 + sqrt(2)*sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(-4*c^2*d^2*e^2 + b^2*e^4)*c*e^2)*c^3*d*e^2 - 2*(4*c^2*d^2*e^2 - b^2*e^4)*c^3*d*e^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(-4*c^2*d^2*e^(-2) + b^2))/c))/((16*c^5*d^5*e^2 - 8*b^2*c^3*d^3*e^4 + 8*b*c^4*d^3*e^4 - 4*c^5*d^3*e^4 + b^4*c*d*e^6 - 2*b^3*c^2*d*e^6 + b^2*c^3*d*e^6)*abs(c))","B",0
37,1,25,0,0.244547," ","integrate((-b*x^2+a)/(a^2+(2*a*b-1)*x^2+b^2*x^4),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(b x^{2} + a + x\right) - \frac{1}{2} \, \log\left(b x^{2} + a - x\right)"," ",0,"1/2*log(b*x^2 + a + x) - 1/2*log(b*x^2 + a - x)","A",0
38,1,51,0,0.176431," ","integrate((b*x^2+a)/(a^2+(2*a*b-1)*x^2+b^2*x^4),x, algorithm=""giac"")","\frac{\arctan\left(\frac{2 \, b x + 1}{\sqrt{4 \, a b - 1}}\right)}{\sqrt{4 \, a b - 1}} + \frac{\arctan\left(\frac{2 \, b x - 1}{\sqrt{4 \, a b - 1}}\right)}{\sqrt{4 \, a b - 1}}"," ",0,"arctan((2*b*x + 1)/sqrt(4*a*b - 1))/sqrt(4*a*b - 1) + arctan((2*b*x - 1)/sqrt(4*a*b - 1))/sqrt(4*a*b - 1)","A",0
39,1,77,0,0.308346," ","integrate((2*x^2+1)/(4*x^4+b*x^2+1),x, algorithm=""giac"")","\frac{\sqrt{b + 4} {\left(b - 8\right)} \arctan\left(\frac{4 \, \sqrt{\frac{1}{2}} x}{\sqrt{b + \sqrt{b^{2} - 16}}}\right)}{b^{2} - 4 \, b - 32} + \frac{\sqrt{b + 4} {\left(b - 8\right)} \arctan\left(\frac{4 \, \sqrt{\frac{1}{2}} x}{\sqrt{b - \sqrt{b^{2} - 16}}}\right)}{b^{2} - 4 \, b - 32}"," ",0,"sqrt(b + 4)*(b - 8)*arctan(4*sqrt(1/2)*x/sqrt(b + sqrt(b^2 - 16)))/(b^2 - 4*b - 32) + sqrt(b + 4)*(b - 8)*arctan(4*sqrt(1/2)*x/sqrt(b - sqrt(b^2 - 16)))/(b^2 - 4*b - 32)","A",0
40,1,80,0,0.311977," ","integrate((2*x^2+1)/(4*x^4-b*x^2+1),x, algorithm=""giac"")","\frac{{\left(b + 8\right)} \sqrt{-b + 4} \arctan\left(\frac{x}{\sqrt{-\frac{1}{8} \, b + \frac{1}{8} \, \sqrt{b^{2} - 16}}}\right)}{b^{2} + 4 \, b - 32} - \frac{{\left(b + 8\right)} \sqrt{-b + 4} \arctan\left(\frac{x}{\sqrt{-\frac{1}{8} \, b - \frac{1}{8} \, \sqrt{b^{2} - 16}}}\right)}{b^{2} + 4 \, b - 32}"," ",0,"(b + 8)*sqrt(-b + 4)*arctan(x/sqrt(-1/8*b + 1/8*sqrt(b^2 - 16)))/(b^2 + 4*b - 32) - (b + 8)*sqrt(-b + 4)*arctan(x/sqrt(-1/8*b - 1/8*sqrt(b^2 - 16)))/(b^2 + 4*b - 32)","A",0
41,1,39,0,0.169915," ","integrate((2*x^2+1)/(4*x^4+6*x^2+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{10} \arctan\left(\frac{4 \, x}{\sqrt{10} + \sqrt{2}}\right) + \frac{1}{10} \, \sqrt{10} \arctan\left(\frac{4 \, x}{\sqrt{10} - \sqrt{2}}\right)"," ",0,"1/10*sqrt(10)*arctan(4*x/(sqrt(10) + sqrt(2))) + 1/10*sqrt(10)*arctan(4*x/(sqrt(10) - sqrt(2)))","A",0
42,1,11,0,0.151293," ","integrate((2*x^2+1)/(4*x^4+5*x^2+1),x, algorithm=""giac"")","\frac{1}{3} \, \arctan\left(2 \, x\right) + \frac{1}{3} \, \arctan\left(x\right)"," ",0,"1/3*arctan(2*x) + 1/3*arctan(x)","A",0
43,1,11,0,0.162144," ","integrate((2*x^2+1)/(4*x^4+4*x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} x\right)"," ",0,"1/2*sqrt(2)*arctan(sqrt(2)*x)","A",0
44,1,33,0,0.173837," ","integrate((2*x^2+1)/(4*x^4+3*x^2+1),x, algorithm=""giac"")","\frac{1}{7} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(4 \, x + 1\right)}\right) + \frac{1}{7} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(4 \, x - 1\right)}\right)"," ",0,"1/7*sqrt(7)*arctan(1/7*sqrt(7)*(4*x + 1)) + 1/7*sqrt(7)*arctan(1/7*sqrt(7)*(4*x - 1))","A",0
45,1,45,0,0.189500," ","integrate((2*x^2+1)/(4*x^4+2*x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{6} \arctan\left(\frac{4}{3} \, \sqrt{3} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(2 \, x + \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{6} \, \sqrt{6} \arctan\left(\frac{4}{3} \, \sqrt{3} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(2 \, x - \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/6*sqrt(6)*arctan(4/3*sqrt(3)*(1/4)^(3/4)*(2*x + (1/4)^(1/4))) + 1/6*sqrt(6)*arctan(4/3*sqrt(3)*(1/4)^(3/4)*(2*x - (1/4)^(1/4)))","A",0
46,1,52,0,0.256547," ","integrate((2*x^2+1)/(4*x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{5} \arctan\left(\frac{2}{5} \, \sqrt{10} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(4 \, x + \sqrt{6} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{5} \, \sqrt{5} \arctan\left(\frac{2}{5} \, \sqrt{10} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(4 \, x - \sqrt{6} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/5*sqrt(5)*arctan(2/5*sqrt(10)*(1/4)^(3/4)*(4*x + sqrt(6)*(1/4)^(1/4))) + 1/5*sqrt(5)*arctan(2/5*sqrt(10)*(1/4)^(3/4)*(4*x - sqrt(6)*(1/4)^(1/4)))","A",0
47,1,46,0,0.157612," ","integrate((2*x^2+1)/(4*x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{2} \, \arctan\left(2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/2*arctan(2*sqrt(2)*(1/4)^(3/4)*(2*x + sqrt(2)*(1/4)^(1/4))) + 1/2*arctan(2*sqrt(2)*(1/4)^(3/4)*(2*x - sqrt(2)*(1/4)^(1/4)))","B",0
48,1,52,0,0.241899," ","integrate((2*x^2+1)/(4*x^4-x^2+1),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{6} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(4 \, x + \sqrt{10} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{6} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(4 \, x - \sqrt{10} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/3*sqrt(3)*arctan(2/3*sqrt(6)*(1/4)^(3/4)*(4*x + sqrt(10)*(1/4)^(1/4))) + 1/3*sqrt(3)*arctan(2/3*sqrt(6)*(1/4)^(3/4)*(4*x - sqrt(10)*(1/4)^(1/4)))","A",0
49,1,46,0,0.174744," ","integrate((2*x^2+1)/(4*x^4-2*x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(4 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(2 \, x + \sqrt{3} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(4 \, \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(2 \, x - \sqrt{3} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"1/2*sqrt(2)*arctan(4*(1/4)^(3/4)*(2*x + sqrt(3)*(1/4)^(1/4))) + 1/2*sqrt(2)*arctan(4*(1/4)^(3/4)*(2*x - sqrt(3)*(1/4)^(1/4)))","A",0
50,1,42,0,0.192544," ","integrate((2*x^2+1)/(4*x^4-3*x^2+1),x, algorithm=""giac"")","\arctan\left(2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(4 \, x + \sqrt{14} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right) + \arctan\left(2 \, \sqrt{2} \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(4 \, x - \sqrt{14} \left(\frac{1}{4}\right)^{\frac{1}{4}}\right)}\right)"," ",0,"arctan(2*sqrt(2)*(1/4)^(3/4)*(4*x + sqrt(14)*(1/4)^(1/4))) + arctan(2*sqrt(2)*(1/4)^(3/4)*(4*x - sqrt(14)*(1/4)^(1/4)))","B",0
51,1,12,0,0.157977," ","integrate((2*x^2+1)/(4*x^4-4*x^2+1),x, algorithm=""giac"")","-\frac{x}{2 \, x^{2} - 1}"," ",0,"-x/(2*x^2 - 1)","A",0
52,1,33,0,0.170794," ","integrate((2*x^2+1)/(4*x^4-5*x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| 2 \, x + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| 2 \, x - 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*log(abs(2*x + 1)) - 1/2*log(abs(2*x - 1)) - 1/2*log(abs(x + 1)) + 1/2*log(abs(x - 1))","A",0
53,1,77,0,0.339978," ","integrate((2*x^2+1)/(4*x^4-6*x^2+1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \log\left({\left| x + \frac{1}{4} \, \sqrt{10} + \frac{1}{4} \, \sqrt{2} \right|}\right) + \frac{1}{4} \, \sqrt{2} \log\left({\left| x + \frac{1}{4} \, \sqrt{10} - \frac{1}{4} \, \sqrt{2} \right|}\right) - \frac{1}{4} \, \sqrt{2} \log\left({\left| x - \frac{1}{4} \, \sqrt{10} + \frac{1}{4} \, \sqrt{2} \right|}\right) + \frac{1}{4} \, \sqrt{2} \log\left({\left| x - \frac{1}{4} \, \sqrt{10} - \frac{1}{4} \, \sqrt{2} \right|}\right)"," ",0,"-1/4*sqrt(2)*log(abs(x + 1/4*sqrt(10) + 1/4*sqrt(2))) + 1/4*sqrt(2)*log(abs(x + 1/4*sqrt(10) - 1/4*sqrt(2))) - 1/4*sqrt(2)*log(abs(x - 1/4*sqrt(10) + 1/4*sqrt(2))) + 1/4*sqrt(2)*log(abs(x - 1/4*sqrt(10) - 1/4*sqrt(2)))","B",0
54,1,73,0,0.313972," ","integrate((-2*x^2+1)/(4*x^4+b*x^2+1),x, algorithm=""giac"")","-\frac{\sqrt{b - 4} b \arctan\left(\frac{4 \, \sqrt{\frac{1}{2}} x}{\sqrt{b + \sqrt{b^{2} - 16}}}\right)}{b^{2} - 4 \, b} - \frac{\sqrt{b - 4} b \arctan\left(\frac{4 \, \sqrt{\frac{1}{2}} x}{\sqrt{b - \sqrt{b^{2} - 16}}}\right)}{b^{2} - 4 \, b}"," ",0,"-sqrt(b - 4)*b*arctan(4*sqrt(1/2)*x/sqrt(b + sqrt(b^2 - 16)))/(b^2 - 4*b) - sqrt(b - 4)*b*arctan(4*sqrt(1/2)*x/sqrt(b - sqrt(b^2 - 16)))/(b^2 - 4*b)","A",0
55,1,39,0,0.176380," ","integrate((-2*x^2+1)/(4*x^4+6*x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{4 \, x}{\sqrt{10} + \sqrt{2}}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{4 \, x}{\sqrt{10} - \sqrt{2}}\right)"," ",0,"-1/2*sqrt(2)*arctan(4*x/(sqrt(10) + sqrt(2))) + 1/2*sqrt(2)*arctan(4*x/(sqrt(10) - sqrt(2)))","A",0
56,1,9,0,0.174443," ","integrate((-2*x^2+1)/(4*x^4+5*x^2+1),x, algorithm=""giac"")","\arctan\left(2 \, x\right) - \arctan\left(x\right)"," ",0,"arctan(2*x) - arctan(x)","A",0
57,1,11,0,0.157486," ","integrate((-2*x^2+1)/(4*x^4+4*x^2+1),x, algorithm=""giac"")","\frac{x}{2 \, x^{2} + 1}"," ",0,"x/(2*x^2 + 1)","A",0
58,1,25,0,0.154195," ","integrate((-2*x^2+1)/(4*x^4+3*x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(2 \, x^{2} + x + 1\right) - \frac{1}{2} \, \log\left(2 \, x^{2} - x + 1\right)"," ",0,"1/2*log(2*x^2 + x + 1) - 1/2*log(2*x^2 - x + 1)","A",0
59,1,34,0,0.172344," ","integrate((-2*x^2+1)/(4*x^4+2*x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(x^{2} + \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right) - \frac{1}{4} \, \sqrt{2} \log\left(x^{2} - \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right)"," ",0,"1/4*sqrt(2)*log(x^2 + (1/4)^(1/4)*x + 1/2) - 1/4*sqrt(2)*log(x^2 - (1/4)^(1/4)*x + 1/2)","A",0
60,1,41,0,0.261509," ","integrate((-2*x^2+1)/(4*x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(x^{2} + \frac{1}{2} \, \sqrt{6} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right) - \frac{1}{6} \, \sqrt{3} \log\left(x^{2} - \frac{1}{2} \, \sqrt{6} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right)"," ",0,"1/6*sqrt(3)*log(x^2 + 1/2*sqrt(6)*(1/4)^(1/4)*x + 1/2) - 1/6*sqrt(3)*log(x^2 - 1/2*sqrt(6)*(1/4)^(1/4)*x + 1/2)","A",0
61,1,34,0,0.157237," ","integrate((-2*x^2+1)/(4*x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, \log\left(x^{2} + \sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right) - \frac{1}{4} \, \log\left(x^{2} - \sqrt{2} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right)"," ",0,"1/4*log(x^2 + sqrt(2)*(1/4)^(1/4)*x + 1/2) - 1/4*log(x^2 - sqrt(2)*(1/4)^(1/4)*x + 1/2)","A",0
62,1,41,0,0.242178," ","integrate((-2*x^2+1)/(4*x^4-x^2+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{5} \log\left(x^{2} + \frac{1}{2} \, \sqrt{10} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right) - \frac{1}{10} \, \sqrt{5} \log\left(x^{2} - \frac{1}{2} \, \sqrt{10} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right)"," ",0,"1/10*sqrt(5)*log(x^2 + 1/2*sqrt(10)*(1/4)^(1/4)*x + 1/2) - 1/10*sqrt(5)*log(x^2 - 1/2*sqrt(10)*(1/4)^(1/4)*x + 1/2)","A",0
63,1,40,0,0.178247," ","integrate((-2*x^2+1)/(4*x^4-2*x^2+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} \log\left(x^{2} + \sqrt{3} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right) - \frac{1}{12} \, \sqrt{6} \log\left(x^{2} - \sqrt{3} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right)"," ",0,"1/12*sqrt(6)*log(x^2 + sqrt(3)*(1/4)^(1/4)*x + 1/2) - 1/12*sqrt(6)*log(x^2 - sqrt(3)*(1/4)^(1/4)*x + 1/2)","A",0
64,1,41,0,0.206467," ","integrate((-2*x^2+1)/(4*x^4-3*x^2+1),x, algorithm=""giac"")","\frac{1}{14} \, \sqrt{7} \log\left(x^{2} + \frac{1}{2} \, \sqrt{14} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right) - \frac{1}{14} \, \sqrt{7} \log\left(x^{2} - \frac{1}{2} \, \sqrt{14} \left(\frac{1}{4}\right)^{\frac{1}{4}} x + \frac{1}{2}\right)"," ",0,"1/14*sqrt(7)*log(x^2 + 1/2*sqrt(14)*(1/4)^(1/4)*x + 1/2) - 1/14*sqrt(7)*log(x^2 - 1/2*sqrt(14)*(1/4)^(1/4)*x + 1/2)","A",0
65,1,29,0,0.158016," ","integrate((-2*x^2+1)/(4*x^4-4*x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left({\left| x + \frac{1}{2} \, \sqrt{2} \right|}\right) - \frac{1}{4} \, \sqrt{2} \log\left({\left| x - \frac{1}{2} \, \sqrt{2} \right|}\right)"," ",0,"1/4*sqrt(2)*log(abs(x + 1/2*sqrt(2))) - 1/4*sqrt(2)*log(abs(x - 1/2*sqrt(2)))","B",0
66,1,33,0,0.153086," ","integrate((-2*x^2+1)/(4*x^4-5*x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \log\left({\left| 2 \, x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| 2 \, x - 1 \right|}\right) + \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/6*log(abs(2*x + 1)) - 1/6*log(abs(2*x - 1)) + 1/6*log(abs(x + 1)) - 1/6*log(abs(x - 1))","A",0
67,1,77,0,0.322104," ","integrate((-2*x^2+1)/(4*x^4-6*x^2+1),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{10} \log\left({\left| x + \frac{1}{4} \, \sqrt{10} + \frac{1}{4} \, \sqrt{2} \right|}\right) + \frac{1}{20} \, \sqrt{10} \log\left({\left| x + \frac{1}{4} \, \sqrt{10} - \frac{1}{4} \, \sqrt{2} \right|}\right) - \frac{1}{20} \, \sqrt{10} \log\left({\left| x - \frac{1}{4} \, \sqrt{10} + \frac{1}{4} \, \sqrt{2} \right|}\right) - \frac{1}{20} \, \sqrt{10} \log\left({\left| x - \frac{1}{4} \, \sqrt{10} - \frac{1}{4} \, \sqrt{2} \right|}\right)"," ",0,"1/20*sqrt(10)*log(abs(x + 1/4*sqrt(10) + 1/4*sqrt(2))) + 1/20*sqrt(10)*log(abs(x + 1/4*sqrt(10) - 1/4*sqrt(2))) - 1/20*sqrt(10)*log(abs(x - 1/4*sqrt(10) + 1/4*sqrt(2))) - 1/20*sqrt(10)*log(abs(x - 1/4*sqrt(10) - 1/4*sqrt(2)))","A",0
68,-2,0,0,0.000000," ","integrate((x^2+1)/(x^4+b*x^2+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b]=[0]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b]=[0]Precision problem choosing root in common_EXT, current precision 14Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
69,1,26,0,0.177358," ","integrate((x^2+1)/(x^4+5*x^2+1),x, algorithm=""giac"")","\frac{1}{14} \, \sqrt{7} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(\frac{\sqrt{7} {\left(x^{2} - 1\right)}}{7 \, x}\right)\right)}"," ",0,"1/14*sqrt(7)*(pi*sgn(x) + 2*arctan(1/7*sqrt(7)*(x^2 - 1)/x))","A",0
70,1,26,0,0.186294," ","integrate((x^2+1)/(x^4+4*x^2+1),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{6} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(\frac{\sqrt{6} {\left(x^{2} - 1\right)}}{6 \, x}\right)\right)}"," ",0,"1/12*sqrt(6)*(pi*sgn(x) + 2*arctan(1/6*sqrt(6)*(x^2 - 1)/x))","A",0
71,1,26,0,0.163161," ","integrate((x^2+1)/(x^4+3*x^2+1),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{5} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(\frac{\sqrt{5} {\left(x^{2} - 1\right)}}{5 \, x}\right)\right)}"," ",0,"1/10*sqrt(5)*(pi*sgn(x) + 2*arctan(1/5*sqrt(5)*(x^2 - 1)/x))","A",0
72,1,2,0,0.155324," ","integrate((x^2+1)/(x^4+2*x^2+1),x, algorithm=""giac"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
73,1,26,0,0.161928," ","integrate((x^2+1)/(x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(\frac{\sqrt{3} {\left(x^{2} - 1\right)}}{3 \, x}\right)\right)}"," ",0,"1/6*sqrt(3)*(pi*sgn(x) + 2*arctan(1/3*sqrt(3)*(x^2 - 1)/x))","A",0
74,1,39,0,0.191816," ","integrate((x^2+1)/(x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)))","A",0
75,1,30,0,0.167857," ","integrate((x^2+1)/(x^4-x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) + \frac{1}{2} \, \arctan\left(\frac{x^{4} - 3 \, x^{2} + 1}{2 \, {\left(x^{3} - x\right)}}\right)"," ",0,"1/4*pi*sgn(x) + 1/2*arctan(1/2*(x^4 - 3*x^2 + 1)/(x^3 - x))","A",0
76,1,11,0,0.152298," ","integrate((x^2+1)/(x^4-2*x^2+1),x, algorithm=""giac"")","-\frac{1}{x - \frac{1}{x}}"," ",0,"-1/(x - 1/x)","A",0
77,1,43,0,0.165142," ","integrate((x^2+1)/(x^4-3*x^2+1),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left({\left| x + \frac{1}{x - \frac{1}{x}} - \frac{1}{x} + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| x + \frac{1}{x - \frac{1}{x}} - \frac{1}{x} - 2 \right|}\right)"," ",0,"-1/4*log(abs(x + 1/(x - 1/x) - 1/x + 2)) + 1/4*log(abs(x + 1/(x - 1/x) - 1/x - 2))","A",0
78,1,39,0,0.214994," ","integrate((x^2+1)/(x^4-4*x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} - \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} - \frac{2}{x} \right|}}\right)"," ",0,"1/4*sqrt(2)*log(abs(2*x - 2*sqrt(2) - 2/x)/abs(2*x + 2*sqrt(2) - 2/x))","A",0
79,1,39,0,0.244005," ","integrate((x^2+1)/(x^4-5*x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{3} - \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{3} - \frac{2}{x} \right|}}\right)"," ",0,"1/6*sqrt(3)*log(abs(2*x - 2*sqrt(3) - 2/x)/abs(2*x + 2*sqrt(3) - 2/x))","A",0
80,-2,0,0,0.000000," ","integrate((-x^2+1)/(x^4+b*x^2+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b]=[0]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b]=[0]Precision problem choosing root in common_EXT, current precision 14Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
81,1,26,0,0.167118," ","integrate((-x^2+1)/(x^4+5*x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} {\left(\pi \mathrm{sgn}\left(x\right) - 2 \, \arctan\left(\frac{\sqrt{3} {\left(x^{2} + 1\right)}}{3 \, x}\right)\right)}"," ",0,"1/6*sqrt(3)*(pi*sgn(x) - 2*arctan(1/3*sqrt(3)*(x^2 + 1)/x))","A",0
82,1,26,0,0.162277," ","integrate((-x^2+1)/(x^4+4*x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} {\left(\pi \mathrm{sgn}\left(x\right) - 2 \, \arctan\left(\frac{\sqrt{2} {\left(x^{2} + 1\right)}}{2 \, x}\right)\right)}"," ",0,"1/4*sqrt(2)*(pi*sgn(x) - 2*arctan(1/2*sqrt(2)*(x^2 + 1)/x))","A",0
83,1,26,0,0.182745," ","integrate((-x^2+1)/(x^4+3*x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) - \frac{1}{2} \, \arctan\left(\frac{x^{4} + x^{2} + 1}{2 \, {\left(x^{3} + x\right)}}\right)"," ",0,"1/4*pi*sgn(x) - 1/2*arctan(1/2*(x^4 + x^2 + 1)/(x^3 + x))","A",0
84,1,7,0,0.180765," ","integrate((-x^2+1)/(x^4+2*x^2+1),x, algorithm=""giac"")","\frac{1}{x + \frac{1}{x}}"," ",0,"1/(x + 1/x)","A",0
85,1,35,0,0.148771," ","integrate((-x^2+1)/(x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| x + \frac{1}{x + \frac{1}{x}} + \frac{1}{x} + 2 \right|}\right) - \frac{1}{4} \, \log\left({\left| x + \frac{1}{x + \frac{1}{x}} + \frac{1}{x} - 2 \right|}\right)"," ",0,"1/4*log(abs(x + 1/(x + 1/x) + 1/x + 2)) - 1/4*log(abs(x + 1/(x + 1/x) + 1/x - 2))","A",0
86,1,34,0,0.150164," ","integrate((-x^2+1)/(x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{4} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"1/4*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/4*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
87,1,39,0,0.178581," ","integrate((-x^2+1)/(x^4-x^2+1),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{3} + \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{3} + \frac{2}{x} \right|}}\right)"," ",0,"-1/6*sqrt(3)*log(abs(2*x - 2*sqrt(3) + 2/x)/abs(2*x + 2*sqrt(3) + 2/x))","A",0
88,1,15,0,0.147578," ","integrate((-x^2+1)/(x^4-2*x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*log(abs(x + 1)) - 1/2*log(abs(x - 1))","B",0
89,1,39,0,0.182086," ","integrate((-x^2+1)/(x^4-3*x^2+1),x, algorithm=""giac"")","-\frac{1}{10} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{5} + \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{5} + \frac{2}{x} \right|}}\right)"," ",0,"-1/10*sqrt(5)*log(abs(2*x - 2*sqrt(5) + 2/x)/abs(2*x + 2*sqrt(5) + 2/x))","A",0
90,1,39,0,0.321642," ","integrate((-x^2+1)/(x^4-4*x^2+1),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{6} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{6} + \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{6} + \frac{2}{x} \right|}}\right)"," ",0,"-1/12*sqrt(6)*log(abs(2*x - 2*sqrt(6) + 2/x)/abs(2*x + 2*sqrt(6) + 2/x))","A",0
91,1,39,0,0.224774," ","integrate((-x^2+1)/(x^4-5*x^2+1),x, algorithm=""giac"")","-\frac{1}{14} \, \sqrt{7} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{7} + \frac{2}{x} \right|}}{{\left| 2 \, x + 2 \, \sqrt{7} + \frac{2}{x} \right|}}\right)"," ",0,"-1/14*sqrt(7)*log(abs(2*x - 2*sqrt(7) + 2/x)/abs(2*x + 2*sqrt(7) + 2/x))","A",0
92,1,33,0,0.159843," ","integrate((-3*x^2-1)/(9*x^4+2*x^2+1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(3 \, x + 1\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(3 \, x - 1\right)}\right)"," ",0,"-1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*x + 1)) - 1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*x - 1))","A",0
93,1,33,0,0.176589," ","integrate((3*x^2+1)/(-9*x^4-2*x^2-1),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(3 \, x + 1\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(3 \, x - 1\right)}\right)"," ",0,"-1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*x + 1)) - 1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*x - 1))","A",0
94,1,25,0,0.173494," ","integrate((2*x^2+3)/(x^4-2*x^2+1),x, algorithm=""giac"")","-\frac{5 \, x}{2 \, {\left(x^{2} - 1\right)}} + \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-5/2*x/(x^2 - 1) + 1/4*log(abs(x + 1)) - 1/4*log(abs(x - 1))","A",0
95,1,44,0,0.174190," ","integrate((3*x^2+2)/(3*x^4-8*x^2+5),x, algorithm=""giac"")","\frac{7}{20} \, \sqrt{15} \log\left(\frac{{\left| 6 \, x - 2 \, \sqrt{15} \right|}}{{\left| 6 \, x + 2 \, \sqrt{15} \right|}}\right) + \frac{5}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{5}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"7/20*sqrt(15)*log(abs(6*x - 2*sqrt(15))/abs(6*x + 2*sqrt(15))) + 5/4*log(abs(x + 1)) - 5/4*log(abs(x - 1))","B",0
96,1,60,0,0.155454," ","integrate((e*x^2+d)/(3*x^4-8*x^2+5),x, algorithm=""giac"")","\frac{1}{60} \, \sqrt{15} {\left(3 \, d + 5 \, e\right)} \log\left(\frac{{\left| 6 \, x - 2 \, \sqrt{15} \right|}}{{\left| 6 \, x + 2 \, \sqrt{15} \right|}}\right) + \frac{1}{4} \, {\left(d + e\right)} \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, {\left(d + e\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/60*sqrt(15)*(3*d + 5*e)*log(abs(6*x - 2*sqrt(15))/abs(6*x + 2*sqrt(15))) + 1/4*(d + e)*log(abs(x + 1)) - 1/4*(d + e)*log(abs(x - 1))","B",0
97,1,41,0,0.157793," ","integrate((x^2+3)/(x^4+3*x^2+1),x, algorithm=""giac"")","\frac{1}{5} \, {\left(2 \, \sqrt{5} - 5\right)} \arctan\left(\frac{2 \, x}{\sqrt{5} + 1}\right) + \frac{1}{5} \, {\left(2 \, \sqrt{5} + 5\right)} \arctan\left(\frac{2 \, x}{\sqrt{5} - 1}\right)"," ",0,"1/5*(2*sqrt(5) - 5)*arctan(2*x/(sqrt(5) + 1)) + 1/5*(2*sqrt(5) + 5)*arctan(2*x/(sqrt(5) - 1))","A",0
98,1,69,0,0.153851," ","integrate((b*x^2+a)/(x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} {\left(a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \, {\left(a - b\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, {\left(a - b\right)} \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*(a + b)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(a + b)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*(a - b)*log(x^2 + x + 1) - 1/4*(a - b)*log(x^2 - x + 1)","A",0
99,1,109,0,0.156805," ","integrate((b*x^2+a)/(x^4+x^2+1)^2,x, algorithm=""giac"")","\frac{1}{36} \, \sqrt{3} {\left(4 \, a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{36} \, \sqrt{3} {\left(4 \, a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, {\left(2 \, a - b\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, {\left(2 \, a - b\right)} \log\left(x^{2} - x + 1\right) - \frac{a x^{3} - 2 \, b x^{3} - a x - b x}{6 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"1/36*sqrt(3)*(4*a + b)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/36*sqrt(3)*(4*a + b)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*(2*a - b)*log(x^2 + x + 1) - 1/8*(2*a - b)*log(x^2 - x + 1) - 1/6*(a*x^3 - 2*b*x^3 - a*x - b*x)/(x^4 + x^2 + 1)","A",0
100,1,544,0,0.877786," ","integrate((b*x^2+a)/(x^4+x^2+2),x, algorithm=""giac"")","-\frac{1}{14336} \, \sqrt{7} {\left(32 \, \sqrt{7} 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \, \sqrt{7} 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 24 \cdot 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} + 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} - 128 \, \sqrt{7} 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} + 64 \cdot 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32}\right)} \arctan\left(\frac{2 \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(x + 2^{\frac{1}{4}} \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}}\right)}}{\sqrt{\sqrt{2} + 4}}\right) - \frac{1}{14336} \, \sqrt{7} {\left(32 \, \sqrt{7} 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \, \sqrt{7} 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 24 \cdot 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} + 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} - 128 \, \sqrt{7} 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} + 64 \cdot 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32}\right)} \arctan\left(\frac{2 \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(x - 2^{\frac{1}{4}} \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}}\right)}}{\sqrt{\sqrt{2} + 4}}\right) - \frac{1}{28672} \, \sqrt{7} {\left(24 \, \sqrt{7} 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} - \sqrt{7} 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 32 \cdot 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \cdot 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 128 \cdot 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} - 64 \, \sqrt{7} 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32}\right)} \log\left(x^{2} + 2 \cdot 2^{\frac{1}{4}} x \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}} + \sqrt{2}\right) + \frac{1}{28672} \, \sqrt{7} {\left(24 \, \sqrt{7} 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} - \sqrt{7} 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 32 \cdot 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \cdot 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 128 \cdot 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} - 64 \, \sqrt{7} 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32}\right)} \log\left(x^{2} - 2 \cdot 2^{\frac{1}{4}} x \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}} + \sqrt{2}\right)"," ",0,"-1/14336*sqrt(7)*(32*sqrt(7)*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*sqrt(7)*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 24*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) + 2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) - 128*sqrt(7)*2^(3/4)*a*sqrt(sqrt(2) + 4) + 64*2^(1/4)*a*sqrt(-8*sqrt(2) + 32))*arctan(2*2^(3/4)*sqrt(1/2)*(x + 2^(1/4)*sqrt(-1/8*sqrt(2) + 1/2))/sqrt(sqrt(2) + 4)) - 1/14336*sqrt(7)*(32*sqrt(7)*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*sqrt(7)*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 24*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) + 2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) - 128*sqrt(7)*2^(3/4)*a*sqrt(sqrt(2) + 4) + 64*2^(1/4)*a*sqrt(-8*sqrt(2) + 32))*arctan(2*2^(3/4)*sqrt(1/2)*(x - 2^(1/4)*sqrt(-1/8*sqrt(2) + 1/2))/sqrt(sqrt(2) + 4)) - 1/28672*sqrt(7)*(24*sqrt(7)*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) - sqrt(7)*2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) + 32*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 128*2^(3/4)*a*sqrt(sqrt(2) + 4) - 64*sqrt(7)*2^(1/4)*a*sqrt(-8*sqrt(2) + 32))*log(x^2 + 2*2^(1/4)*x*sqrt(-1/8*sqrt(2) + 1/2) + sqrt(2)) + 1/28672*sqrt(7)*(24*sqrt(7)*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) - sqrt(7)*2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) + 32*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 128*2^(3/4)*a*sqrt(sqrt(2) + 4) - 64*sqrt(7)*2^(1/4)*a*sqrt(-8*sqrt(2) + 32))*log(x^2 - 2*2^(1/4)*x*sqrt(-1/8*sqrt(2) + 1/2) + sqrt(2))","B",0
101,1,988,0,0.945811," ","integrate((b*x^2+a)/(x^4+x^2+2)^2,x, algorithm=""giac"")","\frac{1}{401408} \, \sqrt{7} {\left(32 \, \sqrt{7} 2^{\frac{1}{4}} a {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} - 128 \, \sqrt{7} 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \, \sqrt{7} 2^{\frac{1}{4}} a \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 384 \, \sqrt{7} 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 24 \cdot 2^{\frac{3}{4}} a {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} + 96 \cdot 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} + 2^{\frac{3}{4}} a {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} - 4 \cdot 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 1408 \, \sqrt{7} 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} - 256 \, \sqrt{7} 2^{\frac{3}{4}} b \sqrt{\sqrt{2} + 4} - 704 \cdot 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32} + 128 \cdot 2^{\frac{1}{4}} b \sqrt{-8 \, \sqrt{2} + 32}\right)} \arctan\left(\frac{2 \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(x + 2^{\frac{1}{4}} \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}}\right)}}{\sqrt{\sqrt{2} + 4}}\right) + \frac{1}{401408} \, \sqrt{7} {\left(32 \, \sqrt{7} 2^{\frac{1}{4}} a {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} - 128 \, \sqrt{7} 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \, \sqrt{7} 2^{\frac{1}{4}} a \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 384 \, \sqrt{7} 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 24 \cdot 2^{\frac{3}{4}} a {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} + 96 \cdot 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} + 2^{\frac{3}{4}} a {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} - 4 \cdot 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 1408 \, \sqrt{7} 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} - 256 \, \sqrt{7} 2^{\frac{3}{4}} b \sqrt{\sqrt{2} + 4} - 704 \cdot 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32} + 128 \cdot 2^{\frac{1}{4}} b \sqrt{-8 \, \sqrt{2} + 32}\right)} \arctan\left(\frac{2 \cdot 2^{\frac{3}{4}} \sqrt{\frac{1}{2}} {\left(x - 2^{\frac{1}{4}} \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}}\right)}}{\sqrt{\sqrt{2} + 4}}\right) + \frac{1}{802816} \, \sqrt{7} {\left(24 \, \sqrt{7} 2^{\frac{3}{4}} a {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} - 96 \, \sqrt{7} 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} - \sqrt{7} 2^{\frac{3}{4}} a {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 4 \, \sqrt{7} 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 32 \cdot 2^{\frac{1}{4}} a {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} - 128 \cdot 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \cdot 2^{\frac{1}{4}} a \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 384 \cdot 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} + 1408 \cdot 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} - 256 \cdot 2^{\frac{3}{4}} b \sqrt{\sqrt{2} + 4} + 704 \, \sqrt{7} 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32} - 128 \, \sqrt{7} 2^{\frac{1}{4}} b \sqrt{-8 \, \sqrt{2} + 32}\right)} \log\left(x^{2} + 2 \cdot 2^{\frac{1}{4}} x \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}} + \sqrt{2}\right) - \frac{1}{802816} \, \sqrt{7} {\left(24 \, \sqrt{7} 2^{\frac{3}{4}} a {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} - 96 \, \sqrt{7} 2^{\frac{3}{4}} b {\left(\sqrt{2} + 4\right)} \sqrt{-8 \, \sqrt{2} + 32} - \sqrt{7} 2^{\frac{3}{4}} a {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 4 \, \sqrt{7} 2^{\frac{3}{4}} b {\left(-8 \, \sqrt{2} + 32\right)}^{\frac{3}{2}} + 32 \cdot 2^{\frac{1}{4}} a {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} - 128 \cdot 2^{\frac{1}{4}} b {\left(\sqrt{2} + 4\right)}^{\frac{3}{2}} + 96 \cdot 2^{\frac{1}{4}} a \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} - 384 \cdot 2^{\frac{1}{4}} b \sqrt{\sqrt{2} + 4} {\left(\sqrt{2} - 4\right)} + 1408 \cdot 2^{\frac{3}{4}} a \sqrt{\sqrt{2} + 4} - 256 \cdot 2^{\frac{3}{4}} b \sqrt{\sqrt{2} + 4} + 704 \, \sqrt{7} 2^{\frac{1}{4}} a \sqrt{-8 \, \sqrt{2} + 32} - 128 \, \sqrt{7} 2^{\frac{1}{4}} b \sqrt{-8 \, \sqrt{2} + 32}\right)} \log\left(x^{2} - 2 \cdot 2^{\frac{1}{4}} x \sqrt{-\frac{1}{8} \, \sqrt{2} + \frac{1}{2}} + \sqrt{2}\right) - \frac{a x^{3} - 4 \, b x^{3} - 3 \, a x - 2 \, b x}{28 \, {\left(x^{4} + x^{2} + 2\right)}}"," ",0,"1/401408*sqrt(7)*(32*sqrt(7)*2^(1/4)*a*(sqrt(2) + 4)^(3/2) - 128*sqrt(7)*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*sqrt(7)*2^(1/4)*a*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 384*sqrt(7)*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 24*2^(3/4)*a*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) + 96*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) + 2^(3/4)*a*(-8*sqrt(2) + 32)^(3/2) - 4*2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) + 1408*sqrt(7)*2^(3/4)*a*sqrt(sqrt(2) + 4) - 256*sqrt(7)*2^(3/4)*b*sqrt(sqrt(2) + 4) - 704*2^(1/4)*a*sqrt(-8*sqrt(2) + 32) + 128*2^(1/4)*b*sqrt(-8*sqrt(2) + 32))*arctan(2*2^(3/4)*sqrt(1/2)*(x + 2^(1/4)*sqrt(-1/8*sqrt(2) + 1/2))/sqrt(sqrt(2) + 4)) + 1/401408*sqrt(7)*(32*sqrt(7)*2^(1/4)*a*(sqrt(2) + 4)^(3/2) - 128*sqrt(7)*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*sqrt(7)*2^(1/4)*a*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 384*sqrt(7)*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 24*2^(3/4)*a*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) + 96*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) + 2^(3/4)*a*(-8*sqrt(2) + 32)^(3/2) - 4*2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) + 1408*sqrt(7)*2^(3/4)*a*sqrt(sqrt(2) + 4) - 256*sqrt(7)*2^(3/4)*b*sqrt(sqrt(2) + 4) - 704*2^(1/4)*a*sqrt(-8*sqrt(2) + 32) + 128*2^(1/4)*b*sqrt(-8*sqrt(2) + 32))*arctan(2*2^(3/4)*sqrt(1/2)*(x - 2^(1/4)*sqrt(-1/8*sqrt(2) + 1/2))/sqrt(sqrt(2) + 4)) + 1/802816*sqrt(7)*(24*sqrt(7)*2^(3/4)*a*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) - 96*sqrt(7)*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) - sqrt(7)*2^(3/4)*a*(-8*sqrt(2) + 32)^(3/2) + 4*sqrt(7)*2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) + 32*2^(1/4)*a*(sqrt(2) + 4)^(3/2) - 128*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*2^(1/4)*a*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 384*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) + 1408*2^(3/4)*a*sqrt(sqrt(2) + 4) - 256*2^(3/4)*b*sqrt(sqrt(2) + 4) + 704*sqrt(7)*2^(1/4)*a*sqrt(-8*sqrt(2) + 32) - 128*sqrt(7)*2^(1/4)*b*sqrt(-8*sqrt(2) + 32))*log(x^2 + 2*2^(1/4)*x*sqrt(-1/8*sqrt(2) + 1/2) + sqrt(2)) - 1/802816*sqrt(7)*(24*sqrt(7)*2^(3/4)*a*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) - 96*sqrt(7)*2^(3/4)*b*(sqrt(2) + 4)*sqrt(-8*sqrt(2) + 32) - sqrt(7)*2^(3/4)*a*(-8*sqrt(2) + 32)^(3/2) + 4*sqrt(7)*2^(3/4)*b*(-8*sqrt(2) + 32)^(3/2) + 32*2^(1/4)*a*(sqrt(2) + 4)^(3/2) - 128*2^(1/4)*b*(sqrt(2) + 4)^(3/2) + 96*2^(1/4)*a*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) - 384*2^(1/4)*b*sqrt(sqrt(2) + 4)*(sqrt(2) - 4) + 1408*2^(3/4)*a*sqrt(sqrt(2) + 4) - 256*2^(3/4)*b*sqrt(sqrt(2) + 4) + 704*sqrt(7)*2^(1/4)*a*sqrt(-8*sqrt(2) + 32) - 128*sqrt(7)*2^(1/4)*b*sqrt(-8*sqrt(2) + 32))*log(x^2 - 2*2^(1/4)*x*sqrt(-1/8*sqrt(2) + 1/2) + sqrt(2)) - 1/28*(a*x^3 - 4*b*x^3 - 3*a*x - 2*b*x)/(x^4 + x^2 + 2)","B",0
102,1,122,0,0.377742," ","integrate((-x^2+2^(1/2))/(1+x^4-x^2*2^(1/2)),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{4} \, \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 4} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{8} \, \sqrt{2 \, \sqrt{2} + 4} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right)"," ",0,"1/4*sqrt(-2*sqrt(2) + 4)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/4*sqrt(-2*sqrt(2) + 4)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*sqrt(2*sqrt(2) + 4)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/8*sqrt(2*sqrt(2) + 4)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1)","A",0
103,1,126,0,0.327764," ","integrate((x^2+2^(1/2))/(1+x^4+x^2*2^(1/2)),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{-2 \, \sqrt{2} + 4} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{8} \, \sqrt{-2 \, \sqrt{2} + 4} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"1/4*sqrt(2*sqrt(2) + 4)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/4*sqrt(2*sqrt(2) + 4)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*sqrt(-2*sqrt(2) + 4)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/8*sqrt(-2*sqrt(2) + 4)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","A",0
104,1,1501,0,0.321764," ","integrate((-x^2+2^(1/2))/(x^4+b*x^2+1),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b + 2} b^{4} + \sqrt{2} \sqrt{b - 2} b^{4} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{3} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{3} - \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{3} - 3 \, \sqrt{2} b^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} b^{3} - \sqrt{2} \sqrt{b + 2} b^{3} - \sqrt{2} \sqrt{b - 2} b^{3} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{2} + 3 \, \sqrt{2} b^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b - \sqrt{2} \sqrt{b^{2} - 4} b^{2} - 10 \, \sqrt{2} \sqrt{b + 2} b^{2} - 2 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} - 6 \, \sqrt{2} \sqrt{b - 2} b^{2} - 2 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} - 2 \, \sqrt{b + 2} \sqrt{b - 2} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b + 24 \, \sqrt{2} b^{2} + 2 \, \sqrt{b^{2} - 4} b^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} b + 6 \, \sqrt{2} \sqrt{b + 2} b + 4 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b + 2 \, \sqrt{2} \sqrt{b - 2} b + 4 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b + 4 \, \sqrt{b + 2} \sqrt{b - 2} b + 6 \, b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} - 6 \, \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} - 12 \, \sqrt{2} b - 4 \, \sqrt{b^{2} - 4} b - 2 \, \sqrt{b + 2} b - 2 \, \sqrt{b - 2} b - 4 \, \sqrt{2} \sqrt{b^{2} - 4} + 20 \, \sqrt{2} \sqrt{b + 2} + 8 \, \sqrt{b^{2} - 4} \sqrt{b + 2} + 4 \, \sqrt{2} \sqrt{b - 2} + 8 \, \sqrt{b^{2} - 4} \sqrt{b - 2} + 8 \, \sqrt{b + 2} \sqrt{b - 2} - 48 \, \sqrt{2} - 8 \, \sqrt{b^{2} - 4} + 4 \, \sqrt{b + 2} - 4 \, \sqrt{b - 2} - 24\right)} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, b + \frac{1}{2} \, \sqrt{b^{2} - 4}}}\right)}{4 \, {\left(b^{4} - 2 \, b^{3} - 7 \, b^{2} + 8 \, b + 12\right)}} + \frac{{\left(\sqrt{2} \sqrt{b + 2} b^{4} - \sqrt{2} \sqrt{b - 2} b^{4} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{3} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{3} - \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{3} + 3 \, \sqrt{2} b^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} b^{3} - \sqrt{2} \sqrt{b + 2} b^{3} + \sqrt{2} \sqrt{b - 2} b^{3} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{2} - 3 \, \sqrt{2} b^{3} + 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b - \sqrt{2} \sqrt{b^{2} - 4} b^{2} - 10 \, \sqrt{2} \sqrt{b + 2} b^{2} + 2 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} + 6 \, \sqrt{2} \sqrt{b - 2} b^{2} - 2 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} - 2 \, \sqrt{b + 2} \sqrt{b - 2} b^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b - 24 \, \sqrt{2} b^{2} + 2 \, \sqrt{b^{2} - 4} b^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} b + 6 \, \sqrt{2} \sqrt{b + 2} b - 4 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b - 2 \, \sqrt{2} \sqrt{b - 2} b + 4 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b + 4 \, \sqrt{b + 2} \sqrt{b - 2} b - 6 \, b^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} + 6 \, \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} + 12 \, \sqrt{2} b - 4 \, \sqrt{b^{2} - 4} b - 2 \, \sqrt{b + 2} b + 2 \, \sqrt{b - 2} b - 4 \, \sqrt{2} \sqrt{b^{2} - 4} + 20 \, \sqrt{2} \sqrt{b + 2} - 8 \, \sqrt{b^{2} - 4} \sqrt{b + 2} - 4 \, \sqrt{2} \sqrt{b - 2} + 8 \, \sqrt{b^{2} - 4} \sqrt{b - 2} + 8 \, \sqrt{b + 2} \sqrt{b - 2} + 48 \, \sqrt{2} - 8 \, \sqrt{b^{2} - 4} + 4 \, \sqrt{b + 2} + 4 \, \sqrt{b - 2} + 24\right)} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, b - \frac{1}{2} \, \sqrt{b^{2} - 4}}}\right)}{4 \, {\left(b^{4} - 2 \, b^{3} - 7 \, b^{2} + 8 \, b + 12\right)}}"," ",0,"1/4*(sqrt(2)*sqrt(b + 2)*b^4 + sqrt(2)*sqrt(b - 2)*b^4 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^3 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^3 - sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^3 - 3*sqrt(2)*b^4 + 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*b^3 - sqrt(2)*sqrt(b + 2)*b^3 - sqrt(2)*sqrt(b - 2)*b^3 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^2 + 3*sqrt(2)*b^3 - 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b - sqrt(2)*sqrt(b^2 - 4)*b^2 - 10*sqrt(2)*sqrt(b + 2)*b^2 - 2*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 - 6*sqrt(2)*sqrt(b - 2)*b^2 - 2*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 - 2*sqrt(b + 2)*sqrt(b - 2)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b + 24*sqrt(2)*b^2 + 2*sqrt(b^2 - 4)*b^2 - 12*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) - 4*sqrt(2)*sqrt(b^2 - 4)*b + 6*sqrt(2)*sqrt(b + 2)*b + 4*sqrt(b^2 - 4)*sqrt(b + 2)*b + 2*sqrt(2)*sqrt(b - 2)*b + 4*sqrt(b^2 - 4)*sqrt(b - 2)*b + 4*sqrt(b + 2)*sqrt(b - 2)*b + 6*b^2 + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2) + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2) + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2) - 6*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) - 12*sqrt(2)*b - 4*sqrt(b^2 - 4)*b - 2*sqrt(b + 2)*b - 2*sqrt(b - 2)*b - 4*sqrt(2)*sqrt(b^2 - 4) + 20*sqrt(2)*sqrt(b + 2) + 8*sqrt(b^2 - 4)*sqrt(b + 2) + 4*sqrt(2)*sqrt(b - 2) + 8*sqrt(b^2 - 4)*sqrt(b - 2) + 8*sqrt(b + 2)*sqrt(b - 2) - 48*sqrt(2) - 8*sqrt(b^2 - 4) + 4*sqrt(b + 2) - 4*sqrt(b - 2) - 24)*arctan(x/sqrt(1/2*b + 1/2*sqrt(b^2 - 4)))/(b^4 - 2*b^3 - 7*b^2 + 8*b + 12) + 1/4*(sqrt(2)*sqrt(b + 2)*b^4 - sqrt(2)*sqrt(b - 2)*b^4 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^3 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^3 - sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^3 + 3*sqrt(2)*b^4 - 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*b^3 - sqrt(2)*sqrt(b + 2)*b^3 + sqrt(2)*sqrt(b - 2)*b^3 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^2 - 3*sqrt(2)*b^3 + 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b - sqrt(2)*sqrt(b^2 - 4)*b^2 - 10*sqrt(2)*sqrt(b + 2)*b^2 + 2*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 + 6*sqrt(2)*sqrt(b - 2)*b^2 - 2*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 - 2*sqrt(b + 2)*sqrt(b - 2)*b^2 - 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b - 24*sqrt(2)*b^2 + 2*sqrt(b^2 - 4)*b^2 + 12*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) - 4*sqrt(2)*sqrt(b^2 - 4)*b + 6*sqrt(2)*sqrt(b + 2)*b - 4*sqrt(b^2 - 4)*sqrt(b + 2)*b - 2*sqrt(2)*sqrt(b - 2)*b + 4*sqrt(b^2 - 4)*sqrt(b - 2)*b + 4*sqrt(b + 2)*sqrt(b - 2)*b - 6*b^2 - 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2) + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2) + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2) + 6*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) + 12*sqrt(2)*b - 4*sqrt(b^2 - 4)*b - 2*sqrt(b + 2)*b + 2*sqrt(b - 2)*b - 4*sqrt(2)*sqrt(b^2 - 4) + 20*sqrt(2)*sqrt(b + 2) - 8*sqrt(b^2 - 4)*sqrt(b + 2) - 4*sqrt(2)*sqrt(b - 2) + 8*sqrt(b^2 - 4)*sqrt(b - 2) + 8*sqrt(b + 2)*sqrt(b - 2) + 48*sqrt(2) - 8*sqrt(b^2 - 4) + 4*sqrt(b + 2) + 4*sqrt(b - 2) + 24)*arctan(x/sqrt(1/2*b - 1/2*sqrt(b^2 - 4)))/(b^4 - 2*b^3 - 7*b^2 + 8*b + 12)","B",0
105,1,1501,0,0.352857," ","integrate((x^2+2^(1/2))/(x^4+b*x^2+1),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b + 2} b^{4} + \sqrt{2} \sqrt{b - 2} b^{4} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{3} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{3} - \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{3} - 3 \, \sqrt{2} b^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} b^{3} - \sqrt{2} \sqrt{b + 2} b^{3} - \sqrt{2} \sqrt{b - 2} b^{3} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{2} + 3 \, \sqrt{2} b^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b - \sqrt{2} \sqrt{b^{2} - 4} b^{2} - 10 \, \sqrt{2} \sqrt{b + 2} b^{2} + 2 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} - 6 \, \sqrt{2} \sqrt{b - 2} b^{2} + 2 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} + 2 \, \sqrt{b + 2} \sqrt{b - 2} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b + 24 \, \sqrt{2} b^{2} - 2 \, \sqrt{b^{2} - 4} b^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} b + 6 \, \sqrt{2} \sqrt{b + 2} b - 4 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b + 2 \, \sqrt{2} \sqrt{b - 2} b - 4 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b - 4 \, \sqrt{b + 2} \sqrt{b - 2} b - 6 \, b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} + 6 \, \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} - 12 \, \sqrt{2} b + 4 \, \sqrt{b^{2} - 4} b + 2 \, \sqrt{b + 2} b + 2 \, \sqrt{b - 2} b - 4 \, \sqrt{2} \sqrt{b^{2} - 4} + 20 \, \sqrt{2} \sqrt{b + 2} - 8 \, \sqrt{b^{2} - 4} \sqrt{b + 2} + 4 \, \sqrt{2} \sqrt{b - 2} - 8 \, \sqrt{b^{2} - 4} \sqrt{b - 2} - 8 \, \sqrt{b + 2} \sqrt{b - 2} - 48 \, \sqrt{2} + 8 \, \sqrt{b^{2} - 4} - 4 \, \sqrt{b + 2} + 4 \, \sqrt{b - 2} + 24\right)} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, b + \frac{1}{2} \, \sqrt{b^{2} - 4}}}\right)}{4 \, {\left(b^{4} - 2 \, b^{3} - 7 \, b^{2} + 8 \, b + 12\right)}} + \frac{{\left(\sqrt{2} \sqrt{b + 2} b^{4} - \sqrt{2} \sqrt{b - 2} b^{4} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{3} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{3} - \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{3} + 3 \, \sqrt{2} b^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} b^{3} - \sqrt{2} \sqrt{b + 2} b^{3} + \sqrt{2} \sqrt{b - 2} b^{3} - \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} + \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} + \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b^{2} - 3 \, \sqrt{2} b^{3} + 3 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} b - \sqrt{2} \sqrt{b^{2} - 4} b^{2} - 10 \, \sqrt{2} \sqrt{b + 2} b^{2} - 2 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b^{2} + 6 \, \sqrt{2} \sqrt{b - 2} b^{2} + 2 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b^{2} + 2 \, \sqrt{b + 2} \sqrt{b - 2} b^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} b + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} b + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} b - 24 \, \sqrt{2} b^{2} - 2 \, \sqrt{b^{2} - 4} b^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} b + 6 \, \sqrt{2} \sqrt{b + 2} b + 4 \, \sqrt{b^{2} - 4} \sqrt{b + 2} b - 2 \, \sqrt{2} \sqrt{b - 2} b - 4 \, \sqrt{b^{2} - 4} \sqrt{b - 2} b - 4 \, \sqrt{b + 2} \sqrt{b - 2} b + 6 \, b^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b + 2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4} \sqrt{b - 2} + 4 \, \sqrt{2} \sqrt{b + 2} \sqrt{b - 2} - 6 \, \sqrt{b^{2} - 4} \sqrt{b + 2} \sqrt{b - 2} + 12 \, \sqrt{2} b + 4 \, \sqrt{b^{2} - 4} b + 2 \, \sqrt{b + 2} b - 2 \, \sqrt{b - 2} b - 4 \, \sqrt{2} \sqrt{b^{2} - 4} + 20 \, \sqrt{2} \sqrt{b + 2} + 8 \, \sqrt{b^{2} - 4} \sqrt{b + 2} - 4 \, \sqrt{2} \sqrt{b - 2} - 8 \, \sqrt{b^{2} - 4} \sqrt{b - 2} - 8 \, \sqrt{b + 2} \sqrt{b - 2} + 48 \, \sqrt{2} + 8 \, \sqrt{b^{2} - 4} - 4 \, \sqrt{b + 2} - 4 \, \sqrt{b - 2} - 24\right)} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, b - \frac{1}{2} \, \sqrt{b^{2} - 4}}}\right)}{4 \, {\left(b^{4} - 2 \, b^{3} - 7 \, b^{2} + 8 \, b + 12\right)}}"," ",0,"1/4*(sqrt(2)*sqrt(b + 2)*b^4 + sqrt(2)*sqrt(b - 2)*b^4 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^3 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^3 - sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^3 - 3*sqrt(2)*b^4 + 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*b^3 - sqrt(2)*sqrt(b + 2)*b^3 - sqrt(2)*sqrt(b - 2)*b^3 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^2 + 3*sqrt(2)*b^3 - 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b - sqrt(2)*sqrt(b^2 - 4)*b^2 - 10*sqrt(2)*sqrt(b + 2)*b^2 + 2*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 - 6*sqrt(2)*sqrt(b - 2)*b^2 + 2*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 + 2*sqrt(b + 2)*sqrt(b - 2)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b + 24*sqrt(2)*b^2 - 2*sqrt(b^2 - 4)*b^2 - 12*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) - 4*sqrt(2)*sqrt(b^2 - 4)*b + 6*sqrt(2)*sqrt(b + 2)*b - 4*sqrt(b^2 - 4)*sqrt(b + 2)*b + 2*sqrt(2)*sqrt(b - 2)*b - 4*sqrt(b^2 - 4)*sqrt(b - 2)*b - 4*sqrt(b + 2)*sqrt(b - 2)*b - 6*b^2 + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2) + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2) + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2) + 6*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) - 12*sqrt(2)*b + 4*sqrt(b^2 - 4)*b + 2*sqrt(b + 2)*b + 2*sqrt(b - 2)*b - 4*sqrt(2)*sqrt(b^2 - 4) + 20*sqrt(2)*sqrt(b + 2) - 8*sqrt(b^2 - 4)*sqrt(b + 2) + 4*sqrt(2)*sqrt(b - 2) - 8*sqrt(b^2 - 4)*sqrt(b - 2) - 8*sqrt(b + 2)*sqrt(b - 2) - 48*sqrt(2) + 8*sqrt(b^2 - 4) - 4*sqrt(b + 2) + 4*sqrt(b - 2) + 24)*arctan(x/sqrt(1/2*b + 1/2*sqrt(b^2 - 4)))/(b^4 - 2*b^3 - 7*b^2 + 8*b + 12) + 1/4*(sqrt(2)*sqrt(b + 2)*b^4 - sqrt(2)*sqrt(b - 2)*b^4 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^3 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^3 - sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^3 + 3*sqrt(2)*b^4 - 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*b^3 - sqrt(2)*sqrt(b + 2)*b^3 + sqrt(2)*sqrt(b - 2)*b^3 - sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 + sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 + sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b^2 - 3*sqrt(2)*b^3 + 3*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2)*b - sqrt(2)*sqrt(b^2 - 4)*b^2 - 10*sqrt(2)*sqrt(b + 2)*b^2 - 2*sqrt(b^2 - 4)*sqrt(b + 2)*b^2 + 6*sqrt(2)*sqrt(b - 2)*b^2 + 2*sqrt(b^2 - 4)*sqrt(b - 2)*b^2 + 2*sqrt(b + 2)*sqrt(b - 2)*b^2 - 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*b + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2)*b + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2)*b - 24*sqrt(2)*b^2 - 2*sqrt(b^2 - 4)*b^2 + 12*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) - 4*sqrt(2)*sqrt(b^2 - 4)*b + 6*sqrt(2)*sqrt(b + 2)*b + 4*sqrt(b^2 - 4)*sqrt(b + 2)*b - 2*sqrt(2)*sqrt(b - 2)*b - 4*sqrt(b^2 - 4)*sqrt(b - 2)*b - 4*sqrt(b + 2)*sqrt(b - 2)*b + 6*b^2 - 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b + 2) + 4*sqrt(2)*sqrt(b^2 - 4)*sqrt(b - 2) + 4*sqrt(2)*sqrt(b + 2)*sqrt(b - 2) - 6*sqrt(b^2 - 4)*sqrt(b + 2)*sqrt(b - 2) + 12*sqrt(2)*b + 4*sqrt(b^2 - 4)*b + 2*sqrt(b + 2)*b - 2*sqrt(b - 2)*b - 4*sqrt(2)*sqrt(b^2 - 4) + 20*sqrt(2)*sqrt(b + 2) + 8*sqrt(b^2 - 4)*sqrt(b + 2) - 4*sqrt(2)*sqrt(b - 2) - 8*sqrt(b^2 - 4)*sqrt(b - 2) - 8*sqrt(b + 2)*sqrt(b - 2) + 48*sqrt(2) + 8*sqrt(b^2 - 4) - 4*sqrt(b + 2) - 4*sqrt(b - 2) - 24)*arctan(x/sqrt(1/2*b - 1/2*sqrt(b^2 - 4)))/(b^4 - 2*b^3 - 7*b^2 + 8*b + 12)","B",0
106,-2,0,0,0.000000," ","integrate((-x^2+2*a)/(x^4-a*x^2+a^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-16,[2,0]%%%}+%%%{-4,[0,1]%%%},0,%%%{64,[4,0]%%%}+%%%{8,[2,2]%%%}+%%%{16,[2,1]%%%}+%%%{6,[0,2]%%%},0,%%%{-64,[4,2]%%%}+%%%{-128,[4,1]%%%}+%%%{48,[2,3]%%%}+%%%{16,[2,2]%%%}+%%%{-4,[0,3]%%%},0,%%%{16,[4,4]%%%}+%%%{-64,[4,3]%%%}+%%%{64,[4,2]%%%}+%%%{8,[2,4]%%%}+%%%{-16,[2,3]%%%}+%%%{1,[0,4]%%%}] at parameters values [16,-63]Warning, choosing root of [1,0,%%%{-16,[2,0]%%%}+%%%{-4,[0,1]%%%},0,%%%{64,[4,0]%%%}+%%%{8,[2,2]%%%}+%%%{16,[2,1]%%%}+%%%{6,[0,2]%%%},0,%%%{-64,[4,2]%%%}+%%%{-128,[4,1]%%%}+%%%{48,[2,3]%%%}+%%%{16,[2,2]%%%}+%%%{-4,[0,3]%%%},0,%%%{16,[4,4]%%%}+%%%{-64,[4,3]%%%}+%%%{64,[4,2]%%%}+%%%{8,[2,4]%%%}+%%%{-16,[2,3]%%%}+%%%{1,[0,4]%%%}] at parameters values [39,13]-((-32*a^5-40*a^4*abs(a)+8*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^3-1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^2*im(sign(sin(acos(a/2/abs(a))/2)))-1/24*(-2880*sqrt(3)*a^5+1728*a^4*sqrt(5*a^2+4*a*abs(a))-2304*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))-(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))^2-(-144*a^4*abs(a)+48*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))+1/24*(-3456*sqrt(3)*a^5+3456*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))-(-96*a^5-120*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2+1/24*(-3456*sqrt(3)*a^5+3456*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))+(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+(64*sqrt(3)*a^5-128*a^5-64*a^4*abs(a))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))+1/8*(-320*sqrt(3)*a^5+192*a^4*sqrt(5*a^2-4*a*abs(a))+256*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))^3+1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))+(96*a^5-120*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))+1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2+(-144*a^4*abs(a)+48*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))-1/24*(-2880*sqrt(3)*a^5+1728*a^4*sqrt(5*a^2-4*a*abs(a))+2304*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+(-128*sqrt(3)*a^5+384*abs(a)*a^4+256*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))+1/8*(-320*sqrt(3)*a^5+192*a^4*sqrt(5*a^2+4*a*abs(a))-256*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))^3+(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+(128*sqrt(3)*a^5+384*abs(a)*a^4+256*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))-(32*a^5-40*a^4*abs(a)+8*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*re(sign(sin(acos(a/2/abs(a))/2)))^3+(128*a^3*sqrt(abs(a))*abs(a)+64*sqrt(3)*a^4*sqrt(abs(a))-64*a^4*sqrt(abs(a)))*re(sign(sin(acos(a/2/abs(a))/2))))/(256*a^3*sqrt(2*a^2+a*abs(a))*sqrt(3)*abs(a)-256*a^3*sqrt(2*a^2-a*abs(a))*sqrt(3)*abs(a))*ln(x^2-2*sqrt((1+a*1/2/abs(a))/2)*sqrt(abs(a))*sign(cos(acos(a*1/2/abs(a))/2))*x+sqrt(abs(a))*sqrt(abs(a)))-(1/8*(-320*sqrt(3)*a^5+192*a^4*sqrt(5*a^2+4*a*abs(a))-256*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^3+(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^2*im(sign(sin(acos(a/2/abs(a))/2)))+(-96*a^5-120*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))-1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))^2-1/24*(-3456*sqrt(3)*a^5+3456*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))-(-144*a^4*abs(a)+48*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))-1/24*(-2880*sqrt(3)*a^5+1728*a^4*sqrt(5*a^2+4*a*abs(a))-2304*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2-(-144*a^4*abs(a)+48*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))+1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+(-128*sqrt(3)*a^5+384*abs(a)*a^4-256*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*im(sign(cos(acos(a/2/abs(a))/2)))-(32*a^5-40*a^4*abs(a)+8*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))^3-(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))+1/24*(-2880*sqrt(3)*a^5+1728*a^4*sqrt(5*a^2-4*a*abs(a))+2304*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2+1/24*(-3456*sqrt(3)*a^5+3456*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))+(96*a^5-120*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+(64*sqrt(3)*a^5-128*a^5+64*a^4*abs(a))/sqrt(abs(a))*im(sign(sin(acos(a/2/abs(a))/2)))-(-32*a^5-40*a^4*abs(a)+8*sqrt(3)*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))^3+1/12*(-864*sqrt(3)*a^5+864*a^4*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))+(-72*a^4*abs(a)+24*sqrt(3)*a^4*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+(64*sqrt(3)*a^5-128*a^5-64*a^4*abs(a))/sqrt(abs(a))*re(sign(cos(acos(a/2/abs(a))/2)))-1/8*(-320*sqrt(3)*a^5+192*a^4*sqrt(5*a^2-4*a*abs(a))+256*sqrt(3)*a^4*abs(a))/sqrt(abs(a))*re(sign(sin(acos(a/2/abs(a))/2)))^3+(-128*sqrt(3)*a^5+384*abs(a)*a^4+256*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*re(sign(sin(acos(a/2/abs(a))/2))))/(128*a^3*sqrt(2*a^2+a*abs(a))*sqrt(3)*abs(a)-128*a^3*sqrt(2*a^2-a*abs(a))*sqrt(3)*abs(a))*atan((x-sign(cos(acos(a*1/2/abs(a))/2))*sqrt((1+a*1/2/abs(a))/2)*sqrt(abs(a)))/sign(sin(acos(a*1/2/abs(a))/2))/sqrt((1-a*1/2/abs(a))/2)/sqrt(abs(a)))-(2*abs(a)*sqrt(abs(a))*a^2*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)-2*abs(a)*sqrt(abs(a))*a^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-3*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)+9*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-9*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2+3*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^3-2*sqrt(3)*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)+2*sqrt(3)*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)+a^2*sqrt(abs(a))*a*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^3-3*a^2*sqrt(abs(a))*a*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)+3*a^2*sqrt(abs(a))*a*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^2-a^2*sqrt(abs(a))*a*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3+sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2-sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^2+9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)-9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^2+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^3)*1/4/sqrt(3)/a^4*ln(x^2+2*sqrt(abs(a))*cos(acos(a*1/2/abs(a))/2)*x+sqrt(abs(a))*sqrt(abs(a)))+(2*abs(a)*sqrt(abs(a))*a^2*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)-2*abs(a)*sqrt(abs(a))*a^2*cos(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^3+3*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)-3*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2+a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3+3*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^2-9*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)+9*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^2-3*a^2*sqrt(abs(a))*a*cos(re(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^3+2*sqrt(3)*a^2*sqrt(abs(a))*a*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)-2*sqrt(3)*a^2*sqrt(abs(a))*a*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)+9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cos(re(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^3+sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^2-sqrt(3)*abs(a)*a^2*sqrt(abs(a))*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3)*1/2/sqrt(3)/a^4*atan((x+cos(acos(a*1/2/abs(a))/2)*sqrt(abs(a)))/sin(acos(a*1/2/abs(a))/2)/sqrt(abs(a)))","F(-2)",0
107,-2,0,0,0.000000," ","integrate((-x^2+2*a^(1/2))/(a+x^4-x^2*a^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
108,1,92,0,0.177248," ","integrate((2*b^(2/3)+x^2)/(b^(4/3)+b^(2/3)*x^2+x^4),x, algorithm=""giac"")","\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + b^{\frac{1}{3}}\right)}}{3 \, {\left| b \right|}^{\frac{1}{3}}}\right)}{2 \, {\left| b \right|}^{\frac{1}{3}}} + \frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - b^{\frac{1}{3}}\right)}}{3 \, {\left| b \right|}^{\frac{1}{3}}}\right)}{2 \, {\left| b \right|}^{\frac{1}{3}}} + \frac{\log\left(x^{2} + b^{\frac{1}{3}} x + b^{\frac{2}{3}}\right)}{4 \, b^{\frac{1}{3}}} - \frac{\log\left(x^{2} - b^{\frac{1}{3}} x + b^{\frac{2}{3}}\right)}{4 \, b^{\frac{1}{3}}}"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + b^(1/3))/abs(b)^(1/3))/abs(b)^(1/3) + 1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - b^(1/3))/abs(b)^(1/3))/abs(b)^(1/3) + 1/4*log(x^2 + b^(1/3)*x + b^(2/3))/b^(1/3) - 1/4*log(x^2 - b^(1/3)*x + b^(2/3))/b^(1/3)","A",0
109,-2,0,0,0.000000," ","integrate((B*x^2+A)/(x^4-a*x^2+a^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,%%%{-16,[2,0]%%%}+%%%{-4,[0,1]%%%},0,%%%{64,[4,0]%%%}+%%%{8,[2,2]%%%}+%%%{16,[2,1]%%%}+%%%{6,[0,2]%%%},0,%%%{-64,[4,2]%%%}+%%%{-128,[4,1]%%%}+%%%{48,[2,3]%%%}+%%%{16,[2,2]%%%}+%%%{-4,[0,3]%%%},0,%%%{16,[4,4]%%%}+%%%{-64,[4,3]%%%}+%%%{64,[4,2]%%%}+%%%{8,[2,4]%%%}+%%%{-16,[2,3]%%%}+%%%{1,[0,4]%%%}] at parameters values [71,-96]Warning, choosing root of [1,0,%%%{-16,[2,0]%%%}+%%%{-4,[0,1]%%%},0,%%%{64,[4,0]%%%}+%%%{8,[2,2]%%%}+%%%{16,[2,1]%%%}+%%%{6,[0,2]%%%},0,%%%{-64,[4,2]%%%}+%%%{-128,[4,1]%%%}+%%%{48,[2,3]%%%}+%%%{16,[2,2]%%%}+%%%{-4,[0,3]%%%},0,%%%{16,[4,4]%%%}+%%%{-64,[4,3]%%%}+%%%{64,[4,2]%%%}+%%%{8,[2,4]%%%}+%%%{-16,[2,3]%%%}+%%%{1,[0,4]%%%}] at parameters values [72,-72]((64*a^3*sqrt(abs(a))*abs(a)+32*sqrt(3)*a^4*sqrt(abs(a))+32*a^4*sqrt(abs(a)))*A*im(sign(cos(acos(a/2/abs(a))/2)))+(64*sqrt(3)*a^5+192*abs(a)*a^4-128*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*A*im(sign(sin(acos(a/2/abs(a))/2)))+(-64*sqrt(3)*a^5+192*abs(a)*a^4-128*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*A*re(sign(cos(acos(a/2/abs(a))/2)))+(32*sqrt(3)*a^5-64*a^5+32*a^4*abs(a))/sqrt(abs(a))*A*re(sign(sin(acos(a/2/abs(a))/2)))+(-32*a^6-40*a^5*abs(a)+8*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^3-1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^2*im(sign(sin(acos(a/2/abs(a))/2)))-1/24*(-2880*sqrt(3)*a^6+1728*abs(a)*a^4*sqrt(5*a^2+4*a*abs(a))-2304*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))-(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))^2-(-144*a^5*abs(a)+48*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))+1/24*(-3456*sqrt(3)*a^6+3456*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))-(-96*a^6-120*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2+1/24*(-3456*sqrt(3)*a^6+3456*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))+(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+1/8*(-320*sqrt(3)*a^6+192*abs(a)*a^4*sqrt(5*a^2-4*a*abs(a))+256*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))^3+1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))+(96*a^6-120*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))+1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2+(-144*a^5*abs(a)+48*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))-1/24*(-2880*sqrt(3)*a^6+1728*abs(a)*a^4*sqrt(5*a^2-4*a*abs(a))+2304*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2+1/8*(-320*sqrt(3)*a^6+192*abs(a)*a^4*sqrt(5*a^2+4*a*abs(a))-256*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*re(sign(cos(acos(a/2/abs(a))/2)))^3+(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*re(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2-(32*a^6-40*a^5*abs(a)+8*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*re(sign(sin(acos(a/2/abs(a))/2)))^3)/(256*a^4*sqrt(2*a^2+a*abs(a))*sqrt(3)*abs(a)-256*a^4*sqrt(2*a^2-a*abs(a))*sqrt(3)*abs(a))*ln(x^2-2*sqrt((1+a*1/2/abs(a))/2)*sqrt(abs(a))*sign(cos(acos(a*1/2/abs(a))/2))*x+sqrt(abs(a))*sqrt(abs(a)))+((64*sqrt(3)*a^5+192*abs(a)*a^4+128*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*A*im(sign(cos(acos(a/2/abs(a))/2)))+(64*a^3*sqrt(abs(a))*abs(a)+32*sqrt(3)*a^4*sqrt(abs(a))-32*a^4*sqrt(abs(a)))*A*im(sign(sin(acos(a/2/abs(a))/2)))+(64*a^3*sqrt(abs(a))*abs(a)+32*sqrt(3)*a^4*sqrt(abs(a))+32*a^4*sqrt(abs(a)))*A*re(sign(cos(acos(a/2/abs(a))/2)))+(64*sqrt(3)*a^5+192*abs(a)*a^4-128*sqrt(3)*a^4*abs(a))*1/2/sqrt(abs(a))*A*re(sign(sin(acos(a/2/abs(a))/2)))+1/8*(-320*sqrt(3)*a^6+192*abs(a)*a^4*sqrt(5*a^2+4*a*abs(a))-256*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^3+(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^2*im(sign(sin(acos(a/2/abs(a))/2)))+(-96*a^6-120*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))-1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))^2-1/24*(-3456*sqrt(3)*a^6+3456*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))-(-144*a^5*abs(a)+48*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))-1/24*(-2880*sqrt(3)*a^6+1728*abs(a)*a^4*sqrt(5*a^2+4*a*abs(a))-2304*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2-(-144*a^5*abs(a)+48*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))+1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2-(32*a^6-40*a^5*abs(a)+8*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))^3-(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(cos(acos(a/2/abs(a))/2)))+1/24*(-2880*sqrt(3)*a^6+1728*abs(a)*a^4*sqrt(5*a^2-4*a*abs(a))+2304*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))-(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))^2+1/24*(-3456*sqrt(3)*a^6+3456*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))+(96*a^6-120*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*im(sign(sin(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2-(-32*a^6-40*a^5*abs(a)+8*sqrt(3)*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*re(sign(cos(acos(a/2/abs(a))/2)))^3+1/12*(-864*sqrt(3)*a^6+864*a^5*sqrt(5*a^2+4*a*abs(a)))/sqrt(abs(a))*B*re(sign(cos(acos(a/2/abs(a))/2)))^2*re(sign(sin(acos(a/2/abs(a))/2)))+(-72*a^5*abs(a)+24*sqrt(3)*a^5*sqrt(5*a^2-4*a*abs(a)))/sqrt(abs(a))*B*re(sign(cos(acos(a/2/abs(a))/2)))*re(sign(sin(acos(a/2/abs(a))/2)))^2-1/8*(-320*sqrt(3)*a^6+192*abs(a)*a^4*sqrt(5*a^2-4*a*abs(a))+256*sqrt(3)*a^5*abs(a))/sqrt(abs(a))*B*re(sign(sin(acos(a/2/abs(a))/2)))^3)/(128*a^4*sqrt(2*a^2+a*abs(a))*sqrt(3)*abs(a)-128*a^4*sqrt(2*a^2-a*abs(a))*sqrt(3)*abs(a))*atan((x-sign(cos(acos(a*1/2/abs(a))/2))*sqrt((1+a*1/2/abs(a))/2)*sqrt(abs(a)))/sign(sin(acos(a*1/2/abs(a))/2))/sqrt((1-a*1/2/abs(a))/2)/sqrt(abs(a)))+(-abs(a)*sqrt(abs(a))*A*a*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)+abs(a)*sqrt(abs(a))*A*a*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)+sqrt(3)*a^2*sqrt(abs(a))*A*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)-sqrt(3)*a^2*sqrt(abs(a))*A*cos(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-3*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)+9*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-9*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2+3*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^3+a^2*sqrt(abs(a))*B*a*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^3-3*a^2*sqrt(abs(a))*B*a*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)+3*a^2*sqrt(abs(a))*B*a*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^2-a^2*sqrt(abs(a))*B*a*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3+sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2-sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^2+9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)-9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^2+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^3)*1/4/sqrt(3)/a^4*ln(x^2+2*sqrt(abs(a))*cos(acos(a*1/2/abs(a))/2)*x+sqrt(abs(a))*sqrt(abs(a)))-(-abs(a)*sqrt(abs(a))*A*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)+abs(a)*sqrt(abs(a))*A*a*cos(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-sqrt(3)*a^2*sqrt(abs(a))*A*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)+sqrt(3)*a^2*sqrt(abs(a))*A*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^3+3*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)-3*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^3*cosh(im(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2+a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3+3*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^2-9*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)+9*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^2-3*a^2*sqrt(abs(a))*B*a*cos(re(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^2*sinh(im(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)+9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)-9*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^2*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^2+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cos(re(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)*sinh(im(acos(a/2/abs(a)))/2)^3+sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cosh(im(acos(a/2/abs(a)))/2)^3*sin(re(acos(a/2/abs(a)))/2)^3-3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cosh(im(acos(a/2/abs(a)))/2)^2*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)+3*sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*cosh(im(acos(a/2/abs(a)))/2)*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^2-sqrt(3)*abs(a)*a^2*sqrt(abs(a))*B*sin(re(acos(a/2/abs(a)))/2)^3*sinh(im(acos(a/2/abs(a)))/2)^3)*1/2/sqrt(3)/a^4*atan((x+cos(acos(a*1/2/abs(a))/2)*sqrt(abs(a)))/sin(acos(a*1/2/abs(a))/2)/sqrt(abs(a)))","F(-2)",0
110,-2,0,0,0.000000," ","integrate((B*x^2+A)/(a+x^4-x^2*a^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
111,-2,0,0,0.000000," ","integrate((B*x^2+A)/(a+c*x^4-x^2*(a*c)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
112,-2,0,0,0.000000," ","integrate((B*x^2+A)/(a+c*x^4-x^2*a^(1/2)*c^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
113,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^4+x^2+3)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 3}{\sqrt{-x^{4} + x^{2} + 3}}\,{d x}"," ",0,"integrate(-(x^2 - 3)/sqrt(-x^4 + x^2 + 3), x)","F",0
114,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^4+2*x^2+3)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 3}{\sqrt{-x^{4} + 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(-(x^2 - 3)/sqrt(-x^4 + 2*x^2 + 3), x)","F",0
115,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^4+3*x^2+3)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 3}{\sqrt{-x^{4} + 3 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(-(x^2 - 3)/sqrt(-x^4 + 3*x^2 + 3), x)","F",0
116,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^4-x^2+3)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 3}{\sqrt{-x^{4} - x^{2} + 3}}\,{d x}"," ",0,"integrate(-(x^2 - 3)/sqrt(-x^4 - x^2 + 3), x)","F",0
117,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^4-2*x^2+3)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 3}{\sqrt{-x^{4} - 2 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(-(x^2 - 3)/sqrt(-x^4 - 2*x^2 + 3), x)","F",0
118,0,0,0,0.000000," ","integrate((-x^2+3)/(-x^4-3*x^2+3)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 3}{\sqrt{-x^{4} - 3 \, x^{2} + 3}}\,{d x}"," ",0,"integrate(-(x^2 - 3)/sqrt(-x^4 - 3*x^2 + 3), x)","F",0
119,0,0,0,0.000000," ","integrate((2*c*x^2-(-4*a*c+b^2)^(1/2)+b)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, c x^{2} + b - \sqrt{b^{2} - 4 \, a c}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((2*c*x^2 + b - sqrt(b^2 - 4*a*c))/sqrt(c*x^4 + b*x^2 + a), x)","F",0
120,1,94,0,0.153315," ","integrate((e*x^2+d)^4*(c*x^4+a),x, algorithm=""giac"")","\frac{1}{13} \, c x^{13} e^{4} + \frac{4}{11} \, c d x^{11} e^{3} + \frac{2}{3} \, c d^{2} x^{9} e^{2} + \frac{4}{7} \, c d^{3} x^{7} e + \frac{1}{9} \, a x^{9} e^{4} + \frac{1}{5} \, c d^{4} x^{5} + \frac{4}{7} \, a d x^{7} e^{3} + \frac{6}{5} \, a d^{2} x^{5} e^{2} + \frac{4}{3} \, a d^{3} x^{3} e + a d^{4} x"," ",0,"1/13*c*x^13*e^4 + 4/11*c*d*x^11*e^3 + 2/3*c*d^2*x^9*e^2 + 4/7*c*d^3*x^7*e + 1/9*a*x^9*e^4 + 1/5*c*d^4*x^5 + 4/7*a*d*x^7*e^3 + 6/5*a*d^2*x^5*e^2 + 4/3*a*d^3*x^3*e + a*d^4*x","A",0
121,1,71,0,0.148592," ","integrate((e*x^2+d)^3*(c*x^4+a),x, algorithm=""giac"")","\frac{1}{11} \, c x^{11} e^{3} + \frac{1}{3} \, c d x^{9} e^{2} + \frac{3}{7} \, c d^{2} x^{7} e + \frac{1}{5} \, c d^{3} x^{5} + \frac{1}{7} \, a x^{7} e^{3} + \frac{3}{5} \, a d x^{5} e^{2} + a d^{2} x^{3} e + a d^{3} x"," ",0,"1/11*c*x^11*e^3 + 1/3*c*d*x^9*e^2 + 3/7*c*d^2*x^7*e + 1/5*c*d^3*x^5 + 1/7*a*x^7*e^3 + 3/5*a*d*x^5*e^2 + a*d^2*x^3*e + a*d^3*x","A",0
122,1,50,0,0.198955," ","integrate((e*x^2+d)^2*(c*x^4+a),x, algorithm=""giac"")","\frac{1}{9} \, c x^{9} e^{2} + \frac{2}{7} \, c d x^{7} e + \frac{1}{5} \, c d^{2} x^{5} + \frac{1}{5} \, a x^{5} e^{2} + \frac{2}{3} \, a d x^{3} e + a d^{2} x"," ",0,"1/9*c*x^9*e^2 + 2/7*c*d*x^7*e + 1/5*c*d^2*x^5 + 1/5*a*x^5*e^2 + 2/3*a*d*x^3*e + a*d^2*x","A",0
123,1,28,0,0.178157," ","integrate((e*x^2+d)*(c*x^4+a),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e + \frac{1}{5} \, c d x^{5} + \frac{1}{3} \, a x^{3} e + a d x"," ",0,"1/7*c*x^7*e + 1/5*c*d*x^5 + 1/3*a*x^3*e + a*d*x","A",0
124,1,44,0,0.168953," ","integrate((c*x^4+a)/(e*x^2+d),x, algorithm=""giac"")","\frac{{\left(c d^{2} + a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{\sqrt{d}} + \frac{1}{3} \, {\left(c x^{3} e^{2} - 3 \, c d x e\right)} e^{\left(-3\right)}"," ",0,"(c*d^2 + a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/sqrt(d) + 1/3*(c*x^3*e^2 - 3*c*d*x*e)*e^(-3)","A",0
125,1,62,0,0.156808," ","integrate((c*x^4+a)/(e*x^2+d)^2,x, algorithm=""giac"")","c x e^{\left(-2\right)} - \frac{{\left(3 \, c d^{2} - a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c d^{2} x + a x e^{2}\right)} e^{\left(-2\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"c*x*e^(-2) - 1/2*(3*c*d^2 - a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(3/2) + 1/2*(c*d^2*x + a*x*e^2)*e^(-2)/((x^2*e + d)*d)","A",0
126,1,77,0,0.160189," ","integrate((c*x^4+a)/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{3 \, {\left(c d^{2} + a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{8 \, d^{\frac{5}{2}}} - \frac{{\left(5 \, c d^{2} x^{3} e + 3 \, c d^{3} x - 3 \, a x^{3} e^{3} - 5 \, a d x e^{2}\right)} e^{\left(-2\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{2}}"," ",0,"3/8*(c*d^2 + a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(5/2) - 1/8*(5*c*d^2*x^3*e + 3*c*d^3*x - 3*a*x^3*e^3 - 5*a*d*x*e^2)*e^(-2)/((x^2*e + d)^2*d^2)","A",0
127,1,100,0,0.153892," ","integrate((c*x^4+a)/(e*x^2+d)^4,x, algorithm=""giac"")","\frac{{\left(c d^{2} + 5 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{16 \, d^{\frac{7}{2}}} + \frac{{\left(3 \, c d^{2} x^{5} e^{2} - 8 \, c d^{3} x^{3} e + 15 \, a x^{5} e^{4} - 3 \, c d^{4} x + 40 \, a d x^{3} e^{3} + 33 \, a d^{2} x e^{2}\right)} e^{\left(-2\right)}}{48 \, {\left(x^{2} e + d\right)}^{3} d^{3}}"," ",0,"1/16*(c*d^2 + 5*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(7/2) + 1/48*(3*c*d^2*x^5*e^2 - 8*c*d^3*x^3*e + 15*a*x^5*e^4 - 3*c*d^4*x + 40*a*d*x^3*e^3 + 33*a*d^2*x*e^2)*e^(-2)/((x^2*e + d)^3*d^3)","A",0
128,1,128,0,0.158736," ","integrate((e*x^2+d)^3*(c*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{15} \, c^{2} x^{15} e^{3} + \frac{3}{13} \, c^{2} d x^{13} e^{2} + \frac{3}{11} \, c^{2} d^{2} x^{11} e + \frac{1}{9} \, c^{2} d^{3} x^{9} + \frac{2}{11} \, a c x^{11} e^{3} + \frac{2}{3} \, a c d x^{9} e^{2} + \frac{6}{7} \, a c d^{2} x^{7} e + \frac{2}{5} \, a c d^{3} x^{5} + \frac{1}{7} \, a^{2} x^{7} e^{3} + \frac{3}{5} \, a^{2} d x^{5} e^{2} + a^{2} d^{2} x^{3} e + a^{2} d^{3} x"," ",0,"1/15*c^2*x^15*e^3 + 3/13*c^2*d*x^13*e^2 + 3/11*c^2*d^2*x^11*e + 1/9*c^2*d^3*x^9 + 2/11*a*c*x^11*e^3 + 2/3*a*c*d*x^9*e^2 + 6/7*a*c*d^2*x^7*e + 2/5*a*c*d^3*x^5 + 1/7*a^2*x^7*e^3 + 3/5*a^2*d*x^5*e^2 + a^2*d^2*x^3*e + a^2*d^3*x","A",0
129,1,91,0,0.149043," ","integrate((e*x^2+d)^2*(c*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{13} \, c^{2} x^{13} e^{2} + \frac{2}{11} \, c^{2} d x^{11} e + \frac{1}{9} \, c^{2} d^{2} x^{9} + \frac{2}{9} \, a c x^{9} e^{2} + \frac{4}{7} \, a c d x^{7} e + \frac{2}{5} \, a c d^{2} x^{5} + \frac{1}{5} \, a^{2} x^{5} e^{2} + \frac{2}{3} \, a^{2} d x^{3} e + a^{2} d^{2} x"," ",0,"1/13*c^2*x^13*e^2 + 2/11*c^2*d*x^11*e + 1/9*c^2*d^2*x^9 + 2/9*a*c*x^9*e^2 + 4/7*a*c*d*x^7*e + 2/5*a*c*d^2*x^5 + 1/5*a^2*x^5*e^2 + 2/3*a^2*d*x^3*e + a^2*d^2*x","A",0
130,1,53,0,0.152102," ","integrate((e*x^2+d)*(c*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, c^{2} x^{11} e + \frac{1}{9} \, c^{2} d x^{9} + \frac{2}{7} \, a c x^{7} e + \frac{2}{5} \, a c d x^{5} + \frac{1}{3} \, a^{2} x^{3} e + a^{2} d x"," ",0,"1/11*c^2*x^11*e + 1/9*c^2*d*x^9 + 2/7*a*c*x^7*e + 2/5*a*c*d*x^5 + 1/3*a^2*x^3*e + a^2*d*x","A",0
131,1,21,0,0.165982," ","integrate((c*x^4+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} + \frac{2}{5} \, a c x^{5} + a^{2} x"," ",0,"1/9*c^2*x^9 + 2/5*a*c*x^5 + a^2*x","A",0
132,1,105,0,0.155768," ","integrate((c*x^4+a)^2/(e*x^2+d),x, algorithm=""giac"")","\frac{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{\sqrt{d}} + \frac{1}{105} \, {\left(15 \, c^{2} x^{7} e^{6} - 21 \, c^{2} d x^{5} e^{5} + 35 \, c^{2} d^{2} x^{3} e^{4} - 105 \, c^{2} d^{3} x e^{3} + 70 \, a c x^{3} e^{6} - 210 \, a c d x e^{5}\right)} e^{\left(-7\right)}"," ",0,"(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/sqrt(d) + 1/105*(15*c^2*x^7*e^6 - 21*c^2*d*x^5*e^5 + 35*c^2*d^2*x^3*e^4 - 105*c^2*d^3*x*e^3 + 70*a*c*x^3*e^6 - 210*a*c*d*x*e^5)*e^(-7)","A",0
133,1,128,0,0.170780," ","integrate((c*x^4+a)^2/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{1}{15} \, {\left(3 \, c^{2} x^{5} e^{8} - 10 \, c^{2} d x^{3} e^{7} + 45 \, c^{2} d^{2} x e^{6} + 30 \, a c x e^{8}\right)} e^{\left(-10\right)} - \frac{{\left(7 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c^{2} d^{4} x + 2 \, a c d^{2} x e^{2} + a^{2} x e^{4}\right)} e^{\left(-4\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"1/15*(3*c^2*x^5*e^8 - 10*c^2*d*x^3*e^7 + 45*c^2*d^2*x*e^6 + 30*a*c*x*e^8)*e^(-10) - 1/2*(7*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(3/2) + 1/2*(c^2*d^4*x + 2*a*c*d^2*x*e^2 + a^2*x*e^4)*e^(-4)/((x^2*e + d)*d)","A",0
134,1,145,0,0.172430," ","integrate((c*x^4+a)^2/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{2} x^{3} e^{6} - 9 \, c^{2} d x e^{5}\right)} e^{\left(-9\right)} + \frac{{\left(35 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{8 \, d^{\frac{5}{2}}} - \frac{{\left(13 \, c^{2} d^{4} x^{3} e + 11 \, c^{2} d^{5} x + 10 \, a c d^{2} x^{3} e^{3} + 6 \, a c d^{3} x e^{2} - 3 \, a^{2} x^{3} e^{5} - 5 \, a^{2} d x e^{4}\right)} e^{\left(-4\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{2}}"," ",0,"1/3*(c^2*x^3*e^6 - 9*c^2*d*x*e^5)*e^(-9) + 1/8*(35*c^2*d^4 + 6*a*c*d^2*e^2 + 3*a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(5/2) - 1/8*(13*c^2*d^4*x^3*e + 11*c^2*d^5*x + 10*a*c*d^2*x^3*e^3 + 6*a*c*d^3*x*e^2 - 3*a^2*x^3*e^5 - 5*a^2*d*x*e^4)*e^(-4)/((x^2*e + d)^2*d^2)","A",0
135,1,167,0,0.163620," ","integrate((c*x^4+a)^2/(e*x^2+d)^4,x, algorithm=""giac"")","c^{2} x e^{\left(-4\right)} - \frac{{\left(35 \, c^{2} d^{4} - 2 \, a c d^{2} e^{2} - 5 \, a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{16 \, d^{\frac{7}{2}}} + \frac{{\left(87 \, c^{2} d^{4} x^{5} e^{2} + 136 \, c^{2} d^{5} x^{3} e + 6 \, a c d^{2} x^{5} e^{4} + 57 \, c^{2} d^{6} x - 16 \, a c d^{3} x^{3} e^{3} + 15 \, a^{2} x^{5} e^{6} - 6 \, a c d^{4} x e^{2} + 40 \, a^{2} d x^{3} e^{5} + 33 \, a^{2} d^{2} x e^{4}\right)} e^{\left(-4\right)}}{48 \, {\left(x^{2} e + d\right)}^{3} d^{3}}"," ",0,"c^2*x*e^(-4) - 1/16*(35*c^2*d^4 - 2*a*c*d^2*e^2 - 5*a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(7/2) + 1/48*(87*c^2*d^4*x^5*e^2 + 136*c^2*d^5*x^3*e + 6*a*c*d^2*x^5*e^4 + 57*c^2*d^6*x - 16*a*c*d^3*x^3*e^3 + 15*a^2*x^5*e^6 - 6*a*c*d^4*x*e^2 + 40*a^2*d*x^3*e^5 + 33*a^2*d^2*x*e^4)*e^(-4)/((x^2*e + d)^3*d^3)","A",0
136,1,198,0,0.251892," ","integrate((c*x^4+a)^2/(e*x^2+d)^5,x, algorithm=""giac"")","\frac{{\left(35 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} + 35 \, a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{128 \, d^{\frac{9}{2}}} - \frac{{\left(279 \, c^{2} d^{4} x^{7} e^{3} + 511 \, c^{2} d^{5} x^{5} e^{2} - 18 \, a c d^{2} x^{7} e^{5} + 385 \, c^{2} d^{6} x^{3} e - 66 \, a c d^{3} x^{5} e^{4} + 105 \, c^{2} d^{7} x - 105 \, a^{2} x^{7} e^{7} + 66 \, a c d^{4} x^{3} e^{3} - 385 \, a^{2} d x^{5} e^{6} + 18 \, a c d^{5} x e^{2} - 511 \, a^{2} d^{2} x^{3} e^{5} - 279 \, a^{2} d^{3} x e^{4}\right)} e^{\left(-4\right)}}{384 \, {\left(x^{2} e + d\right)}^{4} d^{4}}"," ",0,"1/128*(35*c^2*d^4 + 6*a*c*d^2*e^2 + 35*a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(9/2) - 1/384*(279*c^2*d^4*x^7*e^3 + 511*c^2*d^5*x^5*e^2 - 18*a*c*d^2*x^7*e^5 + 385*c^2*d^6*x^3*e - 66*a*c*d^3*x^5*e^4 + 105*c^2*d^7*x - 105*a^2*x^7*e^7 + 66*a*c*d^4*x^3*e^3 - 385*a^2*d*x^5*e^6 + 18*a*c*d^5*x*e^2 - 511*a^2*d^2*x^3*e^5 - 279*a^2*d^3*x*e^4)*e^(-4)/((x^2*e + d)^4*d^4)","A",0
137,1,498,0,0.185465," ","integrate((e*x^2+d)^4/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} + 4 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} - 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} + 4 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} - 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} - 4 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} + 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{4}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} - 6 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} - 4 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} + 4 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{4}} + \frac{3 \, c^{4} x^{5} e^{4} + 20 \, c^{4} d x^{3} e^{3} + 90 \, c^{4} d^{2} x e^{2} - 15 \, a c^{3} x e^{4}}{15 \, c^{5}}"," ",0,"1/4*sqrt(2)*((a*c^3)^(1/4)*c^3*d^4 - 6*(a*c^3)^(1/4)*a*c^2*d^2*e^2 + 4*(a*c^3)^(3/4)*c*d^3*e + (a*c^3)^(1/4)*a^2*c*e^4 - 4*(a*c^3)^(3/4)*a*d*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^4) + 1/4*sqrt(2)*((a*c^3)^(1/4)*c^3*d^4 - 6*(a*c^3)^(1/4)*a*c^2*d^2*e^2 + 4*(a*c^3)^(3/4)*c*d^3*e + (a*c^3)^(1/4)*a^2*c*e^4 - 4*(a*c^3)^(3/4)*a*d*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^4) + 1/8*sqrt(2)*((a*c^3)^(1/4)*c^3*d^4 - 6*(a*c^3)^(1/4)*a*c^2*d^2*e^2 - 4*(a*c^3)^(3/4)*c*d^3*e + (a*c^3)^(1/4)*a^2*c*e^4 + 4*(a*c^3)^(3/4)*a*d*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4) - 1/8*sqrt(2)*((a*c^3)^(1/4)*c^3*d^4 - 6*(a*c^3)^(1/4)*a*c^2*d^2*e^2 - 4*(a*c^3)^(3/4)*c*d^3*e + (a*c^3)^(1/4)*a^2*c*e^4 + 4*(a*c^3)^(3/4)*a*d*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4) + 1/15*(3*c^4*x^5*e^4 + 20*c^4*d*x^3*e^3 + 90*c^4*d^2*x*e^2 - 15*a*c^3*x*e^4)/c^5","A",0
138,1,405,0,0.205173," ","integrate((e*x^2+d)^3/(c*x^4+a),x, algorithm=""giac"")","\frac{c^{2} x^{3} e^{3} + 9 \, c^{2} d x e^{2}}{3 \, c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{4}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{4}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{4}}"," ",0,"1/3*(c^2*x^3*e^3 + 9*c^2*d*x*e^2)/c^3 + 1/4*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 + 3*(a*c^3)^(3/4)*c*d^2*e - (a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^4) + 1/4*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 + 3*(a*c^3)^(3/4)*c*d^2*e - (a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^4) + 1/8*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 - 3*(a*c^3)^(3/4)*c*d^2*e + (a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4) - 1/8*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 - 3*(a*c^3)^(3/4)*c*d^2*e + (a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^4)","A",0
139,1,318,0,0.179340," ","integrate((e*x^2+d)^2/(c*x^4+a),x, algorithm=""giac"")","\frac{x e^{2}}{c} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} + 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} + 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}}"," ",0,"x*e^2/c + 1/4*sqrt(2)*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(1/4)*a*c*e^2 + 2*(a*c^3)^(3/4)*d*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/4*sqrt(2)*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(1/4)*a*c*e^2 + 2*(a*c^3)^(3/4)*d*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(1/4)*a*c*e^2 - 2*(a*c^3)^(3/4)*d*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) - 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(1/4)*a*c*e^2 - 2*(a*c^3)^(3/4)*d*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3)","A",0
140,1,245,0,0.175632," ","integrate((e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c^{3}} + \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}} - \frac{\sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c^{3}}"," ",0,"1/4*sqrt(2)*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/4*sqrt(2)*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c^3) + 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3) - 1/8*sqrt(2)*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3)","A",0
141,1,179,0,0.181353," ","integrate(1/(c*x^4+a),x, algorithm=""giac"")","\frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{4 \, a c} + \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c} - \frac{\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, a c}"," ",0,"1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c) + 1/4*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a*c) + 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c) - 1/8*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c)","A",0
142,1,339,0,0.206570," ","integrate(1/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{3}{2}}}{{\left(c d^{2} + a e^{2}\right)} \sqrt{d}}"," ",0,"1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + 1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) - 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + arctan(x*e^(1/2)/sqrt(d))*e^(3/2)/((c*d^2 + a*e^2)*sqrt(d))","A",0
143,1,517,0,0.252856," ","integrate(1/(e*x^2+d)^2/(c*x^4+a),x, algorithm=""giac"")","\frac{{\left(5 \, c d^{2} e^{2} + a e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4}\right)} \sqrt{d}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{4} + 2 \, \sqrt{2} a^{2} c^{2} d^{2} e^{2} + \sqrt{2} a^{3} c e^{4}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{4} + 2 \, \sqrt{2} a^{2} c^{2} d^{2} e^{2} + \sqrt{2} a^{3} c e^{4}\right)}} + \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} + 2 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}} - \frac{{\left(\sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} - \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} + 2 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{8 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}} + \frac{x e^{2}}{2 \, {\left(c d^{3} + a d e^{2}\right)} {\left(x^{2} e + d\right)}}"," ",0,"1/2*(5*c*d^2*e^2 + a*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/((c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4)*sqrt(d)) + 1/2*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(1/4)*a*c*e^2 - 2*(a*c^3)^(3/4)*d*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^4 + 2*sqrt(2)*a^2*c^2*d^2*e^2 + sqrt(2)*a^3*c*e^4) + 1/2*((a*c^3)^(1/4)*c^2*d^2 - (a*c^3)^(1/4)*a*c*e^2 - 2*(a*c^3)^(3/4)*d*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^4 + 2*sqrt(2)*a^2*c^2*d^2*e^2 + sqrt(2)*a^3*c*e^4) + 1/8*(sqrt(2)*(a*c^3)^(1/4)*c^2*d^2 - sqrt(2)*(a*c^3)^(1/4)*a*c*e^2 + 2*sqrt(2)*(a*c^3)^(3/4)*d*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4) - 1/8*(sqrt(2)*(a*c^3)^(1/4)*c^2*d^2 - sqrt(2)*(a*c^3)^(1/4)*a*c*e^2 + 2*sqrt(2)*(a*c^3)^(3/4)*d*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4) + 1/2*x*e^2/((c*d^3 + a*d*e^2)*(x^2*e + d))","A",0
144,1,425,0,0.187953," ","integrate((e*x^2+d)^3/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{3 \, c d^{2} x^{3} e + c d^{3} x - a x^{3} e^{3} - 3 \, a d x e^{2}}{4 \, {\left(c x^{4} + a\right)} a c} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{4}} - \frac{3 \, \sqrt{2} {\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{4}}"," ",0,"1/4*(3*c*d^2*x^3*e + c*d^3*x - a*x^3*e^3 - 3*a*d*x*e^2)/((c*x^4 + a)*a*c) + 3/16*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 + (a*c^3)^(3/4)*c*d^2*e + (a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^4) + 3/16*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 + (a*c^3)^(3/4)*c*d^2*e + (a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^4) + 3/32*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 - (a*c^3)^(3/4)*c*d^2*e - (a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4) - 3/32*sqrt(2)*((a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 - (a*c^3)^(3/4)*c*d^2*e - (a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4)","A",0
145,1,350,0,0.190305," ","integrate((e*x^2+d)^2/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{2 \, c d x^{3} e + c d^{2} x - a x e^{2}}{4 \, {\left(c x^{4} + a\right)} a c} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} + 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} + 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d^{2} + \left(a c^{3}\right)^{\frac{1}{4}} a c e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} d e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}}"," ",0,"1/4*(2*c*d*x^3*e + c*d^2*x - a*x*e^2)/((c*x^4 + a)*a*c) + 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(1/4)*a*c*e^2 + 2*(a*c^3)^(3/4)*d*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(1/4)*a*c*e^2 + 2*(a*c^3)^(3/4)*d*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/32*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(1/4)*a*c*e^2 - 2*(a*c^3)^(3/4)*d*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3) - 1/32*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d^2 + (a*c^3)^(1/4)*a*c*e^2 - 2*(a*c^3)^(3/4)*d*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3)","A",0
146,1,273,0,0.440160," ","integrate((e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x^{3} e + d x}{4 \, {\left(c x^{4} + a\right)} a} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c^{3}} + \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}} - \frac{\sqrt{2} {\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c^{3}}"," ",0,"1/4*(x^3*e + d*x)/((c*x^4 + a)*a) + 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/16*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c^3) + 1/32*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3) - 1/32*sqrt(2)*(3*(a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^3)","A",0
147,1,194,0,0.181629," ","integrate(1/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{x}{4 \, {\left(c x^{4} + a\right)} a} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{16 \, a^{2} c} + \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c} - \frac{3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, a^{2} c}"," ",0,"1/4*x/((c*x^4 + a)*a) + 3/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c) + 3/16*sqrt(2)*(a*c^3)^(1/4)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(a^2*c) + 3/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c) - 3/32*sqrt(2)*(a*c^3)^(1/4)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c)","A",0
148,1,603,0,0.209183," ","integrate(1/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} - \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{7}{2}}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{d}} - \frac{c x^{3} e - c d x}{4 \, {\left(c x^{4} + a\right)} {\left(a c d^{2} + a^{2} e^{2}\right)}}"," ",0,"1/8*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 - (a*c^3)^(3/4)*c*d^2*e - 5*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + 1/8*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 - (a*c^3)^(3/4)*c*d^2*e - 5*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + 1/16*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 + (a*c^3)^(3/4)*c*d^2*e + 5*(a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) - 1/16*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 + (a*c^3)^(3/4)*c*d^2*e + 5*(a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(7/2)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(d)) - 1/4*(c*x^3*e - c*d*x)/((c*x^4 + a)*(a*c*d^2 + a^2*e^2))","A",0
149,1,855,0,0.246806," ","integrate(1/(e*x^2+d)^2/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(9 \, c d^{2} e^{4} + a e^{6}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, {\left(c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6}\right)} \sqrt{d}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} + 12 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e - 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} - 18 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{6} + 3 \, \sqrt{2} a^{3} c^{3} d^{4} e^{2} + 3 \, \sqrt{2} a^{4} c^{2} d^{2} e^{4} + \sqrt{2} a^{5} c e^{6}\right)}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} + 12 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} - 2 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e - 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} - 18 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{6} + 3 \, \sqrt{2} a^{3} c^{3} d^{4} e^{2} + 3 \, \sqrt{2} a^{4} c^{2} d^{2} e^{4} + \sqrt{2} a^{5} c e^{6}\right)}} + \frac{{\left(3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} + 12 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} + 2 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e - 7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} + 18 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{4} d^{6} + 3 \, a^{3} c^{3} d^{4} e^{2} + 3 \, a^{4} c^{2} d^{2} e^{4} + a^{5} c e^{6}\right)}} - \frac{{\left(3 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{4} + 12 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e^{2} + 2 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} e - 7 \, \sqrt{2} \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{4} + 18 \, \sqrt{2} \left(a c^{3}\right)^{\frac{3}{4}} a d e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{32 \, {\left(a^{2} c^{4} d^{6} + 3 \, a^{3} c^{3} d^{4} e^{2} + 3 \, a^{4} c^{2} d^{2} e^{4} + a^{5} c e^{6}\right)}} - \frac{2 \, c^{2} d^{2} x^{5} e^{2} + c^{2} d^{3} x^{3} e - 2 \, a c x^{5} e^{4} - c^{2} d^{4} x + a c d x^{3} e^{3} + a c d^{2} x e^{2} - 2 \, a^{2} x e^{4}}{4 \, {\left(a c^{2} d^{5} + 2 \, a^{2} c d^{3} e^{2} + a^{3} d e^{4}\right)} {\left(c x^{6} e + c d x^{4} + a x^{2} e + a d\right)}}"," ",0,"1/2*(9*c*d^2*e^4 + a*e^6)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/((c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6)*sqrt(d)) + 1/8*(3*(a*c^3)^(1/4)*c^3*d^4 + 12*(a*c^3)^(1/4)*a*c^2*d^2*e^2 - 2*(a*c^3)^(3/4)*c*d^3*e - 7*(a*c^3)^(1/4)*a^2*c*e^4 - 18*(a*c^3)^(3/4)*a*d*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^6 + 3*sqrt(2)*a^3*c^3*d^4*e^2 + 3*sqrt(2)*a^4*c^2*d^2*e^4 + sqrt(2)*a^5*c*e^6) + 1/8*(3*(a*c^3)^(1/4)*c^3*d^4 + 12*(a*c^3)^(1/4)*a*c^2*d^2*e^2 - 2*(a*c^3)^(3/4)*c*d^3*e - 7*(a*c^3)^(1/4)*a^2*c*e^4 - 18*(a*c^3)^(3/4)*a*d*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^6 + 3*sqrt(2)*a^3*c^3*d^4*e^2 + 3*sqrt(2)*a^4*c^2*d^2*e^4 + sqrt(2)*a^5*c*e^6) + 1/32*(3*sqrt(2)*(a*c^3)^(1/4)*c^3*d^4 + 12*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^2*e^2 + 2*sqrt(2)*(a*c^3)^(3/4)*c*d^3*e - 7*sqrt(2)*(a*c^3)^(1/4)*a^2*c*e^4 + 18*sqrt(2)*(a*c^3)^(3/4)*a*d*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4*d^6 + 3*a^3*c^3*d^4*e^2 + 3*a^4*c^2*d^2*e^4 + a^5*c*e^6) - 1/32*(3*sqrt(2)*(a*c^3)^(1/4)*c^3*d^4 + 12*sqrt(2)*(a*c^3)^(1/4)*a*c^2*d^2*e^2 + 2*sqrt(2)*(a*c^3)^(3/4)*c*d^3*e - 7*sqrt(2)*(a*c^3)^(1/4)*a^2*c*e^4 + 18*sqrt(2)*(a*c^3)^(3/4)*a*d*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(a^2*c^4*d^6 + 3*a^3*c^3*d^4*e^2 + 3*a^4*c^2*d^2*e^4 + a^5*c*e^6) - 1/4*(2*c^2*d^2*x^5*e^2 + c^2*d^3*x^3*e - 2*a*c*x^5*e^4 - c^2*d^4*x + a*c*d*x^3*e^3 + a*c*d^2*x*e^2 - 2*a^2*x*e^4)/((a*c^2*d^5 + 2*a^2*c*d^3*e^2 + a^3*d*e^4)*(c*x^6*e + c*d*x^4 + a*x^2*e + a*d))","A",0
150,0,0,0,0.000000," ","integrate((e*x^2+d)^4/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{4}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^4/sqrt(c*x^4 + a), x)","F",0
151,0,0,0,0.000000," ","integrate((e*x^2+d)^3/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{3}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^3/sqrt(c*x^4 + a), x)","F",0
152,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(c*x^4 + a), x)","F",0
153,0,0,0,0.000000," ","integrate((e*x^2+d)/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(c*x^4 + a), x)","F",0
154,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*(e*x^2 + d)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} {\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*(e*x^2 + d)^2), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^3/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} {\left(e x^{2} + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*(e*x^2 + d)^3), x)","F",0
157,0,0,0,0.000000," ","integrate((e*x^2+d)^3/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{3}}{\sqrt{-c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^3/sqrt(-c*x^4 + a), x)","F",0
158,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{-c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(-c*x^4 + a), x)","F",0
159,0,0,0,0.000000," ","integrate((e*x^2+d)/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{-c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(-c*x^4 + a), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + a)*(e*x^2 + d)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + a} {\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + a)*(e*x^2 + d)^2), x)","F",0
162,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^3/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + a} {\left(e x^{2} + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + a)*(e*x^2 + d)^3), x)","F",0
163,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^4/(-c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + a} {\left(e x^{2} + d\right)}^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + a)*(e*x^2 + d)^4), x)","F",0
164,0,0,0,0.000000," ","integrate((e*x^2+d)/(c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{c x^{4} - a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(c*x^4 - a), x)","F",0
165,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} - a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 - a)*(e*x^2 + d)), x)","F",0
166,0,0,0,0.000000," ","integrate((a^(1/2)+x^2*c^(1/2))/(c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c} x^{2} + \sqrt{a}}{\sqrt{c x^{4} - a}}\,{d x}"," ",0,"integrate((sqrt(c)*x^2 + sqrt(a))/sqrt(c*x^4 - a), x)","F",0
167,0,0,0,0.000000," ","integrate((1+x^2*(c/a)^(1/2))/(c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} \sqrt{\frac{c}{a}} + 1}{\sqrt{c x^{4} - a}}\,{d x}"," ",0,"integrate((x^2*sqrt(c/a) + 1)/sqrt(c*x^4 - a), x)","F",0
168,0,0,0,0.000000," ","integrate((e*x^2+d)/(-c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{-c x^{4} - a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(-c*x^4 - a), x)","F",0
169,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} - a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 - a)*(e*x^2 + d)), x)","F",0
170,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(-5*x^4+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-5 \, x^{4} + 4} {\left(b x^{2} + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-5*x^4 + 4)*(b*x^2 + a)), x)","F",0
171,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(5*x^4+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{5 \, x^{4} + 4} {\left(b x^{2} + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(5*x^4 + 4)*(b*x^2 + a)), x)","F",0
172,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(-d*x^4+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d x^{4} + 4} {\left(b x^{2} + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-d*x^4 + 4)*(b*x^2 + a)), x)","F",0
173,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^4+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{d x^{4} + 4} {\left(b x^{2} + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(d*x^4 + 4)*(b*x^2 + a)), x)","F",0
174,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(-x^4 + 1), x)","F",0
175,0,0,0,0.000000," ","integrate((e*x^2+c)^q*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{p} {\left(e x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + a)^p*(e*x^2 + c)^q, x)","F",0
176,0,0,0,0.000000," ","integrate((e*x^2+c)^3*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + c\right)}^{3} {\left(b x^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + c)^3*(b*x^4 + a)^p, x)","F",0
177,0,0,0,0.000000," ","integrate((e*x^2+c)^2*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + c\right)}^{2} {\left(b x^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + c)^2*(b*x^4 + a)^p, x)","F",0
178,0,0,0,0.000000," ","integrate((e*x^2+c)*(b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + c\right)} {\left(b x^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + c)*(b*x^4 + a)^p, x)","F",0
179,0,0,0,0.000000," ","integrate((b*x^4+a)^p,x, algorithm=""giac"")","\int {\left(b x^{4} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^4 + a)^p, x)","F",0
180,0,0,0,0.000000," ","integrate((b*x^4+a)^p/(e*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{p}}{e x^{2} + c}\,{d x}"," ",0,"integrate((b*x^4 + a)^p/(e*x^2 + c), x)","F",0
181,0,0,0,0.000000," ","integrate((b*x^4+a)^p/(e*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + a\right)}^{p}}{{\left(e x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + a)^p/(e*x^2 + c)^2, x)","F",0
182,0,0,0,0.000000," ","integrate((-x^2+1)^3*(b*x^4+1)^p,x, algorithm=""giac"")","\int -{\left(x^{2} - 1\right)}^{3} {\left(b x^{4} + 1\right)}^{p}\,{d x}"," ",0,"integrate(-(x^2 - 1)^3*(b*x^4 + 1)^p, x)","F",0
183,0,0,0,0.000000," ","integrate((-x^2+1)^2*(b*x^4+1)^p,x, algorithm=""giac"")","\int {\left(x^{2} - 1\right)}^{2} {\left(b x^{4} + 1\right)}^{p}\,{d x}"," ",0,"integrate((x^2 - 1)^2*(b*x^4 + 1)^p, x)","F",0
184,0,0,0,0.000000," ","integrate((-x^2+1)*(b*x^4+1)^p,x, algorithm=""giac"")","\int -{\left(x^{2} - 1\right)} {\left(b x^{4} + 1\right)}^{p}\,{d x}"," ",0,"integrate(-(x^2 - 1)*(b*x^4 + 1)^p, x)","F",0
185,0,0,0,0.000000," ","integrate((b*x^4+1)^p,x, algorithm=""giac"")","\int {\left(b x^{4} + 1\right)}^{p}\,{d x}"," ",0,"integrate((b*x^4 + 1)^p, x)","F",0
186,0,0,0,0.000000," ","integrate((b*x^4+1)^p/(-x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(b x^{4} + 1\right)}^{p}}{x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*x^4 + 1)^p/(x^2 - 1), x)","F",0
187,0,0,0,0.000000," ","integrate((b*x^4+1)^p/(-x^2+1)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + 1\right)}^{p}}{{\left(x^{2} - 1\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + 1)^p/(x^2 - 1)^2, x)","F",0
188,0,0,0,0.000000," ","integrate((b*x^4+1)^p/(-x^2+1)^3,x, algorithm=""giac"")","\int -\frac{{\left(b x^{4} + 1\right)}^{p}}{{\left(x^{2} - 1\right)}^{3}}\,{d x}"," ",0,"integrate(-(b*x^4 + 1)^p/(x^2 - 1)^3, x)","F",0
189,1,144,0,0.212567," ","integrate((e*x^2+d)^4/(-e^2*x^4+d^2),x, algorithm=""giac"")","4 \, {\left({\left(d^{2}\right)}^{\frac{1}{4}} d^{2} e^{\frac{11}{2}} - {\left(d^{2}\right)}^{\frac{1}{4}} d {\left| d \right|} e^{\frac{11}{2}}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{{\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-6\right)} + 2 \, {\left({\left(d^{2}\right)}^{\frac{1}{4}} d^{2} e^{\frac{15}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} d e^{\frac{15}{2}}\right)} e^{\left(-8\right)} \log\left({\left| {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right) - 2 \, {\left({\left(d^{2}\right)}^{\frac{1}{4}} d^{2} e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{1}{4}} d {\left| d \right|} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left({\left| -{\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right) - \frac{1}{15} \, {\left(3 \, x^{5} e^{12} + 20 \, d x^{3} e^{11} + 105 \, d^{2} x e^{10}\right)} e^{\left(-10\right)}"," ",0,"4*((d^2)^(1/4)*d^2*e^(11/2) - (d^2)^(1/4)*d*abs(d)*e^(11/2))*arctan(x*e^(1/2)/(d^2)^(1/4))*e^(-6) + 2*((d^2)^(1/4)*d^2*e^(15/2) + (d^2)^(3/4)*d*e^(15/2))*e^(-8)*log(abs((d^2)^(1/4)*e^(-1/2) + x)) - 2*((d^2)^(1/4)*d^2*e^(11/2) + (d^2)^(1/4)*d*abs(d)*e^(11/2))*e^(-6)*log(abs(-(d^2)^(1/4)*e^(-1/2) + x)) - 1/15*(3*x^5*e^12 + 20*d*x^3*e^11 + 105*d^2*x*e^10)*e^(-10)","B",0
190,1,123,0,0.231881," ","integrate((e*x^2+d)^3/(-e^2*x^4+d^2),x, algorithm=""giac"")","2 \, {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} - {\left(d^{2}\right)}^{\frac{1}{4}} {\left| d \right|} e^{\frac{11}{2}}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{{\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-6\right)} + {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{15}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{15}{2}}\right)} e^{\left(-8\right)} \log\left({\left| {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right) - {\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{1}{4}} {\left| d \right|} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left({\left| -{\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right) - \frac{1}{3} \, {\left(x^{3} e^{7} + 9 \, d x e^{6}\right)} e^{\left(-6\right)}"," ",0,"2*((d^2)^(1/4)*d*e^(11/2) - (d^2)^(1/4)*abs(d)*e^(11/2))*arctan(x*e^(1/2)/(d^2)^(1/4))*e^(-6) + ((d^2)^(1/4)*d*e^(15/2) + (d^2)^(3/4)*e^(15/2))*e^(-8)*log(abs((d^2)^(1/4)*e^(-1/2) + x)) - ((d^2)^(1/4)*d*e^(11/2) + (d^2)^(1/4)*abs(d)*e^(11/2))*e^(-6)*log(abs(-(d^2)^(1/4)*e^(-1/2) + x)) - 1/3*(x^3*e^7 + 9*d*x*e^6)*e^(-6)","B",0
191,1,118,0,0.205724," ","integrate((e*x^2+d)^2/(-e^2*x^4+d^2),x, algorithm=""giac"")","\frac{{\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{7}{2}} - {\left(d^{2}\right)}^{\frac{1}{4}} {\left| d \right|} e^{\frac{7}{2}}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{{\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-4\right)}}{d} + \frac{{\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left({\left| {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right)}{2 \, d} - \frac{{\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{7}{2}} + {\left(d^{2}\right)}^{\frac{1}{4}} {\left| d \right|} e^{\frac{7}{2}}\right)} e^{\left(-4\right)} \log\left({\left| -{\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right)}{2 \, d} - x"," ",0,"((d^2)^(1/4)*d*e^(7/2) - (d^2)^(1/4)*abs(d)*e^(7/2))*arctan(x*e^(1/2)/(d^2)^(1/4))*e^(-4)/d + 1/2*((d^2)^(1/4)*d*e^(11/2) + (d^2)^(3/4)*e^(11/2))*e^(-6)*log(abs((d^2)^(1/4)*e^(-1/2) + x))/d - 1/2*((d^2)^(1/4)*d*e^(7/2) + (d^2)^(1/4)*abs(d)*e^(7/2))*e^(-4)*log(abs(-(d^2)^(1/4)*e^(-1/2) + x))/d - x","B",0
192,1,116,0,0.290053," ","integrate((e*x^2+d)/(-e^2*x^4+d^2),x, algorithm=""giac"")","\frac{{\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{7}{2}} - {\left(d^{2}\right)}^{\frac{1}{4}} {\left| d \right|} e^{\frac{7}{2}}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{{\left(d^{2}\right)}^{\frac{1}{4}}}\right) e^{\left(-4\right)}}{2 \, d^{2}} + \frac{{\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{11}{2}} + {\left(d^{2}\right)}^{\frac{3}{4}} e^{\frac{11}{2}}\right)} e^{\left(-6\right)} \log\left({\left| {\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right)}{4 \, d^{2}} - \frac{{\left({\left(d^{2}\right)}^{\frac{1}{4}} d e^{\frac{7}{2}} + {\left(d^{2}\right)}^{\frac{1}{4}} {\left| d \right|} e^{\frac{7}{2}}\right)} e^{\left(-4\right)} \log\left({\left| -{\left(d^{2}\right)}^{\frac{1}{4}} e^{\left(-\frac{1}{2}\right)} + x \right|}\right)}{4 \, d^{2}}"," ",0,"1/2*((d^2)^(1/4)*d*e^(7/2) - (d^2)^(1/4)*abs(d)*e^(7/2))*arctan(x*e^(1/2)/(d^2)^(1/4))*e^(-4)/d^2 + 1/4*((d^2)^(1/4)*d*e^(11/2) + (d^2)^(3/4)*e^(11/2))*e^(-6)*log(abs((d^2)^(1/4)*e^(-1/2) + x))/d^2 - 1/4*((d^2)^(1/4)*d*e^(7/2) + (d^2)^(1/4)*abs(d)*e^(7/2))*e^(-4)*log(abs(-(d^2)^(1/4)*e^(-1/2) + x))/d^2","B",0
193,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-e^2*x^4+d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -((d^2*exp(2)^3)^(1/4)*abs(d)*exp(1)^2-d*exp(2)*(d^2*exp(2)^3)^(1/4))/(4*d^4*exp(2)*exp(1)^2-4*d^4*exp(2)^2)*ln(abs(x-(d^2/exp(2))^(1/4)))+((d^2*exp(2)^3)^(1/4))^3/(4*d^4*exp(2)^2*exp(1)-4*d^4*exp(1)*exp(2)^2)*ln(abs(x+(d^2/exp(2))^(1/4)))-((d^2*exp(2)^3)^(1/4)*abs(d)*exp(1)^2+d*exp(2)*(d^2*exp(2)^3)^(1/4))/(2*d^4*exp(2)*exp(1)^2-2*d^4*exp(2)^2)*atan(x/(d^2/exp(2))^(1/4))-2*exp(1)^2*1/2/(exp(2)*d^2-d^2*exp(1)^2)/sqrt(d*exp(1))*atan(x*exp(1)/sqrt(d*exp(1)))","F(-2)",0
194,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(-e^2*x^4+d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -(-2*(d^2*exp(2)^3)^(1/4)*abs(d)*exp(1)^2+d*(d^2*exp(2)^3)^(1/4)*exp(1)^2+d*exp(2)*(d^2*exp(2)^3)^(1/4))/(4*d^5*exp(1)^4-8*d^5*exp(2)*exp(1)^2+4*d^5*exp(2)^2)*ln(abs(x-(d^2/exp(2))^(1/4)))+exp(2)*(d^2*exp(2)^3)^(1/4)/(4*d^4*exp(2)*exp(1)^2-8*d^4*exp(1)*exp(2)*exp(1)+4*d^4*exp(2)^2)*ln(abs(x+(d^2/exp(2))^(1/4)))-(-2*(d^2*exp(2)^3)^(1/4)*abs(d)*exp(1)^2-d*(d^2*exp(2)^3)^(1/4)*exp(1)^2-d*exp(2)*(d^2*exp(2)^3)^(1/4))/(2*d^5*exp(1)^4-4*d^5*exp(2)*exp(1)^2+2*d^5*exp(2)^2)*atan(x/(d^2/exp(2))^(1/4))-(-5*exp(2)*exp(1)^2+exp(1)^4)*1/2/(-exp(2)^2*d^3+2*exp(2)*d^3*exp(1)^2-d^3*exp(1)^4)/sqrt(d*exp(1))*atan(x*exp(1)/sqrt(d*exp(1)))+x*exp(1)^2/(-2*exp(2)*d^3+2*d^3*exp(1)^2)/(x^2*exp(1)+d)","F(-2)",0
195,1,24,0,0.245615," ","integrate((e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x, algorithm=""giac"")","\frac{1}{2} \, e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)"," ",0,"1/2*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)","A",0
196,1,131,0,0.528171," ","integrate((e*x^2+d)^(1/2)/(-e^2*x^4+d^2),x, algorithm=""giac"")","-\frac{{\left(\sqrt{2} i \arctan\left(\frac{e^{\frac{1}{2}}}{\sqrt{-\frac{d e + \sqrt{d^{2}} e}{d}}}\right) e^{\frac{1}{2}} - \sqrt{2} i \arctan\left(\frac{e^{\frac{1}{2}}}{\sqrt{-\frac{d e - \sqrt{d^{2}} e}{d}}}\right) e^{\frac{1}{2}}\right)} e^{\left(-1\right)} \mathrm{sgn}\left(x\right)}{4 \, {\left| d \right|}} + \frac{\sqrt{2} i \arctan\left(\frac{\sqrt{\frac{d}{x^{2}} + e}}{\sqrt{-\frac{d e \mathrm{sgn}\left(x\right) + \sqrt{d^{2}} e}{d \mathrm{sgn}\left(x\right)}}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, {\left| d \right|} {\left| \mathrm{sgn}\left(x\right) \right|}}"," ",0,"-1/4*(sqrt(2)*i*arctan(e^(1/2)/sqrt(-(d*e + sqrt(d^2)*e)/d))*e^(1/2) - sqrt(2)*i*arctan(e^(1/2)/sqrt(-(d*e - sqrt(d^2)*e)/d))*e^(1/2))*e^(-1)*sgn(x)/abs(d) + 1/2*sqrt(2)*i*arctan(sqrt(d/x^2 + e)/sqrt(-(d*e*sgn(x) + sqrt(d^2)*e)/(d*sgn(x))))*e^(-1/2)/(abs(d)*abs(sgn(x)))","B",0
197,1,1,0,0.328428," ","integrate(1/(e*x^2+d)^(1/2)/(-e^2*x^4+d^2),x, algorithm=""giac"")","+\infty"," ",0,"+Infinity","A",0
198,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
199,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{\sqrt{-b^{2} x^{4} + a^{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/sqrt(-b^2*x^4 + a^2), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{-b^{2} x^{4} + a^{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/sqrt(-b^2*x^4 + a^2), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{-b^{2} x^{4} + a^{2}}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(-b^2*x^4 + a^2), x)","F",0
202,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b^{2} x^{4} + a^{2}} {\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^4 + a^2)*(b*x^2 + a)^(3/2)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b^{2} x^{4} + a^{2}} {\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^4 + a^2)*(b*x^2 + a)^(5/2)), x)","F",0
205,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{2}}}{\sqrt{-b^{2} x^{4} + a^{2}}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/2)/sqrt(-b^2*x^4 + a^2), x)","F",0
206,0,0,0,0.000000," ","integrate((-b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{-b^{2} x^{4} + a^{2}}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(3/2)/sqrt(-b^2*x^4 + a^2), x)","F",0
207,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{-b^{2} x^{4} + a^{2}}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(-b^2*x^4 + a^2), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)), x)","F",0
209,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b^{2} x^{4} + a^{2}} {\left(-b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^4 + a^2)*(-b*x^2 + a)^(3/2)), x)","F",0
210,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b^{2} x^{4} + a^{2}} {\left(-b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-b^2*x^4 + a^2)*(-b*x^2 + a)^(5/2)), x)","F",0
211,0,0,0,0.000000," ","integrate((x^2-1)^(1/2)/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} - 1}}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 - 1)/sqrt(x^4 - 1), x)","F",0
212,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(x^4 - 1), x)","F",0
213,0,0,0,0.000000," ","integrate((-(x^2-1)^(1/2)+(x^2+1)^(1/2))/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1} - \sqrt{x^{2} - 1}}{\sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate((sqrt(x^2 + 1) - sqrt(x^2 - 1))/sqrt(x^4 - 1), x)","F",0
214,1,10312,0,5.854199," ","integrate((e*x^2+d)^4/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","-\frac{{\left(128 \, b c^{10} d^{6} e^{10} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{6} e^{6} - 384 \, b^{2} c^{9} d^{5} e^{11} + 192 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{5} e^{7} + 480 \, b^{3} c^{8} d^{4} e^{12} - 240 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{4} e^{8} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{4} e^{8} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{4} e^{8} - 320 \, b^{4} c^{7} d^{3} e^{13} - 32 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{8} d^{4} e^{8} + 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{3} e^{9} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{3} e^{9} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{3} e^{9} + 120 \, b^{5} c^{6} d^{2} e^{14} + 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{7} d^{3} e^{9} - 60 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d^{2} e^{10} + 48 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{2} e^{10} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{2} e^{10} - 24 \, b^{6} c^{5} d e^{15} - 48 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{6} d^{2} e^{10} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} d e^{11} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d e^{11} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d e^{11} + 2 \, b^{7} c^{4} e^{16} + 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{5} d e^{11} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{7} c^{2} e^{12} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} e^{12} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} e^{12} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{5} c^{4} e^{12} + {\left(256 \, c^{9} d^{7} e^{9} - 128 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{7} e^{5} - 896 \, b c^{8} d^{6} e^{10} + 448 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{6} e^{6} + 1344 \, b^{2} c^{7} d^{5} e^{11} - 672 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{5} e^{7} + 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{5} e^{7} - 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{5} e^{7} - 1120 \, b^{3} c^{6} d^{4} e^{12} - 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{7} d^{5} e^{7} + 560 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{4} e^{8} - 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{4} e^{8} + 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{4} e^{8} + 560 \, b^{4} c^{5} d^{3} e^{13} + 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{6} d^{4} e^{8} - 280 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d^{3} e^{9} + 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{3} e^{9} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{3} e^{9} - 168 \, b^{5} c^{4} d^{2} e^{14} - 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{5} d^{3} e^{9} + 84 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} d^{2} e^{10} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d^{2} e^{10} + 40 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{2} e^{10} + 28 \, b^{6} c^{3} d e^{15} + 80 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{4} d^{2} e^{10} - 14 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c d e^{11} + 20 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} d e^{11} - 10 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d e^{11} - 2 \, b^{7} c^{2} e^{16} - 20 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{3} d e^{11} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{7} e^{12} - 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c e^{12} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} e^{12} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{5} c^{2} e^{12}\right)} c^{2} - 2 \, {\left(256 \, c^{10} d^{8} e^{8} - 128 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{9} d^{8} e^{6} - 896 \, b c^{9} d^{7} e^{9} + 448 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{7} e^{7} + 1344 \, b^{2} c^{8} d^{6} e^{10} - 672 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{6} e^{8} + 64 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{6} e^{8} - 32 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{9} d^{6} e^{8} - 1120 \, b^{3} c^{7} d^{5} e^{11} + 560 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{5} e^{9} - 160 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{5} e^{9} + 80 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{5} e^{9} - 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{8} d^{6} e^{6} + 560 \, b^{4} c^{6} d^{4} e^{12} - 280 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{4} e^{10} + 160 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{4} e^{10} - 80 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{4} e^{10} + 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{7} d^{5} e^{7} - 168 \, b^{5} c^{5} d^{3} e^{13} + 84 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d^{3} e^{11} - 80 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{3} e^{11} + 40 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{3} e^{11} - 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{6} d^{4} e^{8} + 28 \, b^{6} c^{4} d^{2} e^{14} - 14 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} d^{2} e^{12} + 20 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d^{2} e^{12} - 10 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{2} e^{12} + 80 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{5} d^{3} e^{9} - 2 \, b^{7} c^{3} d e^{15} + \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{7} c^{2} d e^{13} - 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} d e^{13} + \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d e^{13} - 20 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{4} d^{2} e^{10} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{5} c^{3} d e^{11}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e^{6}}{\sqrt{\frac{b c^{5} e^{12} + \sqrt{b^{2} c^{10} e^{24} + 4 \, {\left(c^{6} d^{2} e^{10} - b c^{5} d e^{11}\right)} c^{6} e^{12}}}{c^{6}}}}\right)}{8 \, {\left(16 \, c^{10} d^{6} e^{8} - 48 \, b c^{9} d^{5} e^{9} + 56 \, b^{2} c^{8} d^{4} e^{10} - 8 \, b c^{9} d^{4} e^{10} + 4 \, c^{10} d^{4} e^{10} - 32 \, b^{3} c^{7} d^{3} e^{11} + 16 \, b^{2} c^{8} d^{3} e^{11} - 8 \, b c^{9} d^{3} e^{11} + 9 \, b^{4} c^{6} d^{2} e^{12} - 10 \, b^{3} c^{7} d^{2} e^{12} + 5 \, b^{2} c^{8} d^{2} e^{12} - b^{5} c^{5} d e^{13} + 2 \, b^{4} c^{6} d e^{13} - b^{3} c^{7} d e^{13}\right)} c^{2}} + \frac{{\left(128 \, b c^{10} d^{6} e^{10} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{6} e^{6} - 384 \, b^{2} c^{9} d^{5} e^{11} + 192 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{5} e^{7} + 480 \, b^{3} c^{8} d^{4} e^{12} - 240 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{4} e^{8} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{4} e^{8} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{4} e^{8} - 320 \, b^{4} c^{7} d^{3} e^{13} - 32 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{8} d^{4} e^{8} + 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{3} e^{9} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{3} e^{9} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{3} e^{9} + 120 \, b^{5} c^{6} d^{2} e^{14} + 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{7} d^{3} e^{9} - 60 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d^{2} e^{10} + 48 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{2} e^{10} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{2} e^{10} - 24 \, b^{6} c^{5} d e^{15} - 48 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{6} d^{2} e^{10} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} d e^{11} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d e^{11} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d e^{11} + 2 \, b^{7} c^{4} e^{16} + 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{5} d e^{11} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{7} c^{2} e^{12} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} e^{12} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} e^{12} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{5} c^{4} e^{12} + {\left(256 \, c^{9} d^{7} e^{9} - 128 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{7} e^{5} - 896 \, b c^{8} d^{6} e^{10} + 448 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{6} e^{6} + 1344 \, b^{2} c^{7} d^{5} e^{11} - 672 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{5} e^{7} + 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{5} e^{7} - 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{5} e^{7} - 1120 \, b^{3} c^{6} d^{4} e^{12} - 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{7} d^{5} e^{7} + 560 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{4} e^{8} - 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{4} e^{8} + 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{4} e^{8} + 560 \, b^{4} c^{5} d^{3} e^{13} + 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{6} d^{4} e^{8} - 280 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d^{3} e^{9} + 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{3} e^{9} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{3} e^{9} - 168 \, b^{5} c^{4} d^{2} e^{14} - 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{5} d^{3} e^{9} + 84 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} d^{2} e^{10} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d^{2} e^{10} + 40 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{2} e^{10} + 28 \, b^{6} c^{3} d e^{15} + 80 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{4} d^{2} e^{10} - 14 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c d e^{11} + 20 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} d e^{11} - 10 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d e^{11} - 2 \, b^{7} c^{2} e^{16} - 20 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{3} d e^{11} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{7} e^{12} - 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c e^{12} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} e^{12} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{5} c^{2} e^{12}\right)} c^{2} - 2 \, {\left(256 \, c^{10} d^{8} e^{8} + 128 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{9} d^{8} e^{6} - 896 \, b c^{9} d^{7} e^{9} - 448 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{7} e^{7} + 1344 \, b^{2} c^{8} d^{6} e^{10} + 672 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{6} e^{8} - 64 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{6} e^{8} + 32 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{9} d^{6} e^{8} - 1120 \, b^{3} c^{7} d^{5} e^{11} - 560 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{5} e^{9} + 160 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{5} e^{9} - 80 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{8} d^{5} e^{9} - 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{8} d^{6} e^{6} + 560 \, b^{4} c^{6} d^{4} e^{12} + 280 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{4} e^{10} - 160 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{4} e^{10} + 80 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{7} d^{4} e^{10} + 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{7} d^{5} e^{7} - 168 \, b^{5} c^{5} d^{3} e^{13} - 84 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d^{3} e^{11} + 80 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{3} e^{11} - 40 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{6} d^{3} e^{11} - 160 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{6} d^{4} e^{8} + 28 \, b^{6} c^{4} d^{2} e^{14} + 14 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} d^{2} e^{12} - 20 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d^{2} e^{12} + 10 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{5} d^{2} e^{12} + 80 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{5} d^{3} e^{9} - 2 \, b^{7} c^{3} d e^{15} - \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{7} c^{2} d e^{13} + 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{3} d e^{13} - \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{4} d e^{13} - 20 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{4} d^{2} e^{10} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{5} c^{3} d e^{11}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e^{6}}{\sqrt{\frac{b c^{5} e^{12} - \sqrt{b^{2} c^{10} e^{24} + 4 \, {\left(c^{6} d^{2} e^{10} - b c^{5} d e^{11}\right)} c^{6} e^{12}}}{c^{6}}}}\right)}{8 \, {\left(16 \, c^{10} d^{6} e^{8} - 48 \, b c^{9} d^{5} e^{9} + 56 \, b^{2} c^{8} d^{4} e^{10} - 8 \, b c^{9} d^{4} e^{10} + 4 \, c^{10} d^{4} e^{10} - 32 \, b^{3} c^{7} d^{3} e^{11} + 16 \, b^{2} c^{8} d^{3} e^{11} - 8 \, b c^{9} d^{3} e^{11} + 9 \, b^{4} c^{6} d^{2} e^{12} - 10 \, b^{3} c^{7} d^{2} e^{12} + 5 \, b^{2} c^{8} d^{2} e^{12} - b^{5} c^{5} d e^{13} + 2 \, b^{4} c^{6} d e^{13} - b^{3} c^{7} d e^{13}\right)} c^{2}} + \frac{{\left(3 \, c^{4} x^{5} e^{12} + 20 \, c^{4} d x^{3} e^{11} - 5 \, b c^{3} x^{3} e^{12} + 105 \, c^{4} d^{2} x e^{10} - 75 \, b c^{3} d x e^{11} + 15 \, b^{2} c^{2} x e^{12}\right)} e^{\left(-10\right)}}{15 \, c^{5}}"," ",0,"-1/8*(128*b*c^10*d^6*e^10 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^6*e^6 - 384*b^2*c^9*d^5*e^11 + 192*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^5*e^7 + 480*b^3*c^8*d^4*e^12 - 240*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^4*e^8 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^4*e^8 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^4*e^8 - 320*b^4*c^7*d^3*e^13 - 32*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^8*d^4*e^8 + 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^3*e^9 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^3*e^9 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^3*e^9 + 120*b^5*c^6*d^2*e^14 + 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^7*d^3*e^9 - 60*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d^2*e^10 + 48*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^2*e^10 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^2*e^10 - 24*b^6*c^5*d*e^15 - 48*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^6*d^2*e^10 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*d*e^11 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d*e^11 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d*e^11 + 2*b^7*c^4*e^16 + 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^5*d*e^11 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^7*c^2*e^12 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*e^12 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*e^12 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^5*c^4*e^12 + (256*c^9*d^7*e^9 - 128*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^7*e^5 - 896*b*c^8*d^6*e^10 + 448*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^6*e^6 + 1344*b^2*c^7*d^5*e^11 - 672*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^5*e^7 + 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^5*e^7 - 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^5*e^7 - 1120*b^3*c^6*d^4*e^12 - 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^7*d^5*e^7 + 560*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^4*e^8 - 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^4*e^8 + 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^4*e^8 + 560*b^4*c^5*d^3*e^13 + 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^6*d^4*e^8 - 280*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d^3*e^9 + 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^3*e^9 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^3*e^9 - 168*b^5*c^4*d^2*e^14 - 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^5*d^3*e^9 + 84*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*d^2*e^10 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d^2*e^10 + 40*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^2*e^10 + 28*b^6*c^3*d*e^15 + 80*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^4*d^2*e^10 - 14*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c*d*e^11 + 20*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*d*e^11 - 10*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d*e^11 - 2*b^7*c^2*e^16 - 20*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^3*d*e^11 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^7*e^12 - 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c*e^12 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*e^12 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^5*c^2*e^12)*c^2 - 2*(256*c^10*d^8*e^8 - 128*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^9*d^8*e^6 - 896*b*c^9*d^7*e^9 + 448*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^7*e^7 + 1344*b^2*c^8*d^6*e^10 - 672*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^6*e^8 + 64*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^6*e^8 - 32*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^9*d^6*e^8 - 1120*b^3*c^7*d^5*e^11 + 560*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^5*e^9 - 160*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^5*e^9 + 80*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^5*e^9 - 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^8*d^6*e^6 + 560*b^4*c^6*d^4*e^12 - 280*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^4*e^10 + 160*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^4*e^10 - 80*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^4*e^10 + 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^7*d^5*e^7 - 168*b^5*c^5*d^3*e^13 + 84*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d^3*e^11 - 80*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^3*e^11 + 40*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^3*e^11 - 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^6*d^4*e^8 + 28*b^6*c^4*d^2*e^14 - 14*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*d^2*e^12 + 20*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d^2*e^12 - 10*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^2*e^12 + 80*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^5*d^3*e^9 - 2*b^7*c^3*d*e^15 + sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^7*c^2*d*e^13 - 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*d*e^13 + sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d*e^13 - 20*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^4*d^2*e^10 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^5*c^3*d*e^11)*abs(c))*arctan(2*sqrt(1/2)*x*e^6/sqrt((b*c^5*e^12 + sqrt(b^2*c^10*e^24 + 4*(c^6*d^2*e^10 - b*c^5*d*e^11)*c^6*e^12))/c^6))/((16*c^10*d^6*e^8 - 48*b*c^9*d^5*e^9 + 56*b^2*c^8*d^4*e^10 - 8*b*c^9*d^4*e^10 + 4*c^10*d^4*e^10 - 32*b^3*c^7*d^3*e^11 + 16*b^2*c^8*d^3*e^11 - 8*b*c^9*d^3*e^11 + 9*b^4*c^6*d^2*e^12 - 10*b^3*c^7*d^2*e^12 + 5*b^2*c^8*d^2*e^12 - b^5*c^5*d*e^13 + 2*b^4*c^6*d*e^13 - b^3*c^7*d*e^13)*c^2) + 1/8*(128*b*c^10*d^6*e^10 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^6*e^6 - 384*b^2*c^9*d^5*e^11 + 192*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^5*e^7 + 480*b^3*c^8*d^4*e^12 - 240*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^4*e^8 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^4*e^8 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^4*e^8 - 320*b^4*c^7*d^3*e^13 - 32*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^8*d^4*e^8 + 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^3*e^9 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^3*e^9 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^3*e^9 + 120*b^5*c^6*d^2*e^14 + 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^7*d^3*e^9 - 60*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d^2*e^10 + 48*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^2*e^10 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^2*e^10 - 24*b^6*c^5*d*e^15 - 48*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^6*d^2*e^10 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*d*e^11 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d*e^11 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d*e^11 + 2*b^7*c^4*e^16 + 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^5*d*e^11 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^7*c^2*e^12 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*e^12 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*e^12 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^5*c^4*e^12 + (256*c^9*d^7*e^9 - 128*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^7*e^5 - 896*b*c^8*d^6*e^10 + 448*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^6*e^6 + 1344*b^2*c^7*d^5*e^11 - 672*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^5*e^7 + 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^5*e^7 - 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^5*e^7 - 1120*b^3*c^6*d^4*e^12 - 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^7*d^5*e^7 + 560*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^4*e^8 - 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^4*e^8 + 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^4*e^8 + 560*b^4*c^5*d^3*e^13 + 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^6*d^4*e^8 - 280*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d^3*e^9 + 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^3*e^9 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^3*e^9 - 168*b^5*c^4*d^2*e^14 - 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^5*d^3*e^9 + 84*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*d^2*e^10 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d^2*e^10 + 40*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^2*e^10 + 28*b^6*c^3*d*e^15 + 80*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^4*d^2*e^10 - 14*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c*d*e^11 + 20*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*d*e^11 - 10*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d*e^11 - 2*b^7*c^2*e^16 - 20*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^3*d*e^11 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^7*e^12 - 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c*e^12 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*e^12 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^5*c^2*e^12)*c^2 - 2*(256*c^10*d^8*e^8 + 128*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^9*d^8*e^6 - 896*b*c^9*d^7*e^9 - 448*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^7*e^7 + 1344*b^2*c^8*d^6*e^10 + 672*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^6*e^8 - 64*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^6*e^8 + 32*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^9*d^6*e^8 - 1120*b^3*c^7*d^5*e^11 - 560*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^5*e^9 + 160*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^5*e^9 - 80*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^8*d^5*e^9 - 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^8*d^6*e^6 + 560*b^4*c^6*d^4*e^12 + 280*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^4*e^10 - 160*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^4*e^10 + 80*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^7*d^4*e^10 + 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^7*d^5*e^7 - 168*b^5*c^5*d^3*e^13 - 84*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d^3*e^11 + 80*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^3*e^11 - 40*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^6*d^3*e^11 - 160*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^6*d^4*e^8 + 28*b^6*c^4*d^2*e^14 + 14*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*d^2*e^12 - 20*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d^2*e^12 + 10*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^5*d^2*e^12 + 80*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^5*d^3*e^9 - 2*b^7*c^3*d*e^15 - sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^7*c^2*d*e^13 + 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^3*d*e^13 - sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^4*d*e^13 - 20*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^4*d^2*e^10 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^5*c^3*d*e^11)*abs(c))*arctan(2*sqrt(1/2)*x*e^6/sqrt((b*c^5*e^12 - sqrt(b^2*c^10*e^24 + 4*(c^6*d^2*e^10 - b*c^5*d*e^11)*c^6*e^12))/c^6))/((16*c^10*d^6*e^8 - 48*b*c^9*d^5*e^9 + 56*b^2*c^8*d^4*e^10 - 8*b*c^9*d^4*e^10 + 4*c^10*d^4*e^10 - 32*b^3*c^7*d^3*e^11 + 16*b^2*c^8*d^3*e^11 - 8*b*c^9*d^3*e^11 + 9*b^4*c^6*d^2*e^12 - 10*b^3*c^7*d^2*e^12 + 5*b^2*c^8*d^2*e^12 - b^5*c^5*d*e^13 + 2*b^4*c^6*d*e^13 - b^3*c^7*d*e^13)*c^2) + 1/15*(3*c^4*x^5*e^12 + 20*c^4*d*x^3*e^11 - 5*b*c^3*x^3*e^12 + 105*c^4*d^2*x*e^10 - 75*b*c^3*d*x*e^11 + 15*b^2*c^2*x*e^12)*e^(-10)/c^5","B",0
215,1,8680,0,5.304315," ","integrate((e*x^2+d)^3/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","-\frac{{\left(64 \, b c^{9} d^{5} e^{8} - 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{5} e^{4} - 160 \, b^{2} c^{8} d^{4} e^{9} + 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{4} e^{5} + 160 \, b^{3} c^{7} d^{3} e^{10} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{3} e^{6} + 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{3} e^{6} - 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{3} e^{6} - 80 \, b^{4} c^{6} d^{2} e^{11} - 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{7} d^{3} e^{6} + 40 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d^{2} e^{7} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{2} e^{7} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{2} e^{7} + 20 \, b^{5} c^{5} d e^{12} + 24 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{6} d^{2} e^{7} - 10 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} d e^{8} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d e^{8} - 6 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d e^{8} - 2 \, b^{6} c^{4} e^{13} - 12 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{5} d e^{8} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{2} e^{9} - 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} e^{9} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} e^{9} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{4} e^{9} + {\left(128 \, c^{8} d^{6} e^{7} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{6} d^{6} e^{3} - 384 \, b c^{7} d^{5} e^{8} + 192 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{5} d^{5} e^{4} + 480 \, b^{2} c^{6} d^{4} e^{9} - 240 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{4} d^{4} e^{5} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{5} d^{4} e^{5} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{6} d^{4} e^{5} - 320 \, b^{3} c^{5} d^{3} e^{10} - 32 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{6} d^{4} e^{5} + 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{3} d^{3} e^{6} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{4} d^{3} e^{6} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{5} d^{3} e^{6} + 120 \, b^{4} c^{4} d^{2} e^{11} + 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{5} d^{3} e^{6} - 60 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{2} d^{2} e^{7} + 48 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{3} d^{2} e^{7} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{4} d^{2} e^{7} - 24 \, b^{5} c^{3} d e^{12} - 48 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{4} d^{2} e^{7} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c d e^{8} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{2} d e^{8} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{3} d e^{8} + 2 \, b^{6} c^{2} e^{13} + 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{3} d e^{8} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} e^{9} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c e^{9} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{2} e^{9} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{2} e^{9}\right)} c^{2} - 2 \, {\left(128 \, c^{9} d^{7} e^{6} - 64 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{8} d^{7} e^{4} - 384 \, b c^{8} d^{6} e^{7} + 192 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{6} e^{5} + 480 \, b^{2} c^{7} d^{5} e^{8} - 240 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{5} e^{6} + 32 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{5} e^{6} - 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{8} d^{5} e^{6} - 320 \, b^{3} c^{6} d^{4} e^{9} + 160 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{4} e^{7} - 64 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{4} e^{7} + 32 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{4} e^{7} - 32 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{7} d^{5} e^{4} + 120 \, b^{4} c^{5} d^{3} e^{10} - 60 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d^{3} e^{8} + 48 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{3} e^{8} - 24 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{3} e^{8} + 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{6} d^{4} e^{5} - 24 \, b^{5} c^{4} d^{2} e^{11} + 12 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} d^{2} e^{9} - 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d^{2} e^{9} + 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{2} e^{9} - 48 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{5} d^{3} e^{6} + 2 \, b^{6} c^{3} d e^{12} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{2} d e^{10} + 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} d e^{10} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d e^{10} + 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{4} d^{2} e^{7} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{3} d e^{8}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e^{4}}{\sqrt{\frac{b c^{3} e^{8} + \sqrt{b^{2} c^{6} e^{16} + 4 \, {\left(c^{4} d^{2} e^{6} - b c^{3} d e^{7}\right)} c^{4} e^{8}}}{c^{4}}}}\right)}{8 \, {\left(16 \, c^{9} d^{6} e^{6} - 48 \, b c^{8} d^{5} e^{7} + 56 \, b^{2} c^{7} d^{4} e^{8} - 8 \, b c^{8} d^{4} e^{8} + 4 \, c^{9} d^{4} e^{8} - 32 \, b^{3} c^{6} d^{3} e^{9} + 16 \, b^{2} c^{7} d^{3} e^{9} - 8 \, b c^{8} d^{3} e^{9} + 9 \, b^{4} c^{5} d^{2} e^{10} - 10 \, b^{3} c^{6} d^{2} e^{10} + 5 \, b^{2} c^{7} d^{2} e^{10} - b^{5} c^{4} d e^{11} + 2 \, b^{4} c^{5} d e^{11} - b^{3} c^{6} d e^{11}\right)} c^{2}} + \frac{{\left(64 \, b c^{9} d^{5} e^{8} - 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{5} e^{4} - 160 \, b^{2} c^{8} d^{4} e^{9} + 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{4} e^{5} + 160 \, b^{3} c^{7} d^{3} e^{10} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{3} e^{6} + 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{3} e^{6} - 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{3} e^{6} - 80 \, b^{4} c^{6} d^{2} e^{11} - 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{7} d^{3} e^{6} + 40 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d^{2} e^{7} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{2} e^{7} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{2} e^{7} + 20 \, b^{5} c^{5} d e^{12} + 24 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{6} d^{2} e^{7} - 10 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} d e^{8} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d e^{8} - 6 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d e^{8} - 2 \, b^{6} c^{4} e^{13} - 12 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{5} d e^{8} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{2} e^{9} - 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} e^{9} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} e^{9} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{4} e^{9} + {\left(128 \, c^{8} d^{6} e^{7} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{6} d^{6} e^{3} - 384 \, b c^{7} d^{5} e^{8} + 192 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{5} d^{5} e^{4} + 480 \, b^{2} c^{6} d^{4} e^{9} - 240 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{4} d^{4} e^{5} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{5} d^{4} e^{5} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{6} d^{4} e^{5} - 320 \, b^{3} c^{5} d^{3} e^{10} - 32 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{6} d^{4} e^{5} + 160 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{3} d^{3} e^{6} - 64 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{4} d^{3} e^{6} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{5} d^{3} e^{6} + 120 \, b^{4} c^{4} d^{2} e^{11} + 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{5} d^{3} e^{6} - 60 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{2} d^{2} e^{7} + 48 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{3} d^{2} e^{7} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{4} d^{2} e^{7} - 24 \, b^{5} c^{3} d e^{12} - 48 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{4} d^{2} e^{7} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c d e^{8} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{2} d e^{8} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{3} d e^{8} + 2 \, b^{6} c^{2} e^{13} + 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{3} d e^{8} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} e^{9} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c e^{9} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{2} e^{9} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{2} e^{9}\right)} c^{2} - 2 \, {\left(128 \, c^{9} d^{7} e^{6} + 64 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{8} d^{7} e^{4} - 384 \, b c^{8} d^{6} e^{7} - 192 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{6} e^{5} + 480 \, b^{2} c^{7} d^{5} e^{8} + 240 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{5} e^{6} - 32 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{5} e^{6} + 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{8} d^{5} e^{6} - 320 \, b^{3} c^{6} d^{4} e^{9} - 160 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{4} e^{7} + 64 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{4} e^{7} - 32 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{7} d^{4} e^{7} - 32 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{7} d^{5} e^{4} + 120 \, b^{4} c^{5} d^{3} e^{10} + 60 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d^{3} e^{8} - 48 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{3} e^{8} + 24 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{6} d^{3} e^{8} + 64 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{6} d^{4} e^{5} - 24 \, b^{5} c^{4} d^{2} e^{11} - 12 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} d^{2} e^{9} + 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d^{2} e^{9} - 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{5} d^{2} e^{9} - 48 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{5} d^{3} e^{6} + 2 \, b^{6} c^{3} d e^{12} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{6} c^{2} d e^{10} - 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{3} d e^{10} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{4} d e^{10} + 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{4} d^{2} e^{7} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{4} c^{3} d e^{8}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e^{4}}{\sqrt{\frac{b c^{3} e^{8} - \sqrt{b^{2} c^{6} e^{16} + 4 \, {\left(c^{4} d^{2} e^{6} - b c^{3} d e^{7}\right)} c^{4} e^{8}}}{c^{4}}}}\right)}{8 \, {\left(16 \, c^{9} d^{6} e^{6} - 48 \, b c^{8} d^{5} e^{7} + 56 \, b^{2} c^{7} d^{4} e^{8} - 8 \, b c^{8} d^{4} e^{8} + 4 \, c^{9} d^{4} e^{8} - 32 \, b^{3} c^{6} d^{3} e^{9} + 16 \, b^{2} c^{7} d^{3} e^{9} - 8 \, b c^{8} d^{3} e^{9} + 9 \, b^{4} c^{5} d^{2} e^{10} - 10 \, b^{3} c^{6} d^{2} e^{10} + 5 \, b^{2} c^{7} d^{2} e^{10} - b^{5} c^{4} d e^{11} + 2 \, b^{4} c^{5} d e^{11} - b^{3} c^{6} d e^{11}\right)} c^{2}} + \frac{{\left(c^{2} x^{3} e^{7} + 9 \, c^{2} d x e^{6} - 3 \, b c x e^{7}\right)} e^{\left(-6\right)}}{3 \, c^{3}}"," ",0,"-1/8*(64*b*c^9*d^5*e^8 - 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^5*e^4 - 160*b^2*c^8*d^4*e^9 + 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^4*e^5 + 160*b^3*c^7*d^3*e^10 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^3*e^6 + 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^3*e^6 - 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^3*e^6 - 80*b^4*c^6*d^2*e^11 - 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^7*d^3*e^6 + 40*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d^2*e^7 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^2*e^7 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^2*e^7 + 20*b^5*c^5*d*e^12 + 24*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^6*d^2*e^7 - 10*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*d*e^8 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d*e^8 - 6*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d*e^8 - 2*b^6*c^4*e^13 - 12*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^5*d*e^8 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^2*e^9 - 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*e^9 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*e^9 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^4*e^9 + (128*c^8*d^6*e^7 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^6*d^6*e^3 - 384*b*c^7*d^5*e^8 + 192*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^5*d^5*e^4 + 480*b^2*c^6*d^4*e^9 - 240*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^4*d^4*e^5 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^5*d^4*e^5 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^6*d^4*e^5 - 320*b^3*c^5*d^3*e^10 - 32*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^6*d^4*e^5 + 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^3*d^3*e^6 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^4*d^3*e^6 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^5*d^3*e^6 + 120*b^4*c^4*d^2*e^11 + 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^5*d^3*e^6 - 60*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^2*d^2*e^7 + 48*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^3*d^2*e^7 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^4*d^2*e^7 - 24*b^5*c^3*d*e^12 - 48*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^4*d^2*e^7 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c*d*e^8 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^2*d*e^8 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^3*d*e^8 + 2*b^6*c^2*e^13 + 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^3*d*e^8 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*e^9 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c*e^9 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^2*e^9 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^2*e^9)*c^2 - 2*(128*c^9*d^7*e^6 - 64*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^8*d^7*e^4 - 384*b*c^8*d^6*e^7 + 192*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^6*e^5 + 480*b^2*c^7*d^5*e^8 - 240*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^5*e^6 + 32*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^5*e^6 - 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^8*d^5*e^6 - 320*b^3*c^6*d^4*e^9 + 160*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^4*e^7 - 64*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^4*e^7 + 32*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^4*e^7 - 32*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^7*d^5*e^4 + 120*b^4*c^5*d^3*e^10 - 60*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d^3*e^8 + 48*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^3*e^8 - 24*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^3*e^8 + 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^6*d^4*e^5 - 24*b^5*c^4*d^2*e^11 + 12*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*d^2*e^9 - 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d^2*e^9 + 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^2*e^9 - 48*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^5*d^3*e^6 + 2*b^6*c^3*d*e^12 - sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^2*d*e^10 + 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*d*e^10 - sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d*e^10 + 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^4*d^2*e^7 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^3*d*e^8)*abs(c))*arctan(2*sqrt(1/2)*x*e^4/sqrt((b*c^3*e^8 + sqrt(b^2*c^6*e^16 + 4*(c^4*d^2*e^6 - b*c^3*d*e^7)*c^4*e^8))/c^4))/((16*c^9*d^6*e^6 - 48*b*c^8*d^5*e^7 + 56*b^2*c^7*d^4*e^8 - 8*b*c^8*d^4*e^8 + 4*c^9*d^4*e^8 - 32*b^3*c^6*d^3*e^9 + 16*b^2*c^7*d^3*e^9 - 8*b*c^8*d^3*e^9 + 9*b^4*c^5*d^2*e^10 - 10*b^3*c^6*d^2*e^10 + 5*b^2*c^7*d^2*e^10 - b^5*c^4*d*e^11 + 2*b^4*c^5*d*e^11 - b^3*c^6*d*e^11)*c^2) + 1/8*(64*b*c^9*d^5*e^8 - 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^5*e^4 - 160*b^2*c^8*d^4*e^9 + 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^4*e^5 + 160*b^3*c^7*d^3*e^10 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^3*e^6 + 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^3*e^6 - 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^3*e^6 - 80*b^4*c^6*d^2*e^11 - 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^7*d^3*e^6 + 40*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d^2*e^7 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^2*e^7 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^2*e^7 + 20*b^5*c^5*d*e^12 + 24*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^6*d^2*e^7 - 10*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*d*e^8 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d*e^8 - 6*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d*e^8 - 2*b^6*c^4*e^13 - 12*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^5*d*e^8 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^2*e^9 - 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*e^9 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*e^9 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^4*e^9 + (128*c^8*d^6*e^7 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^6*d^6*e^3 - 384*b*c^7*d^5*e^8 + 192*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^5*d^5*e^4 + 480*b^2*c^6*d^4*e^9 - 240*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^4*d^4*e^5 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^5*d^4*e^5 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^6*d^4*e^5 - 320*b^3*c^5*d^3*e^10 - 32*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^6*d^4*e^5 + 160*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^3*d^3*e^6 - 64*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^4*d^3*e^6 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^5*d^3*e^6 + 120*b^4*c^4*d^2*e^11 + 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^5*d^3*e^6 - 60*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^2*d^2*e^7 + 48*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^3*d^2*e^7 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^4*d^2*e^7 - 24*b^5*c^3*d*e^12 - 48*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^4*d^2*e^7 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c*d*e^8 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^2*d*e^8 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^3*d*e^8 + 2*b^6*c^2*e^13 + 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^3*d*e^8 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*e^9 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c*e^9 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^2*e^9 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^2*e^9)*c^2 - 2*(128*c^9*d^7*e^6 + 64*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^8*d^7*e^4 - 384*b*c^8*d^6*e^7 - 192*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^6*e^5 + 480*b^2*c^7*d^5*e^8 + 240*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^5*e^6 - 32*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^5*e^6 + 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^8*d^5*e^6 - 320*b^3*c^6*d^4*e^9 - 160*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^4*e^7 + 64*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^4*e^7 - 32*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^7*d^4*e^7 - 32*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^7*d^5*e^4 + 120*b^4*c^5*d^3*e^10 + 60*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d^3*e^8 - 48*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^3*e^8 + 24*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^6*d^3*e^8 + 64*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^6*d^4*e^5 - 24*b^5*c^4*d^2*e^11 - 12*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*d^2*e^9 + 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d^2*e^9 - 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^5*d^2*e^9 - 48*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^5*d^3*e^6 + 2*b^6*c^3*d*e^12 + sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^6*c^2*d*e^10 - 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^3*d*e^10 + sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^4*d*e^10 + 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^4*d^2*e^7 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^4*c^3*d*e^8)*abs(c))*arctan(2*sqrt(1/2)*x*e^4/sqrt((b*c^3*e^8 - sqrt(b^2*c^6*e^16 + 4*(c^4*d^2*e^6 - b*c^3*d*e^7)*c^4*e^8))/c^4))/((16*c^9*d^6*e^6 - 48*b*c^8*d^5*e^7 + 56*b^2*c^7*d^4*e^8 - 8*b*c^8*d^4*e^8 + 4*c^9*d^4*e^8 - 32*b^3*c^6*d^3*e^9 + 16*b^2*c^7*d^3*e^9 - 8*b*c^8*d^3*e^9 + 9*b^4*c^5*d^2*e^10 - 10*b^3*c^6*d^2*e^10 + 5*b^2*c^7*d^2*e^10 - b^5*c^4*d*e^11 + 2*b^4*c^5*d*e^11 - b^3*c^6*d*e^11)*c^2) + 1/3*(c^2*x^3*e^7 + 9*c^2*d*x*e^6 - 3*b*c*x*e^7)*e^(-6)/c^3","B",0
216,1,7051,0,4.817913," ","integrate((e*x^2+d)^2/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\frac{x}{c} - \frac{{\left(32 \, b c^{8} d^{4} e^{8} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{4} e^{4} - 64 \, b^{2} c^{7} d^{3} e^{9} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{3} e^{5} + 48 \, b^{3} c^{6} d^{2} e^{10} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{2} e^{6} - 4 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{2} e^{6} - 16 \, b^{4} c^{5} d e^{11} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{6} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d e^{7} - 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d e^{7} + 4 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d e^{7} + 2 \, b^{5} c^{4} e^{12} + 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{5} d e^{7} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} e^{8} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} e^{8} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} e^{8} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{4} e^{8} + {\left(64 \, c^{7} d^{5} e^{7} - 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{5} d^{5} e^{3} - 160 \, b c^{6} d^{4} e^{8} + 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{4} d^{4} e^{4} + 160 \, b^{2} c^{5} d^{3} e^{9} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{3} d^{3} e^{5} + 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{4} d^{3} e^{5} - 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{5} d^{3} e^{5} - 80 \, b^{3} c^{4} d^{2} e^{10} - 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{5} d^{3} e^{5} + 40 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{2} d^{2} e^{6} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{3} d^{2} e^{6} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{4} d^{2} e^{6} + 20 \, b^{4} c^{3} d e^{11} + 24 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{4} d^{2} e^{6} - 10 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c d e^{7} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{2} d e^{7} - 6 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{3} d e^{7} - 2 \, b^{5} c^{2} e^{12} - 12 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{3} d e^{7} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} e^{8} - 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c e^{8} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{2} e^{8} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{2} e^{8}\right)} c^{2} - 2 \, {\left(64 \, c^{8} d^{6} e^{6} - 32 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{6} e^{4} - 160 \, b c^{7} d^{5} e^{7} + 80 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{5} e^{5} + 160 \, b^{2} c^{6} d^{4} e^{8} - 80 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{4} e^{6} + 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{4} e^{6} - 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{4} e^{6} - 80 \, b^{3} c^{5} d^{3} e^{9} + 40 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{3} e^{7} - 24 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{3} e^{7} + 12 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{3} e^{7} - 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{6} d^{4} e^{4} + 20 \, b^{4} c^{4} d^{2} e^{10} - 10 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d^{2} e^{8} + 12 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{2} e^{8} - 6 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{2} e^{8} + 24 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{5} d^{3} e^{5} - 2 \, b^{5} c^{3} d e^{11} + \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} d e^{9} - 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d e^{9} + \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d e^{9} - 12 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{4} d^{2} e^{6} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{3} d e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e^{2}}{\sqrt{\frac{b c e^{4} + \sqrt{b^{2} c^{2} e^{8} + 4 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3}\right)} c^{2} e^{4}}}{c^{2}}}}\right)}{8 \, {\left(16 \, c^{8} d^{6} e^{6} - 48 \, b c^{7} d^{5} e^{7} + 56 \, b^{2} c^{6} d^{4} e^{8} - 8 \, b c^{7} d^{4} e^{8} + 4 \, c^{8} d^{4} e^{8} - 32 \, b^{3} c^{5} d^{3} e^{9} + 16 \, b^{2} c^{6} d^{3} e^{9} - 8 \, b c^{7} d^{3} e^{9} + 9 \, b^{4} c^{4} d^{2} e^{10} - 10 \, b^{3} c^{5} d^{2} e^{10} + 5 \, b^{2} c^{6} d^{2} e^{10} - b^{5} c^{3} d e^{11} + 2 \, b^{4} c^{4} d e^{11} - b^{3} c^{5} d e^{11}\right)} c^{2}} + \frac{{\left(32 \, b c^{8} d^{4} e^{8} - 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{4} e^{4} - 64 \, b^{2} c^{7} d^{3} e^{9} + 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{3} e^{5} + 48 \, b^{3} c^{6} d^{2} e^{10} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{2} e^{6} - 4 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{2} e^{6} - 16 \, b^{4} c^{5} d e^{11} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{6} d^{2} e^{6} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d e^{7} - 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d e^{7} + 4 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d e^{7} + 2 \, b^{5} c^{4} e^{12} + 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{5} d e^{7} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} e^{8} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} e^{8} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} e^{8} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{4} e^{8} + {\left(64 \, c^{7} d^{5} e^{7} - 32 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{5} d^{5} e^{3} - 160 \, b c^{6} d^{4} e^{8} + 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{4} d^{4} e^{4} + 160 \, b^{2} c^{5} d^{3} e^{9} - 80 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{3} d^{3} e^{5} + 16 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{4} d^{3} e^{5} - 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{5} d^{3} e^{5} - 80 \, b^{3} c^{4} d^{2} e^{10} - 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{5} d^{3} e^{5} + 40 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{2} d^{2} e^{6} - 24 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{3} d^{2} e^{6} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{4} d^{2} e^{6} + 20 \, b^{4} c^{3} d e^{11} + 24 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{4} d^{2} e^{6} - 10 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c d e^{7} + 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{2} d e^{7} - 6 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{3} d e^{7} - 2 \, b^{5} c^{2} e^{12} - 12 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{3} d e^{7} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} e^{8} - 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c e^{8} + \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{2} e^{8} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{2} e^{8}\right)} c^{2} - 2 \, {\left(64 \, c^{8} d^{6} e^{6} + 32 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{6} e^{4} - 160 \, b c^{7} d^{5} e^{7} - 80 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{5} e^{5} + 160 \, b^{2} c^{6} d^{4} e^{8} + 80 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{4} e^{6} - 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{4} e^{6} + 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{7} d^{4} e^{6} - 80 \, b^{3} c^{5} d^{3} e^{9} - 40 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{3} e^{7} + 24 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{3} e^{7} - 12 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{6} d^{3} e^{7} - 16 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{6} d^{4} e^{4} + 20 \, b^{4} c^{4} d^{2} e^{10} + 10 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d^{2} e^{8} - 12 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d^{2} e^{8} + 6 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{5} d^{2} e^{8} + 24 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{5} d^{3} e^{5} - 2 \, b^{5} c^{3} d e^{11} - \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{5} c^{2} d e^{9} + 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} c^{3} d e^{9} - \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c^{4} d e^{9} - 12 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c^{4} d^{2} e^{6} + 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{3} c^{3} d e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e^{2}}{\sqrt{\frac{b c e^{4} - \sqrt{b^{2} c^{2} e^{8} + 4 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3}\right)} c^{2} e^{4}}}{c^{2}}}}\right)}{8 \, {\left(16 \, c^{8} d^{6} e^{6} - 48 \, b c^{7} d^{5} e^{7} + 56 \, b^{2} c^{6} d^{4} e^{8} - 8 \, b c^{7} d^{4} e^{8} + 4 \, c^{8} d^{4} e^{8} - 32 \, b^{3} c^{5} d^{3} e^{9} + 16 \, b^{2} c^{6} d^{3} e^{9} - 8 \, b c^{7} d^{3} e^{9} + 9 \, b^{4} c^{4} d^{2} e^{10} - 10 \, b^{3} c^{5} d^{2} e^{10} + 5 \, b^{2} c^{6} d^{2} e^{10} - b^{5} c^{3} d e^{11} + 2 \, b^{4} c^{4} d e^{11} - b^{3} c^{5} d e^{11}\right)} c^{2}}"," ",0,"x/c - 1/8*(32*b*c^8*d^4*e^8 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^4*e^4 - 64*b^2*c^7*d^3*e^9 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^3*e^5 + 48*b^3*c^6*d^2*e^10 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^2*e^6 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^2*e^6 - 4*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^2*e^6 - 16*b^4*c^5*d*e^11 - 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^6*d^2*e^6 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d*e^7 - 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d*e^7 + 4*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d*e^7 + 2*b^5*c^4*e^12 + 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^5*d*e^7 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*e^8 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*e^8 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*e^8 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^4*e^8 + (64*c^7*d^5*e^7 - 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^5*d^5*e^3 - 160*b*c^6*d^4*e^8 + 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^4*d^4*e^4 + 160*b^2*c^5*d^3*e^9 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^3*d^3*e^5 + 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^4*d^3*e^5 - 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^5*d^3*e^5 - 80*b^3*c^4*d^2*e^10 - 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^5*d^3*e^5 + 40*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^2*d^2*e^6 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^3*d^2*e^6 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^4*d^2*e^6 + 20*b^4*c^3*d*e^11 + 24*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^4*d^2*e^6 - 10*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c*d*e^7 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^2*d*e^7 - 6*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^3*d*e^7 - 2*b^5*c^2*e^12 - 12*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^3*d*e^7 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*e^8 - 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c*e^8 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^2*e^8 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^2*e^8)*c^2 - 2*(64*c^8*d^6*e^6 - 32*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^6*e^4 - 160*b*c^7*d^5*e^7 + 80*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^5*e^5 + 160*b^2*c^6*d^4*e^8 - 80*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^4*e^6 + 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^4*e^6 - 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^4*e^6 - 80*b^3*c^5*d^3*e^9 + 40*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^3*e^7 - 24*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^3*e^7 + 12*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^3*e^7 - 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^6*d^4*e^4 + 20*b^4*c^4*d^2*e^10 - 10*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d^2*e^8 + 12*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^2*e^8 - 6*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^2*e^8 + 24*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^5*d^3*e^5 - 2*b^5*c^3*d*e^11 + sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*d*e^9 - 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d*e^9 + sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d*e^9 - 12*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^4*d^2*e^6 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^3*d*e^7)*abs(c))*arctan(2*sqrt(1/2)*x*e^2/sqrt((b*c*e^4 + sqrt(b^2*c^2*e^8 + 4*(c^2*d^2*e^2 - b*c*d*e^3)*c^2*e^4))/c^2))/((16*c^8*d^6*e^6 - 48*b*c^7*d^5*e^7 + 56*b^2*c^6*d^4*e^8 - 8*b*c^7*d^4*e^8 + 4*c^8*d^4*e^8 - 32*b^3*c^5*d^3*e^9 + 16*b^2*c^6*d^3*e^9 - 8*b*c^7*d^3*e^9 + 9*b^4*c^4*d^2*e^10 - 10*b^3*c^5*d^2*e^10 + 5*b^2*c^6*d^2*e^10 - b^5*c^3*d*e^11 + 2*b^4*c^4*d*e^11 - b^3*c^5*d*e^11)*c^2) + 1/8*(32*b*c^8*d^4*e^8 - 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^4*e^4 - 64*b^2*c^7*d^3*e^9 + 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^3*e^5 + 48*b^3*c^6*d^2*e^10 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^2*e^6 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^2*e^6 - 4*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^2*e^6 - 16*b^4*c^5*d*e^11 - 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^6*d^2*e^6 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d*e^7 - 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d*e^7 + 4*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d*e^7 + 2*b^5*c^4*e^12 + 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^5*d*e^7 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*e^8 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*e^8 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*e^8 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^4*e^8 + (64*c^7*d^5*e^7 - 32*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^5*d^5*e^3 - 160*b*c^6*d^4*e^8 + 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^4*d^4*e^4 + 160*b^2*c^5*d^3*e^9 - 80*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^3*d^3*e^5 + 16*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^4*d^3*e^5 - 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^5*d^3*e^5 - 80*b^3*c^4*d^2*e^10 - 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^5*d^3*e^5 + 40*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^2*d^2*e^6 - 24*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^3*d^2*e^6 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^4*d^2*e^6 + 20*b^4*c^3*d*e^11 + 24*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^4*d^2*e^6 - 10*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c*d*e^7 + 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^2*d*e^7 - 6*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^3*d*e^7 - 2*b^5*c^2*e^12 - 12*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^3*d*e^7 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*e^8 - 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c*e^8 + sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^2*e^8 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^2*e^8)*c^2 - 2*(64*c^8*d^6*e^6 + 32*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^6*e^4 - 160*b*c^7*d^5*e^7 - 80*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^5*e^5 + 160*b^2*c^6*d^4*e^8 + 80*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^4*e^6 - 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^4*e^6 + 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^7*d^4*e^6 - 80*b^3*c^5*d^3*e^9 - 40*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^3*e^7 + 24*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^3*e^7 - 12*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^6*d^3*e^7 - 16*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^6*d^4*e^4 + 20*b^4*c^4*d^2*e^10 + 10*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d^2*e^8 - 12*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d^2*e^8 + 6*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^5*d^2*e^8 + 24*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^5*d^3*e^5 - 2*b^5*c^3*d*e^11 - sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^5*c^2*d*e^9 + 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*c^3*d*e^9 - sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c^4*d*e^9 - 12*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c^4*d^2*e^6 + 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^3*c^3*d*e^7)*abs(c))*arctan(2*sqrt(1/2)*x*e^2/sqrt((b*c*e^4 - sqrt(b^2*c^2*e^8 + 4*(c^2*d^2*e^2 - b*c*d*e^3)*c^2*e^4))/c^2))/((16*c^8*d^6*e^6 - 48*b*c^7*d^5*e^7 + 56*b^2*c^6*d^4*e^8 - 8*b*c^7*d^4*e^8 + 4*c^8*d^4*e^8 - 32*b^3*c^5*d^3*e^9 + 16*b^2*c^6*d^3*e^9 - 8*b*c^7*d^3*e^9 + 9*b^4*c^4*d^2*e^10 - 10*b^3*c^5*d^2*e^10 + 5*b^2*c^6*d^2*e^10 - b^5*c^3*d*e^11 + 2*b^4*c^4*d*e^11 - b^3*c^5*d*e^11)*c^2)","B",0
217,1,3276,0,6.094783," ","integrate((e*x^2+d)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\frac{{\left(32 \, c^{5} d^{4} e^{4} - 16 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 64 \, b c^{4} d^{3} e^{5} - 16 \, c^{5} d^{3} e^{5} + 32 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{3} d^{3} e^{3} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} e + 48 \, b^{2} c^{3} d^{2} e^{6} + 24 \, b c^{4} d^{2} e^{6} - 24 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} + 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} - 4 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 16 \, b^{3} c^{2} d e^{7} - 12 \, b^{2} c^{3} d e^{7} + 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c d e^{5} - 8 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d e^{5} + 4 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{3} d e^{5} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 6 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{3} - 4 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{3} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{3} d e^{3} + 2 \, b^{4} c e^{8} + 2 \, b^{3} c^{2} e^{8} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} + 2 \, \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} - \sqrt{2} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{2} d e^{3} + 4 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{3} d e^{3} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} + \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{2} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{\frac{b e^{2} + \sqrt{b^{2} e^{4} + 4 \, {\left(c d^{2} - b d e\right)} c e^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{4} - 48 \, b c^{4} d^{4} e^{5} + 56 \, b^{2} c^{3} d^{3} e^{6} - 8 \, b c^{4} d^{3} e^{6} + 4 \, c^{5} d^{3} e^{6} - 32 \, b^{3} c^{2} d^{2} e^{7} + 16 \, b^{2} c^{3} d^{2} e^{7} - 8 \, b c^{4} d^{2} e^{7} + 9 \, b^{4} c d e^{8} - 10 \, b^{3} c^{2} d e^{8} + 5 \, b^{2} c^{3} d e^{8} - b^{5} e^{9} + 2 \, b^{4} c e^{9} - b^{3} c^{2} e^{9}\right)} {\left| c \right|}} - \frac{{\left(32 \, c^{5} d^{4} e^{4} + 16 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{4} d^{4} e^{2} - 64 \, b c^{4} d^{3} e^{5} - 16 \, c^{5} d^{3} e^{5} - 32 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{3} d^{3} e^{3} + 8 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{3} d^{3} e + 48 \, b^{2} c^{3} d^{2} e^{6} + 24 \, b c^{4} d^{2} e^{6} + 24 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d^{2} e^{4} - 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{3} d^{2} e^{4} + 4 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{4} d^{2} e^{4} - 12 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{2} d^{2} e^{2} - 16 \, b^{3} c^{2} d e^{7} - 12 \, b^{2} c^{3} d e^{7} - 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c d e^{5} + 8 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} d e^{5} - 4 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{3} d e^{5} - 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{3} d^{2} e^{2} + 6 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c d e^{3} - 4 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{2} d e^{3} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} c^{3} d e^{3} + 2 \, b^{4} c e^{8} + 2 \, b^{3} c^{2} e^{8} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{4} e^{6} - 2 \, \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} c e^{6} + \sqrt{2} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c^{2} e^{6} + 8 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{2} d e^{3} + 4 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} c^{3} d e^{3} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{3} e^{4} + 2 \, \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b^{2} c e^{4} - \sqrt{2} \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} \sqrt{b c e^{4} - \sqrt{4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}} c e^{2}} b c^{2} e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b^{2} c e^{4} - 2 \, {\left(4 \, c^{2} d^{2} e^{2} - 4 \, b c d e^{3} + b^{2} e^{4}\right)} b c^{2} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x e}{\sqrt{\frac{b e^{2} - \sqrt{b^{2} e^{4} + 4 \, {\left(c d^{2} - b d e\right)} c e^{2}}}{c}}}\right)}{4 \, {\left(16 \, c^{5} d^{5} e^{4} - 48 \, b c^{4} d^{4} e^{5} + 56 \, b^{2} c^{3} d^{3} e^{6} - 8 \, b c^{4} d^{3} e^{6} + 4 \, c^{5} d^{3} e^{6} - 32 \, b^{3} c^{2} d^{2} e^{7} + 16 \, b^{2} c^{3} d^{2} e^{7} - 8 \, b c^{4} d^{2} e^{7} + 9 \, b^{4} c d e^{8} - 10 \, b^{3} c^{2} d e^{8} + 5 \, b^{2} c^{3} d e^{8} - b^{5} e^{9} + 2 \, b^{4} c e^{9} - b^{3} c^{2} e^{9}\right)} {\left| c \right|}}"," ",0,"1/4*(32*c^5*d^4*e^4 - 16*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 64*b*c^4*d^3*e^5 - 16*c^5*d^3*e^5 + 32*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^3*d^3*e^3 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^3*d^3*e + 48*b^2*c^3*d^2*e^6 + 24*b*c^4*d^2*e^6 - 24*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 + 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 - 4*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 16*b^3*c^2*d*e^7 - 12*b^2*c^3*d*e^7 + 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c*d*e^5 - 8*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^2*d*e^5 + 4*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^3*d*e^5 - 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^3*d^2*e^2 + 6*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c*d*e^3 - 4*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^2*d*e^3 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^3*d*e^3 + 2*b^4*c*e^8 + 2*b^3*c^2*e^8 - sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*e^6 + 2*sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c*e^6 - sqrt(2)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^2*d*e^3 + 4*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^3*d*e^3 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*e^4 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c*e^4 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 + sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^2*e^4 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^2*e^4)*arctan(2*sqrt(1/2)*x*e/sqrt((b*e^2 + sqrt(b^2*e^4 + 4*(c*d^2 - b*d*e)*c*e^2))/c))/((16*c^5*d^5*e^4 - 48*b*c^4*d^4*e^5 + 56*b^2*c^3*d^3*e^6 - 8*b*c^4*d^3*e^6 + 4*c^5*d^3*e^6 - 32*b^3*c^2*d^2*e^7 + 16*b^2*c^3*d^2*e^7 - 8*b*c^4*d^2*e^7 + 9*b^4*c*d*e^8 - 10*b^3*c^2*d*e^8 + 5*b^2*c^3*d*e^8 - b^5*e^9 + 2*b^4*c*e^9 - b^3*c^2*e^9)*abs(c)) - 1/4*(32*c^5*d^4*e^4 + 16*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^4*d^4*e^2 - 64*b*c^4*d^3*e^5 - 16*c^5*d^3*e^5 - 32*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^3*d^3*e^3 + 8*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^3*d^3*e + 48*b^2*c^3*d^2*e^6 + 24*b*c^4*d^2*e^6 + 24*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^2*d^2*e^4 - 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^3*d^2*e^4 + 4*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^4*d^2*e^4 - 12*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^2*d^2*e^2 - 16*b^3*c^2*d*e^7 - 12*b^2*c^3*d*e^7 - 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c*d*e^5 + 8*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^2*d*e^5 - 4*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^3*d*e^5 - 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^3*d^2*e^2 + 6*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c*d*e^3 - 4*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^2*d*e^3 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*c^3*d*e^3 + 2*b^4*c*e^8 + 2*b^3*c^2*e^8 + sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^4*e^6 - 2*sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*c*e^6 + sqrt(2)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c^2*e^6 + 8*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^2*d*e^3 + 4*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c^3*d*e^3 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^3*e^4 + 2*sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b^2*c*e^4 - sqrt(2)*sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*sqrt(b*c*e^4 - sqrt(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*c*e^2)*b*c^2*e^4 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b^2*c*e^4 - 2*(4*c^2*d^2*e^2 - 4*b*c*d*e^3 + b^2*e^4)*b*c^2*e^4)*arctan(2*sqrt(1/2)*x*e/sqrt((b*e^2 - sqrt(b^2*e^4 + 4*(c*d^2 - b*d*e)*c*e^2))/c))/((16*c^5*d^5*e^4 - 48*b*c^4*d^4*e^5 + 56*b^2*c^3*d^3*e^6 - 8*b*c^4*d^3*e^6 + 4*c^5*d^3*e^6 - 32*b^3*c^2*d^2*e^7 + 16*b^2*c^3*d^2*e^7 - 8*b*c^4*d^2*e^7 + 9*b^4*c*d*e^8 - 10*b^3*c^2*d*e^8 + 5*b^2*c^3*d*e^8 - b^5*e^9 + 2*b^4*c*e^9 - b^3*c^2*e^9)*abs(c))","B",0
218,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-95,-68,60,-66,8]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[79,32,2,-92,39]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 10.77Done","F(-2)",0
219,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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xp(1)^3*exp(2)^2+192*b*c^5*d^4*exp(1)*exp(2)^3+112*b*c^5*d^3*exp(1)^2*exp(2)^3+16*b*c^5*d^3*exp(2)^4-64*b*c^4*d^4*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)^3*exp(2)-96*b*c^4*d^4*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)*exp(2)^2-16*b*c^4*d^3*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)^2*exp(2)^2-16*b*c^4*d^3*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(2)^3-8*b*c^4*d^2*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)^3*exp(2)^2-16*b*c^4*d^2*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)*exp(2)^3-56*b*c^3*d^3*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)^2*exp(2)-8*b*c^3*d^3*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2)^2-16*b*c^3*d^2*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)*exp(2)^2-16*b*c^3*d^2*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)^3*exp(2)-32*b*c^3*d^2*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)*exp(2)^2-6*b*c^3*d*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)^2*exp(2)^2-2*b*c^3*d*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2)^3-12*b*c^3*d*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)^2*exp(2)^2-4*b*c^3*d*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2)^3-64*c^6*d^5*exp(1)^2*exp(2)^2-64*c^6*d^5*exp(2)^3-64*c^6*d^4*exp(1)*exp(2)^3+32*c^5*d^5*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)^2*exp(2)+32*c^5*d^5*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(2)^2+8*c^5*d^3*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(1)^2*exp(2)^2+8*c^5*d^3*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*exp(2)^3+32*c^4*d^4*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)*exp(2)+16*c^4*d^3*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)^2*exp(2)+16*c^4*d^3*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2)^2+8*c^4*d^2*sqrt(2)*sqrt(b*c*exp(2)^2+c*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(2))*sqrt(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)*exp(2)^2+16*c^4*d^2*(b^2*exp(2)^2+4*c^2*d^2*exp(2)-4*b*c*d*exp(1)*exp(2))*exp(1)*exp(2)^2)/(8*b^6*d^3*exp(1)^6*exp(2)^3-16*b^6*d^3*exp(1)^4*exp(2)^4+8*b^6*d^3*exp(1)^2*exp(2)^5-64*b^5*c*d^4*exp(1)^7*exp(2)^2+112*b^5*c*d^4*exp(1)^5*exp(2)^3-32*b^5*c*d^4*exp(1)^3*exp(2)^4-16*b^5*c*d^4*exp(1)*exp(2)^5-16*b^5*c*d^3*exp(1)^6*exp(2)^3+32*b^5*c*d^3*exp(1)^4*exp(2)^4-16*b^5*c*d^3*exp(1)^2*exp(2)^5+128*b^4*c^2*d^5*exp(1)^8*exp(2)-64*b^4*c^2*d^5*exp(1)^6*exp(2)^2-248*b^4*c^2*d^5*exp(1)^4*exp(2)^3+176*b^4*c^2*d^5*exp(1)^2*exp(2)^4+8*b^4*c^2*d^5*exp(2)^5+64*b^4*c^2*d^4*exp(1)^7*exp(2)^2-96*b^4*c^2*d^4*exp(1)^5*exp(2)^3+32*b^4*c^2*d^4*exp(1)*exp(2)^5+8*b^4*c^2*d^3*exp(1)^6*exp(2)^3-16*b^4*c^2*d^3*exp(1)^4*exp(2)^4+8*b^4*c^2*d^3*exp(1)^2*exp(2)^5-512*b^3*c^3*d^6*exp(1)^7*exp(2)+832*b^3*c^3*d^6*exp(1)^5*exp(2)^2-128*b^3*c^3*d^6*exp(1)^3*exp(2)^3-192*b^3*c^3*d^6*exp(1)*exp(2)^4-192*b^3*c^3*d^5*exp(1)^6*exp(2)^2+368*b^3*c^3*d^5*exp(1)^4*exp(2)^3-160*b^3*c^3*d^5*exp(1)^2*exp(2)^4-16*b^3*c^3*d^5*exp(2)^5-32*b^3*c^3*d^4*exp(1)^7*exp(2)^2+48*b^3*c^3*d^4*exp(1)^5*exp(2)^3-16*b^3*c^3*d^4*exp(1)*exp(2)^5+768*b^2*c^4*d^7*exp(1)^6*exp(2)-1472*b^2*c^4*d^7*exp(1)^4*exp(2)^2+640*b^2*c^4*d^7*exp(1)^2*exp(2)^3+64*b^2*c^4*d^7*exp(2)^4+192*b^2*c^4*d^6*exp(1)^5*exp(2)^2-384*b^2*c^4*d^6*exp(1)^3*exp(2)^3+192*b^2*c^4*d^6*exp(1)*exp(2)^4+96*b^2*c^4*d^5*exp(1)^6*exp(2)^2-184*b^2*c^4*d^5*exp(1)^4*exp(2)^3+80*b^2*c^4*d^5*exp(1)^2*exp(2)^4+8*b^2*c^4*d^5*exp(2)^5-512*b*c^5*d^8*exp(1)^5*exp(2)+1024*b*c^5*d^8*exp(1)^3*exp(2)^2-512*b*c^5*d^8*exp(1)*exp(2)^3-64*b*c^5*d^7*exp(1)^4*exp(2)^2+128*b*c^5*d^7*exp(1)^2*exp(2)^3-64*b*c^5*d^7*exp(2)^4-96*b*c^5*d^6*exp(1)^5*exp(2)^2+192*b*c^5*d^6*exp(1)^3*exp(2)^3-96*b*c^5*d^6*exp(1)*exp(2)^4+128*c^6*d^9*exp(1)^4*exp(2)-256*c^6*d^9*exp(1)^2*exp(2)^2+128*c^6*d^9*exp(2)^3+32*c^6*d^7*exp(1)^4*exp(2)^2-64*c^6*d^7*exp(1)^2*exp(2)^3+32*c^6*d^7*exp(2)^4)/abs(c)*atan(x/sqrt(-(c^2*exp(2)^3*b*d^4-2*c^2*exp(2)^2*b*d^4*exp(1)^2+c^2*exp(2)*b*d^4*exp(1)^4-2*c*exp(2)^3*b^2*d^3*exp(1)+4*c*exp(2)^2*b^2*d^3*exp(1)^3-2*c*exp(2)*b^2*d^3*exp(1)^5+exp(2)^3*b^3*d^2*exp(1)^2-2*exp(2)^2*b^3*d^2*exp(1)^4+exp(2)*b^3*d^2*exp(1)^6-sqrt((-c^2*exp(2)^3*b*d^4+2*c^2*exp(2)^2*b*d^4*exp(1)^2-c^2*exp(2)*b*d^4*exp(1)^4+2*c*exp(2)^3*b^2*d^3*exp(1)-4*c*exp(2)^2*b^2*d^3*exp(1)^3+2*c*exp(2)*b^2*d^3*exp(1)^5-exp(2)^3*b^3*d^2*exp(1)^2+2*exp(2)^2*b^3*d^2*exp(1)^4-exp(2)*b^3*d^2*exp(1)^6)*(-c^2*exp(2)^3*b*d^4+2*c^2*exp(2)^2*b*d^4*exp(1)^2-c^2*exp(2)*b*d^4*exp(1)^4+2*c*exp(2)^3*b^2*d^3*exp(1)-4*c*exp(2)^2*b^2*d^3*exp(1)^3+2*c*exp(2)*b^2*d^3*exp(1)^5-exp(2)^3*b^3*d^2*exp(1)^2+2*exp(2)^2*b^3*d^2*exp(1)^4-exp(2)*b^3*d^2*exp(1)^6)-4*(-c^3*exp(2)^3*d^4+2*c^3*exp(2)^2*d^4*exp(1)^2-c^3*exp(2)*d^4*exp(1)^4+2*c^2*exp(2)^3*b*d^3*exp(1)-4*c^2*exp(2)^2*b*d^3*exp(1)^3+2*c^2*exp(2)*b*d^3*exp(1)^5-c*exp(2)^3*b^2*d^2*exp(1)^2+2*c*exp(2)^2*b^2*d^2*exp(1)^4-c*exp(2)*b^2*d^2*exp(1)^6)*(c^3*exp(2)^2*d^6-2*c^3*exp(2)*d^6*exp(1)^2+c^3*d^6*exp(1)^4-3*c^2*exp(2)^2*b*d^5*exp(1)+6*c^2*exp(2)*b*d^5*exp(1)^3-3*c^2*b*d^5*exp(1)^5+3*c*exp(2)^2*b^2*d^4*exp(1)^2-6*c*exp(2)*b^2*d^4*exp(1)^4+3*c*b^2*d^4*exp(1)^6-exp(2)^2*b^3*d^3*exp(1)^3+2*exp(2)*b^3*d^3*exp(1)^5-b^3*d^3*exp(1)^7)))/2/(-c^3*exp(2)^3*d^4+2*c^3*exp(2)^2*d^4*exp(1)^2-c^3*exp(2)*d^4*exp(1)^4+2*c^2*exp(2)^3*b*d^3*exp(1)-4*c^2*exp(2)^2*b*d^3*exp(1)^3+2*c^2*exp(2)*b*d^3*exp(1)^5-c*exp(2)^3*b^2*d^2*exp(1)^2+2*c*exp(2)^2*b^2*d^2*exp(1)^4-c*exp(2)*b^2*d^2*exp(1)^6)))+(-5*c*exp(2)*d*exp(1)^2+c*d*exp(1)^4+3*exp(2)*b*exp(1)^3-b*exp(1)^5)*1/2/(-c^2*exp(2)^2*d^4+2*c^2*exp(2)*d^4*exp(1)^2-c^2*d^4*exp(1)^4+2*c*exp(2)^2*b*d^3*exp(1)-4*c*exp(2)*b*d^3*exp(1)^3+2*c*b*d^3*exp(1)^5-exp(2)^2*b^2*d^2*exp(1)^2+2*exp(2)*b^2*d^2*exp(1)^4-b^2*d^2*exp(1)^6)/sqrt(d*exp(1))*atan(x*exp(1)/sqrt(d*exp(1)))-x*exp(1)^2/(-2*c*exp(2)*d^3+2*c*d^3*exp(1)^2+2*exp(2)*b*d^2*exp(1)-2*b*d^2*exp(1)^3)/(x^2*exp(1)+d)","F(-2)",0
220,1,54,0,2.393821," ","integrate((e*x^2+d)^(5/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","-\frac{{\left(5 \, c d - 2 \, b e\right)} e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{4 \, c^{2}} + \frac{\sqrt{x^{2} e + d} x}{2 \, c}"," ",0,"-1/4*(5*c*d - 2*b*e)*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c^2 + 1/2*sqrt(x^2*e + d)*x/c","A",0
221,1,27,0,2.385302," ","integrate((e*x^2+d)^(3/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","-\frac{e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{2 \, c}"," ",0,"-1/2*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c","A",0
222,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^(1/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[-21,-18,-46,11,70]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [b,c,d,exp(1),exp(2)]=[72,91,-18,-31,46]Evaluation time: 2.06Unable to transpose Error: Bad Argument Value","F(-2)",0
225,0,0,0,0.000000," ","integrate((x^2+1)^3*(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)*(x^2 + 1)^3, x)","F",0
226,0,0,0,0.000000," ","integrate((x^2+1)^2*(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)*(x^2 + 1)^2, x)","F",0
227,0,0,0,0.000000," ","integrate((x^2+1)*(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)*(x^2 + 1), x)","F",0
228,0,0,0,0.000000," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{2} + 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)/(x^2 + 1), x)","F",0
229,0,0,0,0.000000," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{2} + 1}}{{\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)/(x^2 + 1)^2, x)","F",0
230,0,0,0,0.000000," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1)^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{2} + 1}}{{\left(x^{2} + 1\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)/(x^2 + 1)^3, x)","F",0
231,0,0,0,0.000000," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1)^4,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + x^{2} + 1}}{{\left(x^{2} + 1\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(x^4 + x^2 + 1)/(x^2 + 1)^4, x)","F",0
232,0,0,0,0.000000," ","integrate((x^2+1)^3/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{3}}{\sqrt{x^{4} + x^{2} + 1}}\,{d x}"," ",0,"integrate((x^2 + 1)^3/sqrt(x^4 + x^2 + 1), x)","F",0
233,0,0,0,0.000000," ","integrate((x^2+1)^2/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{2}}{\sqrt{x^{4} + x^{2} + 1}}\,{d x}"," ",0,"integrate((x^2 + 1)^2/sqrt(x^4 + x^2 + 1), x)","F",0
234,0,0,0,0.000000," ","integrate((x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{\sqrt{x^{4} + x^{2} + 1}}\,{d x}"," ",0,"integrate((x^2 + 1)/sqrt(x^4 + x^2 + 1), x)","F",0
235,0,0,0,0.000000," ","integrate(1/(x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(x^2+1)^2/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)^2), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(x^2+1)^3/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)^3), x)","F",0
238,0,0,0,0.000000," ","integrate((x^2+1)^3/(x^4+x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{3}}{{\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^2 + 1)^3/(x^4 + x^2 + 1)^(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate((x^2+1)^2/(x^4+x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{2}}{{\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^2 + 1)^2/(x^4 + x^2 + 1)^(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate((x^2+1)/(x^4+x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2} + 1}{{\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^2 + 1)/(x^4 + x^2 + 1)^(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate(1/(x^2+1)/(x^4+x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^4 + x^2 + 1)^(3/2)*(x^2 + 1)), x)","F",0
242,0,0,0,0.000000," ","integrate(1/(x^2+1)^2/(x^4+x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}} {\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(1/((x^4 + x^2 + 1)^(3/2)*(x^2 + 1)^2), x)","F",0
243,0,0,0,0.000000," ","integrate(1/(x^2+1)^3/(x^4+x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + x^{2} + 1\right)}^{\frac{3}{2}} {\left(x^{2} + 1\right)}^{3}}\,{d x}"," ",0,"integrate(1/((x^4 + x^2 + 1)^(3/2)*(x^2 + 1)^3), x)","F",0
244,1,142,0,0.153670," ","integrate((e*x^2+d)^4*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{13} \, c x^{13} e^{4} + \frac{4}{11} \, c d x^{11} e^{3} + \frac{1}{11} \, b x^{11} e^{4} + \frac{2}{3} \, c d^{2} x^{9} e^{2} + \frac{4}{9} \, b d x^{9} e^{3} + \frac{4}{7} \, c d^{3} x^{7} e + \frac{1}{9} \, a x^{9} e^{4} + \frac{6}{7} \, b d^{2} x^{7} e^{2} + \frac{1}{5} \, c d^{4} x^{5} + \frac{4}{7} \, a d x^{7} e^{3} + \frac{4}{5} \, b d^{3} x^{5} e + \frac{6}{5} \, a d^{2} x^{5} e^{2} + \frac{1}{3} \, b d^{4} x^{3} + \frac{4}{3} \, a d^{3} x^{3} e + a d^{4} x"," ",0,"1/13*c*x^13*e^4 + 4/11*c*d*x^11*e^3 + 1/11*b*x^11*e^4 + 2/3*c*d^2*x^9*e^2 + 4/9*b*d*x^9*e^3 + 4/7*c*d^3*x^7*e + 1/9*a*x^9*e^4 + 6/7*b*d^2*x^7*e^2 + 1/5*c*d^4*x^5 + 4/7*a*d*x^7*e^3 + 4/5*b*d^3*x^5*e + 6/5*a*d^2*x^5*e^2 + 1/3*b*d^4*x^3 + 4/3*a*d^3*x^3*e + a*d^4*x","A",0
245,1,108,0,0.155050," ","integrate((e*x^2+d)^3*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{11} \, c x^{11} e^{3} + \frac{1}{3} \, c d x^{9} e^{2} + \frac{1}{9} \, b x^{9} e^{3} + \frac{3}{7} \, c d^{2} x^{7} e + \frac{3}{7} \, b d x^{7} e^{2} + \frac{1}{5} \, c d^{3} x^{5} + \frac{1}{7} \, a x^{7} e^{3} + \frac{3}{5} \, b d^{2} x^{5} e + \frac{3}{5} \, a d x^{5} e^{2} + \frac{1}{3} \, b d^{3} x^{3} + a d^{2} x^{3} e + a d^{3} x"," ",0,"1/11*c*x^11*e^3 + 1/3*c*d*x^9*e^2 + 1/9*b*x^9*e^3 + 3/7*c*d^2*x^7*e + 3/7*b*d*x^7*e^2 + 1/5*c*d^3*x^5 + 1/7*a*x^7*e^3 + 3/5*b*d^2*x^5*e + 3/5*a*d*x^5*e^2 + 1/3*b*d^3*x^3 + a*d^2*x^3*e + a*d^3*x","A",0
246,1,76,0,0.148846," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{9} \, c x^{9} e^{2} + \frac{2}{7} \, c d x^{7} e + \frac{1}{7} \, b x^{7} e^{2} + \frac{1}{5} \, c d^{2} x^{5} + \frac{2}{5} \, b d x^{5} e + \frac{1}{5} \, a x^{5} e^{2} + \frac{1}{3} \, b d^{2} x^{3} + \frac{2}{3} \, a d x^{3} e + a d^{2} x"," ",0,"1/9*c*x^9*e^2 + 2/7*c*d*x^7*e + 1/7*b*x^7*e^2 + 1/5*c*d^2*x^5 + 2/5*b*d*x^5*e + 1/5*a*x^5*e^2 + 1/3*b*d^2*x^3 + 2/3*a*d*x^3*e + a*d^2*x","A",0
247,1,43,0,0.148160," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e + \frac{1}{5} \, c d x^{5} + \frac{1}{5} \, b x^{5} e + \frac{1}{3} \, b d x^{3} + \frac{1}{3} \, a x^{3} e + a d x"," ",0,"1/7*c*x^7*e + 1/5*c*d*x^5 + 1/5*b*x^5*e + 1/3*b*d*x^3 + 1/3*a*x^3*e + a*d*x","A",0
248,1,56,0,0.150791," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d),x, algorithm=""giac"")","\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{\sqrt{d}} + \frac{1}{3} \, {\left(c x^{3} e^{2} - 3 \, c d x e + 3 \, b x e^{2}\right)} e^{\left(-3\right)}"," ",0,"(c*d^2 - b*d*e + a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/sqrt(d) + 1/3*(c*x^3*e^2 - 3*c*d*x*e + 3*b*x*e^2)*e^(-3)","A",0
249,1,75,0,0.169821," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""giac"")","c x e^{\left(-2\right)} - \frac{{\left(3 \, c d^{2} - b d e - a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c d^{2} x - b d x e + a x e^{2}\right)} e^{\left(-2\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"c*x*e^(-2) - 1/2*(3*c*d^2 - b*d*e - a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(3/2) + 1/2*(c*d^2*x - b*d*x*e + a*x*e^2)*e^(-2)/((x^2*e + d)*d)","A",0
250,1,101,0,0.232242," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{{\left(3 \, c d^{2} + b d e + 3 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{8 \, d^{\frac{5}{2}}} - \frac{{\left(5 \, c d^{2} x^{3} e - b d x^{3} e^{2} + 3 \, c d^{3} x - 3 \, a x^{3} e^{3} + b d^{2} x e - 5 \, a d x e^{2}\right)} e^{\left(-2\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{2}}"," ",0,"1/8*(3*c*d^2 + b*d*e + 3*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(5/2) - 1/8*(5*c*d^2*x^3*e - b*d*x^3*e^2 + 3*c*d^3*x - 3*a*x^3*e^3 + b*d^2*x*e - 5*a*d*x*e^2)*e^(-2)/((x^2*e + d)^2*d^2)","A",0
251,1,134,0,0.159163," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^4,x, algorithm=""giac"")","\frac{{\left(c d^{2} + b d e + 5 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{16 \, d^{\frac{7}{2}}} + \frac{{\left(3 \, c d^{2} x^{5} e^{2} + 3 \, b d x^{5} e^{3} - 8 \, c d^{3} x^{3} e + 15 \, a x^{5} e^{4} + 8 \, b d^{2} x^{3} e^{2} - 3 \, c d^{4} x + 40 \, a d x^{3} e^{3} - 3 \, b d^{3} x e + 33 \, a d^{2} x e^{2}\right)} e^{\left(-2\right)}}{48 \, {\left(x^{2} e + d\right)}^{3} d^{3}}"," ",0,"1/16*(c*d^2 + b*d*e + 5*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(7/2) + 1/48*(3*c*d^2*x^5*e^2 + 3*b*d*x^5*e^3 - 8*c*d^3*x^3*e + 15*a*x^5*e^4 + 8*b*d^2*x^3*e^2 - 3*c*d^4*x + 40*a*d*x^3*e^3 - 3*b*d^3*x*e + 33*a*d^2*x*e^2)*e^(-2)/((x^2*e + d)^3*d^3)","A",0
252,1,255,0,0.157045," ","integrate((e*x^2+d)^3*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{15} \, c^{2} x^{15} e^{3} + \frac{3}{13} \, c^{2} d x^{13} e^{2} + \frac{2}{13} \, b c x^{13} e^{3} + \frac{3}{11} \, c^{2} d^{2} x^{11} e + \frac{6}{11} \, b c d x^{11} e^{2} + \frac{1}{9} \, c^{2} d^{3} x^{9} + \frac{1}{11} \, b^{2} x^{11} e^{3} + \frac{2}{11} \, a c x^{11} e^{3} + \frac{2}{3} \, b c d^{2} x^{9} e + \frac{1}{3} \, b^{2} d x^{9} e^{2} + \frac{2}{3} \, a c d x^{9} e^{2} + \frac{2}{7} \, b c d^{3} x^{7} + \frac{2}{9} \, a b x^{9} e^{3} + \frac{3}{7} \, b^{2} d^{2} x^{7} e + \frac{6}{7} \, a c d^{2} x^{7} e + \frac{6}{7} \, a b d x^{7} e^{2} + \frac{1}{5} \, b^{2} d^{3} x^{5} + \frac{2}{5} \, a c d^{3} x^{5} + \frac{1}{7} \, a^{2} x^{7} e^{3} + \frac{6}{5} \, a b d^{2} x^{5} e + \frac{3}{5} \, a^{2} d x^{5} e^{2} + \frac{2}{3} \, a b d^{3} x^{3} + a^{2} d^{2} x^{3} e + a^{2} d^{3} x"," ",0,"1/15*c^2*x^15*e^3 + 3/13*c^2*d*x^13*e^2 + 2/13*b*c*x^13*e^3 + 3/11*c^2*d^2*x^11*e + 6/11*b*c*d*x^11*e^2 + 1/9*c^2*d^3*x^9 + 1/11*b^2*x^11*e^3 + 2/11*a*c*x^11*e^3 + 2/3*b*c*d^2*x^9*e + 1/3*b^2*d*x^9*e^2 + 2/3*a*c*d*x^9*e^2 + 2/7*b*c*d^3*x^7 + 2/9*a*b*x^9*e^3 + 3/7*b^2*d^2*x^7*e + 6/7*a*c*d^2*x^7*e + 6/7*a*b*d*x^7*e^2 + 1/5*b^2*d^3*x^5 + 2/5*a*c*d^3*x^5 + 1/7*a^2*x^7*e^3 + 6/5*a*b*d^2*x^5*e + 3/5*a^2*d*x^5*e^2 + 2/3*a*b*d^3*x^3 + a^2*d^2*x^3*e + a^2*d^3*x","A",0
253,1,181,0,0.168529," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{13} \, c^{2} x^{13} e^{2} + \frac{2}{11} \, c^{2} d x^{11} e + \frac{2}{11} \, b c x^{11} e^{2} + \frac{1}{9} \, c^{2} d^{2} x^{9} + \frac{4}{9} \, b c d x^{9} e + \frac{1}{9} \, b^{2} x^{9} e^{2} + \frac{2}{9} \, a c x^{9} e^{2} + \frac{2}{7} \, b c d^{2} x^{7} + \frac{2}{7} \, b^{2} d x^{7} e + \frac{4}{7} \, a c d x^{7} e + \frac{2}{7} \, a b x^{7} e^{2} + \frac{1}{5} \, b^{2} d^{2} x^{5} + \frac{2}{5} \, a c d^{2} x^{5} + \frac{4}{5} \, a b d x^{5} e + \frac{1}{5} \, a^{2} x^{5} e^{2} + \frac{2}{3} \, a b d^{2} x^{3} + \frac{2}{3} \, a^{2} d x^{3} e + a^{2} d^{2} x"," ",0,"1/13*c^2*x^13*e^2 + 2/11*c^2*d*x^11*e + 2/11*b*c*x^11*e^2 + 1/9*c^2*d^2*x^9 + 4/9*b*c*d*x^9*e + 1/9*b^2*x^9*e^2 + 2/9*a*c*x^9*e^2 + 2/7*b*c*d^2*x^7 + 2/7*b^2*d*x^7*e + 4/7*a*c*d*x^7*e + 2/7*a*b*x^7*e^2 + 1/5*b^2*d^2*x^5 + 2/5*a*c*d^2*x^5 + 4/5*a*b*d*x^5*e + 1/5*a^2*x^5*e^2 + 2/3*a*b*d^2*x^3 + 2/3*a^2*d*x^3*e + a^2*d^2*x","A",0
254,1,106,0,0.170289," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, c^{2} x^{11} e + \frac{1}{9} \, c^{2} d x^{9} + \frac{2}{9} \, b c x^{9} e + \frac{2}{7} \, b c d x^{7} + \frac{1}{7} \, b^{2} x^{7} e + \frac{2}{7} \, a c x^{7} e + \frac{1}{5} \, b^{2} d x^{5} + \frac{2}{5} \, a c d x^{5} + \frac{2}{5} \, a b x^{5} e + \frac{2}{3} \, a b d x^{3} + \frac{1}{3} \, a^{2} x^{3} e + a^{2} d x"," ",0,"1/11*c^2*x^11*e + 1/9*c^2*d*x^9 + 2/9*b*c*x^9*e + 2/7*b*c*d*x^7 + 1/7*b^2*x^7*e + 2/7*a*c*x^7*e + 1/5*b^2*d*x^5 + 2/5*a*c*d*x^5 + 2/5*a*b*x^5*e + 2/3*a*b*d*x^3 + 1/3*a^2*x^3*e + a^2*d*x","A",0
255,1,43,0,0.143692," ","integrate((c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} + \frac{2}{5} \, a c x^{5} + \frac{2}{3} \, a b x^{3} + a^{2} x"," ",0,"1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*b^2*x^5 + 2/5*a*c*x^5 + 2/3*a*b*x^3 + a^2*x","A",0
256,1,185,0,0.162049," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d),x, algorithm=""giac"")","\frac{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{\sqrt{d}} + \frac{1}{105} \, {\left(15 \, c^{2} x^{7} e^{6} - 21 \, c^{2} d x^{5} e^{5} + 42 \, b c x^{5} e^{6} + 35 \, c^{2} d^{2} x^{3} e^{4} - 70 \, b c d x^{3} e^{5} - 105 \, c^{2} d^{3} x e^{3} + 35 \, b^{2} x^{3} e^{6} + 70 \, a c x^{3} e^{6} + 210 \, b c d^{2} x e^{4} - 105 \, b^{2} d x e^{5} - 210 \, a c d x e^{5} + 210 \, a b x e^{6}\right)} e^{\left(-7\right)}"," ",0,"(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/sqrt(d) + 1/105*(15*c^2*x^7*e^6 - 21*c^2*d*x^5*e^5 + 42*b*c*x^5*e^6 + 35*c^2*d^2*x^3*e^4 - 70*b*c*d*x^3*e^5 - 105*c^2*d^3*x*e^3 + 35*b^2*x^3*e^6 + 70*a*c*x^3*e^6 + 210*b*c*d^2*x*e^4 - 105*b^2*d*x*e^5 - 210*a*c*d*x*e^5 + 210*a*b*x*e^6)*e^(-7)","A",0
257,1,207,0,0.179757," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{1}{15} \, {\left(3 \, c^{2} x^{5} e^{8} - 10 \, c^{2} d x^{3} e^{7} + 10 \, b c x^{3} e^{8} + 45 \, c^{2} d^{2} x e^{6} - 60 \, b c d x e^{7} + 15 \, b^{2} x e^{8} + 30 \, a c x e^{8}\right)} e^{\left(-10\right)} - \frac{{\left(7 \, c^{2} d^{4} - 10 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + 6 \, a c d^{2} e^{2} - 2 \, a b d e^{3} - a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c^{2} d^{4} x - 2 \, b c d^{3} x e + b^{2} d^{2} x e^{2} + 2 \, a c d^{2} x e^{2} - 2 \, a b d x e^{3} + a^{2} x e^{4}\right)} e^{\left(-4\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"1/15*(3*c^2*x^5*e^8 - 10*c^2*d*x^3*e^7 + 10*b*c*x^3*e^8 + 45*c^2*d^2*x*e^6 - 60*b*c*d*x*e^7 + 15*b^2*x*e^8 + 30*a*c*x*e^8)*e^(-10) - 1/2*(7*c^2*d^4 - 10*b*c*d^3*e + 3*b^2*d^2*e^2 + 6*a*c*d^2*e^2 - 2*a*b*d*e^3 - a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(3/2) + 1/2*(c^2*d^4*x - 2*b*c*d^3*x*e + b^2*d^2*x*e^2 + 2*a*c*d^2*x*e^2 - 2*a*b*d*x*e^3 + a^2*x*e^4)*e^(-4)/((x^2*e + d)*d)","A",0
258,1,244,0,0.182113," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{2} x^{3} e^{6} - 9 \, c^{2} d x e^{5} + 6 \, b c x e^{6}\right)} e^{\left(-9\right)} + \frac{{\left(35 \, c^{2} d^{4} - 30 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + 6 \, a c d^{2} e^{2} + 2 \, a b d e^{3} + 3 \, a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{8 \, d^{\frac{5}{2}}} - \frac{{\left(13 \, c^{2} d^{4} x^{3} e - 18 \, b c d^{3} x^{3} e^{2} + 11 \, c^{2} d^{5} x + 5 \, b^{2} d^{2} x^{3} e^{3} + 10 \, a c d^{2} x^{3} e^{3} - 14 \, b c d^{4} x e - 2 \, a b d x^{3} e^{4} + 3 \, b^{2} d^{3} x e^{2} + 6 \, a c d^{3} x e^{2} - 3 \, a^{2} x^{3} e^{5} + 2 \, a b d^{2} x e^{3} - 5 \, a^{2} d x e^{4}\right)} e^{\left(-4\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{2}}"," ",0,"1/3*(c^2*x^3*e^6 - 9*c^2*d*x*e^5 + 6*b*c*x*e^6)*e^(-9) + 1/8*(35*c^2*d^4 - 30*b*c*d^3*e + 3*b^2*d^2*e^2 + 6*a*c*d^2*e^2 + 2*a*b*d*e^3 + 3*a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(5/2) - 1/8*(13*c^2*d^4*x^3*e - 18*b*c*d^3*x^3*e^2 + 11*c^2*d^5*x + 5*b^2*d^2*x^3*e^3 + 10*a*c*d^2*x^3*e^3 - 14*b*c*d^4*x*e - 2*a*b*d*x^3*e^4 + 3*b^2*d^3*x*e^2 + 6*a*c*d^3*x*e^2 - 3*a^2*x^3*e^5 + 2*a*b*d^2*x*e^3 - 5*a^2*d*x*e^4)*e^(-4)/((x^2*e + d)^2*d^2)","A",0
259,1,296,0,0.182422," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^4,x, algorithm=""giac"")","c^{2} x e^{\left(-4\right)} - \frac{{\left(35 \, c^{2} d^{4} - 10 \, b c d^{3} e - b^{2} d^{2} e^{2} - 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} - 5 \, a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{16 \, d^{\frac{7}{2}}} + \frac{{\left(87 \, c^{2} d^{4} x^{5} e^{2} - 66 \, b c d^{3} x^{5} e^{3} + 136 \, c^{2} d^{5} x^{3} e + 3 \, b^{2} d^{2} x^{5} e^{4} + 6 \, a c d^{2} x^{5} e^{4} - 80 \, b c d^{4} x^{3} e^{2} + 57 \, c^{2} d^{6} x + 6 \, a b d x^{5} e^{5} - 8 \, b^{2} d^{3} x^{3} e^{3} - 16 \, a c d^{3} x^{3} e^{3} - 30 \, b c d^{5} x e + 15 \, a^{2} x^{5} e^{6} + 16 \, a b d^{2} x^{3} e^{4} - 3 \, b^{2} d^{4} x e^{2} - 6 \, a c d^{4} x e^{2} + 40 \, a^{2} d x^{3} e^{5} - 6 \, a b d^{3} x e^{3} + 33 \, a^{2} d^{2} x e^{4}\right)} e^{\left(-4\right)}}{48 \, {\left(x^{2} e + d\right)}^{3} d^{3}}"," ",0,"c^2*x*e^(-4) - 1/16*(35*c^2*d^4 - 10*b*c*d^3*e - b^2*d^2*e^2 - 2*a*c*d^2*e^2 - 2*a*b*d*e^3 - 5*a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(7/2) + 1/48*(87*c^2*d^4*x^5*e^2 - 66*b*c*d^3*x^5*e^3 + 136*c^2*d^5*x^3*e + 3*b^2*d^2*x^5*e^4 + 6*a*c*d^2*x^5*e^4 - 80*b*c*d^4*x^3*e^2 + 57*c^2*d^6*x + 6*a*b*d*x^5*e^5 - 8*b^2*d^3*x^3*e^3 - 16*a*c*d^3*x^3*e^3 - 30*b*c*d^5*x*e + 15*a^2*x^5*e^6 + 16*a*b*d^2*x^3*e^4 - 3*b^2*d^4*x*e^2 - 6*a*c*d^4*x*e^2 + 40*a^2*d*x^3*e^5 - 6*a*b*d^3*x*e^3 + 33*a^2*d^2*x*e^4)*e^(-4)/((x^2*e + d)^3*d^3)","A",0
260,1,364,0,0.194936," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^5,x, algorithm=""giac"")","\frac{{\left(35 \, c^{2} d^{4} + 10 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + 6 \, a c d^{2} e^{2} + 10 \, a b d e^{3} + 35 \, a^{2} e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{128 \, d^{\frac{9}{2}}} - \frac{{\left(279 \, c^{2} d^{4} x^{7} e^{3} - 30 \, b c d^{3} x^{7} e^{4} + 511 \, c^{2} d^{5} x^{5} e^{2} - 9 \, b^{2} d^{2} x^{7} e^{5} - 18 \, a c d^{2} x^{7} e^{5} + 146 \, b c d^{4} x^{5} e^{3} + 385 \, c^{2} d^{6} x^{3} e - 30 \, a b d x^{7} e^{6} - 33 \, b^{2} d^{3} x^{5} e^{4} - 66 \, a c d^{3} x^{5} e^{4} + 110 \, b c d^{5} x^{3} e^{2} + 105 \, c^{2} d^{7} x - 105 \, a^{2} x^{7} e^{7} - 110 \, a b d^{2} x^{5} e^{5} + 33 \, b^{2} d^{4} x^{3} e^{3} + 66 \, a c d^{4} x^{3} e^{3} + 30 \, b c d^{6} x e - 385 \, a^{2} d x^{5} e^{6} - 146 \, a b d^{3} x^{3} e^{4} + 9 \, b^{2} d^{5} x e^{2} + 18 \, a c d^{5} x e^{2} - 511 \, a^{2} d^{2} x^{3} e^{5} + 30 \, a b d^{4} x e^{3} - 279 \, a^{2} d^{3} x e^{4}\right)} e^{\left(-4\right)}}{384 \, {\left(x^{2} e + d\right)}^{4} d^{4}}"," ",0,"1/128*(35*c^2*d^4 + 10*b*c*d^3*e + 3*b^2*d^2*e^2 + 6*a*c*d^2*e^2 + 10*a*b*d*e^3 + 35*a^2*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/d^(9/2) - 1/384*(279*c^2*d^4*x^7*e^3 - 30*b*c*d^3*x^7*e^4 + 511*c^2*d^5*x^5*e^2 - 9*b^2*d^2*x^7*e^5 - 18*a*c*d^2*x^7*e^5 + 146*b*c*d^4*x^5*e^3 + 385*c^2*d^6*x^3*e - 30*a*b*d*x^7*e^6 - 33*b^2*d^3*x^5*e^4 - 66*a*c*d^3*x^5*e^4 + 110*b*c*d^5*x^3*e^2 + 105*c^2*d^7*x - 105*a^2*x^7*e^7 - 110*a*b*d^2*x^5*e^5 + 33*b^2*d^4*x^3*e^3 + 66*a*c*d^4*x^3*e^3 + 30*b*c*d^6*x*e - 385*a^2*d*x^5*e^6 - 146*a*b*d^3*x^3*e^4 + 9*b^2*d^5*x*e^2 + 18*a*c*d^5*x*e^2 - 511*a^2*d^2*x^3*e^5 + 30*a*b*d^4*x*e^3 - 279*a^2*d^3*x*e^4)*e^(-4)/((x^2*e + d)^4*d^4)","A",0
261,1,75,0,0.162493," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""giac"")","c x e^{\left(-2\right)} - \frac{{\left(3 \, c d^{2} - b d e - a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c d^{2} x - b d x e + a x e^{2}\right)} e^{\left(-2\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"c*x*e^(-2) - 1/2*(3*c*d^2 - b*d*e - a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(3/2) + 1/2*(c*d^2*x - b*d*x*e + a*x*e^2)*e^(-2)/((x^2*e + d)*d)","A",0
262,1,75,0,0.153948," ","integrate((a+x^2*(c*x^2+b))/(e*x^2+d)^2,x, algorithm=""giac"")","c x e^{\left(-2\right)} - \frac{{\left(3 \, c d^{2} - b d e - a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c d^{2} x - b d x e + a x e^{2}\right)} e^{\left(-2\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"c*x*e^(-2) - 1/2*(3*c*d^2 - b*d*e - a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(3/2) + 1/2*(c*d^2*x - b*d*x*e + a*x*e^2)*e^(-2)/((x^2*e + d)*d)","A",0
263,1,9285,0,1.628481," ","integrate((e*x^2+d)^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(4 \, {\left(2 \, b^{4} c^{5} - 16 \, a b^{2} c^{6} + 32 \, a^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{6}\right)} c^{2} d^{3} e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 2 \, b^{4} c^{6} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{7} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{7} - 16 \, a b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{8} + 32 \, a^{2} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{7}\right)} d^{4} {\left| c \right|} - 6 \, {\left(2 \, b^{5} c^{4} - 16 \, a b^{3} c^{5} + 32 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} c^{2} d^{2} e^{2} + 2 \, {\left(2 \, b^{3} c^{8} - 8 \, a b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{8}\right)} d^{4} + 4 \, {\left(2 \, b^{6} c^{3} - 18 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 32 \, a^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} c^{2} d e^{3} - 12 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 2 \, a b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 16 \, a^{2} b^{2} c^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} + 32 \, a^{3} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6}\right)} d^{2} {\left| c \right|} e^{2} - 4 \, {\left(2 \, b^{4} c^{7} - 8 \, a b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{7}\right)} d^{3} e - {\left(2 \, b^{7} c^{2} - 20 \, a b^{5} c^{3} + 64 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} c^{2} e^{4} + 8 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, a b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 16 \, a^{2} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + 32 \, a^{3} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} d {\left| c \right|} e^{3} + 6 \, {\left(2 \, b^{5} c^{6} - 12 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{7}\right)} d^{2} e^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, a b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 18 \, a^{2} b^{4} c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 48 \, a^{3} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 32 \, a^{4} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} {\left| c \right|} e^{4} - 4 \, {\left(2 \, b^{6} c^{5} - 14 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6}\right)} d e^{3} + {\left(2 \, b^{7} c^{4} - 16 \, a b^{5} c^{5} + 36 \, a^{2} b^{3} c^{6} - 16 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{5} + \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{8 \, {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} c^{2}} - \frac{{\left(4 \, {\left(2 \, b^{4} c^{5} - 16 \, a b^{2} c^{6} + 32 \, a^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{6}\right)} c^{2} d^{3} e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} - 2 \, b^{4} c^{6} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{7} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{7} + 16 \, a b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{8} - 32 \, a^{2} c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{7}\right)} d^{4} {\left| c \right|} - 6 \, {\left(2 \, b^{5} c^{4} - 16 \, a b^{3} c^{5} + 32 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} c^{2} d^{2} e^{2} + 2 \, {\left(2 \, b^{3} c^{8} - 8 \, a b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{8}\right)} d^{4} + 4 \, {\left(2 \, b^{6} c^{3} - 18 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 32 \, a^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} c^{2} d e^{3} + 12 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, a b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} + 16 \, a^{2} b^{2} c^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} - 32 \, a^{3} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6}\right)} d^{2} {\left| c \right|} e^{2} - 4 \, {\left(2 \, b^{4} c^{7} - 8 \, a b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{7}\right)} d^{3} e - {\left(2 \, b^{7} c^{2} - 20 \, a b^{5} c^{3} + 64 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} c^{2} e^{4} - 8 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 2 \, a b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 16 \, a^{2} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 32 \, a^{3} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} d {\left| c \right|} e^{3} + 6 \, {\left(2 \, b^{5} c^{6} - 12 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{7}\right)} d^{2} e^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 2 \, a b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 18 \, a^{2} b^{4} c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 48 \, a^{3} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 32 \, a^{4} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} {\left| c \right|} e^{4} - 4 \, {\left(2 \, b^{6} c^{5} - 14 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6}\right)} d e^{3} + {\left(2 \, b^{7} c^{4} - 16 \, a b^{5} c^{5} + 36 \, a^{2} b^{3} c^{6} - 16 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{5} - \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{8 \, {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} c^{2}} + \frac{3 \, c^{4} x^{5} e^{4} + 20 \, c^{4} d x^{3} e^{3} - 5 \, b c^{3} x^{3} e^{4} + 90 \, c^{4} d^{2} x e^{2} - 60 \, b c^{3} d x e^{3} + 15 \, b^{2} c^{2} x e^{4} - 15 \, a c^{3} x e^{4}}{15 \, c^{5}}"," ",0,"1/8*(4*(2*b^4*c^5 - 16*a*b^2*c^6 + 32*a^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^6 - 2*(b^2 - 4*a*c)*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6)*c^2*d^3*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*b^4*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - 16*a*b^2*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^8 + 32*a^2*c^8 - 2*(b^2 - 4*a*c)*b^2*c^6 + 8*(b^2 - 4*a*c)*a*c^7)*d^4*abs(c) - 6*(2*b^5*c^4 - 16*a*b^3*c^5 + 32*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*c^2*d^2*e^2 + 2*(2*b^3*c^8 - 8*a*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^8 - 2*(b^2 - 4*a*c)*b*c^8)*d^4 + 4*(2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*c^2*d*e^3 - 12*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*a*b^4*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 16*a^2*b^2*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 32*a^3*c^7 - 2*(b^2 - 4*a*c)*a*b^2*c^5 + 8*(b^2 - 4*a*c)*a^2*c^6)*d^2*abs(c)*e^2 - 4*(2*b^4*c^7 - 8*a*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - 2*(b^2 - 4*a*c)*b^2*c^7)*d^3*e - (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*c^2*e^4 + 8*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 32*a^3*b*c^6 - 2*(b^2 - 4*a*c)*a*b^3*c^4 + 8*(b^2 - 4*a*c)*a^2*b*c^5)*d*abs(c)*e^3 + 6*(2*b^5*c^6 - 12*a*b^3*c^7 + 16*a^2*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^3*c^6 + 4*(b^2 - 4*a*c)*a*b*c^7)*d^2*e^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 32*a^4*c^6 - 2*(b^2 - 4*a*c)*a*b^4*c^3 + 10*(b^2 - 4*a*c)*a^2*b^2*c^4 - 8*(b^2 - 4*a*c)*a^3*c^5)*abs(c)*e^4 - 4*(2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*d*e^3 + (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*e^4)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 + sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) - 1/8*(4*(2*b^4*c^5 - 16*a*b^2*c^6 + 32*a^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^6 - 2*(b^2 - 4*a*c)*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6)*c^2*d^3*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 - 2*b^4*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^7 + 16*a*b^2*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^8 - 32*a^2*c^8 + 2*(b^2 - 4*a*c)*b^2*c^6 - 8*(b^2 - 4*a*c)*a*c^7)*d^4*abs(c) - 6*(2*b^5*c^4 - 16*a*b^3*c^5 + 32*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*c^2*d^2*e^2 + 2*(2*b^3*c^8 - 8*a*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^8 - 2*(b^2 - 4*a*c)*b*c^8)*d^4 + 4*(2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*c^2*d*e^3 + 12*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*a*b^4*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 16*a^2*b^2*c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 - 32*a^3*c^7 + 2*(b^2 - 4*a*c)*a*b^2*c^5 - 8*(b^2 - 4*a*c)*a^2*c^6)*d^2*abs(c)*e^2 - 4*(2*b^4*c^7 - 8*a*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^7 - 2*(b^2 - 4*a*c)*b^2*c^7)*d^3*e - (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*c^2*e^4 - 8*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 32*a^3*b*c^6 + 2*(b^2 - 4*a*c)*a*b^3*c^4 - 8*(b^2 - 4*a*c)*a^2*b*c^5)*d*abs(c)*e^3 + 6*(2*b^5*c^6 - 12*a*b^3*c^7 + 16*a^2*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^3*c^6 + 4*(b^2 - 4*a*c)*a*b*c^7)*d^2*e^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 32*a^4*c^6 + 2*(b^2 - 4*a*c)*a*b^4*c^3 - 10*(b^2 - 4*a*c)*a^2*b^2*c^4 + 8*(b^2 - 4*a*c)*a^3*c^5)*abs(c)*e^4 - 4*(2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*d*e^3 + (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*e^4)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 - sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) + 1/15*(3*c^4*x^5*e^4 + 20*c^4*d*x^3*e^3 - 5*b*c^3*x^3*e^4 + 90*c^4*d^2*x*e^2 - 60*b*c^3*d*x*e^3 + 15*b^2*c^2*x*e^4 - 15*a*c^3*x*e^4)/c^5","B",0
264,1,6407,0,1.354922," ","integrate((e*x^2+d)^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(3 \, {\left(2 \, b^{4} c^{4} - 16 \, a b^{2} c^{5} + 32 \, a^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} c^{2} d^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 16 \, a b^{2} c^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{7} + 32 \, a^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{6}\right)} d^{3} {\left| c \right|} - 3 \, {\left(2 \, b^{5} c^{3} - 16 \, a b^{3} c^{4} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} c^{2} d e^{2} + 2 \, {\left(2 \, b^{3} c^{7} - 8 \, a b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{7}\right)} d^{3} + {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} c^{2} e^{3} - 6 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 32 \, a^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} d {\left| c \right|} e^{2} - 3 \, {\left(2 \, b^{4} c^{6} - 8 \, a b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6}\right)} d^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} {\left| c \right|} e^{3} + 3 \, {\left(2 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} d e^{2} - {\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} + \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} - \frac{{\left(3 \, {\left(2 \, b^{4} c^{4} - 16 \, a b^{2} c^{5} + 32 \, a^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} c^{2} d^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - 2 \, b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} + 16 \, a b^{2} c^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{7} - 32 \, a^{2} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{6}\right)} d^{3} {\left| c \right|} - 3 \, {\left(2 \, b^{5} c^{3} - 16 \, a b^{3} c^{4} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} c^{2} d e^{2} + 2 \, {\left(2 \, b^{3} c^{7} - 8 \, a b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{7}\right)} d^{3} + {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} c^{2} e^{3} + 6 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 32 \, a^{3} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} d {\left| c \right|} e^{2} - 3 \, {\left(2 \, b^{4} c^{6} - 8 \, a b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6}\right)} d^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} {\left| c \right|} e^{3} + 3 \, {\left(2 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} d e^{2} - {\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} - \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{c^{2} x^{3} e^{3} + 9 \, c^{2} d x e^{2} - 3 \, b c x e^{3}}{3 \, c^{3}}"," ",0,"1/8*(3*(2*b^4*c^4 - 16*a*b^2*c^5 + 32*a^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*c^2*d^2*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 2*b^4*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 16*a*b^2*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^7 + 32*a^2*c^7 - 2*(b^2 - 4*a*c)*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6)*d^3*abs(c) - 3*(2*b^5*c^3 - 16*a*b^3*c^4 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*c^2*d*e^2 + 2*(2*b^3*c^7 - 8*a*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^7 - 2*(b^2 - 4*a*c)*b*c^7)*d^3 + (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*c^2*e^3 - 6*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*a*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 16*a^2*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 32*a^3*c^6 - 2*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*d*abs(c)*e^2 - 3*(2*b^4*c^6 - 8*a*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 2*(b^2 - 4*a*c)*b^2*c^6)*d^2*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 32*a^3*b*c^5 - 2*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*abs(c)*e^3 + 3*(2*b^5*c^5 - 12*a*b^3*c^6 + 16*a^2*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*d*e^2 - (2*b^6*c^4 - 14*a*b^4*c^5 + 24*a^2*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*e^3)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 + sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) - 1/8*(3*(2*b^4*c^4 - 16*a*b^2*c^5 + 32*a^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*c^2*d^2*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - 2*b^4*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^6 + 16*a*b^2*c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^7 - 32*a^2*c^7 + 2*(b^2 - 4*a*c)*b^2*c^5 - 8*(b^2 - 4*a*c)*a*c^6)*d^3*abs(c) - 3*(2*b^5*c^3 - 16*a*b^3*c^4 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*c^2*d*e^2 + 2*(2*b^3*c^7 - 8*a*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^7 - 2*(b^2 - 4*a*c)*b*c^7)*d^3 + (2*b^6*c^2 - 18*a*b^4*c^3 + 48*a^2*b^2*c^4 - 32*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*c^2*e^3 + 6*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 2*a*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 16*a^2*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 32*a^3*c^6 + 2*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*d*abs(c)*e^2 - 3*(2*b^4*c^6 - 8*a*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 2*(b^2 - 4*a*c)*b^2*c^6)*d^2*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 2*a*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 16*a^2*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 32*a^3*b*c^5 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*abs(c)*e^3 + 3*(2*b^5*c^5 - 12*a*b^3*c^6 + 16*a^2*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*d*e^2 - (2*b^6*c^4 - 14*a*b^4*c^5 + 24*a^2*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*e^3)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 - sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/3*(c^2*x^3*e^3 + 9*c^2*d*x*e^2 - 3*b*c*x*e^3)/c^3","B",0
265,1,4107,0,1.135565," ","integrate((e*x^2+d)^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{x e^{2}}{c} + \frac{{\left(2 \, {\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} d e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 16 \, a b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{6} + 32 \, a^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d^{2} {\left| c \right|} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} e^{2} + 2 \, {\left(2 \, b^{3} c^{6} - 8 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{6}\right)} d^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|} e^{2} - 2 \, {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} d e + {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} - \frac{{\left(2 \, {\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} d e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 2 \, b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 16 \, a b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 32 \, a^{2} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d^{2} {\left| c \right|} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} e^{2} + 2 \, {\left(2 \, b^{3} c^{6} - 8 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{6}\right)} d^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left| c \right|} e^{2} - 2 \, {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} d e + {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"x*e^2/c + 1/8*(2*(2*b^4*c^3 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2*d*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 16*a*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^6 + 32*a^2*c^6 - 2*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*d^2*abs(c) - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*e^2 + 2*(2*b^3*c^6 - 8*a*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^6 - 2*(b^2 - 4*a*c)*b*c^6)*d^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 2*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c)*e^2 - 2*(2*b^4*c^5 - 8*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5)*d*e + (2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*e^2)*arctan(2*sqrt(1/2)*x/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/8*(2*(2*b^4*c^3 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2*d*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 2*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 16*a*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^6 - 32*a^2*c^6 + 2*(b^2 - 4*a*c)*b^2*c^4 - 8*(b^2 - 4*a*c)*a*c^5)*d^2*abs(c) - (2*b^5*c^2 - 16*a*b^3*c^3 + 32*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*e^2 + 2*(2*b^3*c^6 - 8*a*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^6 - 2*(b^2 - 4*a*c)*b*c^6)*d^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 2*a*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 + 2*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*abs(c)*e^2 - 2*(2*b^4*c^5 - 8*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5)*d*e + (2*b^5*c^4 - 12*a*b^3*c^5 + 16*a^2*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*e^2)*arctan(2*sqrt(1/2)*x/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
266,1,1402,0,0.871982," ","integrate((e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} d - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} d + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/4*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 + 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*d - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/4*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*d + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*e)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
267,1,1024,0,0.599130," ","integrate(1/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left| c \right|}}"," ",0,"1/4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c)) + 1/4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 16*a*b^2*c^2 - 2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 + 32*a^2*c^3 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((a*b^4 - 8*a^2*b^2*c - 2*a*b^3*c + 16*a^3*c^2 + 8*a^2*b*c^2 + a*b^2*c^2 - 4*a^2*c^3)*abs(c))","B",0
268,1,7650,0,2.534555," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(2 \, {\left(2 \, b^{3} c^{5} - 8 \, a b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{5}\right)} d^{5} - 5 \, {\left(2 \, b^{4} c^{4} - 8 \, a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4}\right)} d^{4} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 16 \, a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{5} - 32 \, a^{2} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} + 4 \, {\left(2 \, b^{5} c^{3} - 6 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} d^{3} e^{2} - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 2 \, b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 16 \, a b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 32 \, a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\left(2 \, b^{6} c^{2} + 4 \, a b^{4} c^{3} - 48 \, a^{2} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 7 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 14 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} - {\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} e + 2 \, {\left(2 \, a b^{5} c^{2} - 6 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} d e^{4} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} e^{3} - {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} + \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} - 2 \, a b^{3} c^{3} + 16 \, a^{3} c^{4} + 8 \, a^{2} b c^{4} + a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, a^{3} b c^{3} + 8 \, a^{2} b^{2} c^{3} + a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c - 2 \, a b^{5} c + 4 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, a^{4} b c^{2} + 8 \, a^{3} b^{2} c^{2} + a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}} - \frac{{\left(2 \, {\left(2 \, b^{3} c^{5} - 8 \, a b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{5}\right)} d^{5} - 5 \, {\left(2 \, b^{4} c^{4} - 8 \, a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4}\right)} d^{4} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 2 \, b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 16 \, a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{5} + 32 \, a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} + 4 \, {\left(2 \, b^{5} c^{3} - 6 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} d^{3} e^{2} + 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 2 \, b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 16 \, a b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 32 \, a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\left(2 \, b^{6} c^{2} + 4 \, a b^{4} c^{3} - 48 \, a^{2} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} d^{2} e^{3} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 7 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 14 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} - {\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} e + 2 \, {\left(2 \, a b^{5} c^{2} - 6 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} d e^{4} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} e^{3} - {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} - \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} - 2 \, a b^{3} c^{3} + 16 \, a^{3} c^{4} + 8 \, a^{2} b c^{4} + a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, a^{3} b c^{3} + 8 \, a^{2} b^{2} c^{3} + a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c - 2 \, a b^{5} c + 4 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, a^{4} b c^{2} + 8 \, a^{3} b^{2} c^{2} + a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{3}{2}}}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{d}}"," ",0,"1/8*(2*(2*b^3*c^5 - 8*a*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^5 - 2*(b^2 - 4*a*c)*b*c^5)*d^5 - 5*(2*b^4*c^4 - 8*a*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - 2*(b^2 - 4*a*c)*b^2*c^4)*d^4*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 2*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 + 16*a*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^5 - 32*a^2*c^5 + 2*(b^2 - 4*a*c)*b^2*c^3 - 8*(b^2 - 4*a*c)*a*c^4)*d^3*abs(c*d^2 - b*d*e + a*e^2) + 4*(2*b^5*c^3 - 6*a*b^3*c^4 - 8*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b*c^4)*d^3*e^2 - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 16*a*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 32*a^2*b*c^4 + 2*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*d^2*abs(c*d^2 - b*d*e + a*e^2)*e - (2*b^6*c^2 + 4*a*b^4*c^3 - 48*a^2*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^4*c^2 - 12*(b^2 - 4*a*c)*a*b^2*c^3)*d^2*e^3 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 7*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 2*b^6*c + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 14*a*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 16*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 32*a^3*c^4 + 2*(b^2 - 4*a*c)*b^4*c - 6*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 - (2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*(c*d^2 - b*d*e + a*e^2)^2*e + 2*(2*a*b^5*c^2 - 6*a^2*b^3*c^3 - 8*a^3*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^3)*d*e^4 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(c*d^2 - b*d*e + a*e^2)*e^3 - (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 + sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((a*b^4*c^2 - 8*a^2*b^2*c^3 - 2*a*b^3*c^3 + 16*a^3*c^4 + 8*a^2*b*c^4 + a*b^2*c^4 - 4*a^2*c^5)*d^4*abs(c*d^2 - b*d*e + a*e^2)*abs(c) - 2*(a*b^5*c - 8*a^2*b^3*c^2 - 2*a*b^4*c^2 + 16*a^3*b*c^3 + 8*a^2*b^2*c^3 + a*b^3*c^3 - 4*a^2*b*c^4)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6 - 6*a^2*b^4*c - 2*a*b^5*c + 4*a^2*b^3*c^2 + a*b^4*c^2 + 32*a^4*c^3 + 16*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c - 2*a^2*b^4*c + 16*a^4*b*c^2 + 8*a^3*b^2*c^2 + a^2*b^3*c^2 - 4*a^3*b*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^4) - 1/8*(2*(2*b^3*c^5 - 8*a*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^5 - 2*(b^2 - 4*a*c)*b*c^5)*d^5 - 5*(2*b^4*c^4 - 8*a*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - 2*(b^2 - 4*a*c)*b^2*c^4)*d^4*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 2*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - 16*a*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^5 + 32*a^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*d^3*abs(c*d^2 - b*d*e + a*e^2) + 4*(2*b^5*c^3 - 6*a*b^3*c^4 - 8*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b*c^4)*d^3*e^2 + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 16*a*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + 32*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*d^2*abs(c*d^2 - b*d*e + a*e^2)*e - (2*b^6*c^2 + 4*a*b^4*c^3 - 48*a^2*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^4*c^2 - 12*(b^2 - 4*a*c)*a*b^2*c^3)*d^2*e^3 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 7*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c + 2*b^6*c + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 14*a*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 16*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 32*a^3*c^4 - 2*(b^2 - 4*a*c)*b^4*c + 6*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 - (2*b^4*c^2 - 16*a*b^2*c^3 + 32*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*(c*d^2 - b*d*e + a*e^2)^2*e + 2*(2*a*b^5*c^2 - 6*a^2*b^3*c^3 - 8*a^3*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^3)*d*e^4 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*a*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 16*a^2*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(c*d^2 - b*d*e + a*e^2)*e^3 - (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 - sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((a*b^4*c^2 - 8*a^2*b^2*c^3 - 2*a*b^3*c^3 + 16*a^3*c^4 + 8*a^2*b*c^4 + a*b^2*c^4 - 4*a^2*c^5)*d^4*abs(c*d^2 - b*d*e + a*e^2)*abs(c) - 2*(a*b^5*c - 8*a^2*b^3*c^2 - 2*a*b^4*c^2 + 16*a^3*b*c^3 + 8*a^2*b^2*c^3 + a*b^3*c^3 - 4*a^2*b*c^4)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6 - 6*a^2*b^4*c - 2*a*b^5*c + 4*a^2*b^3*c^2 + a*b^4*c^2 + 32*a^4*c^3 + 16*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c - 2*a^2*b^4*c + 16*a^4*b*c^2 + 8*a^3*b^2*c^2 + a^2*b^3*c^2 - 4*a^3*b*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(3/2)/((c*d^2 - b*d*e + a*e^2)*sqrt(d))","B",0
269,1,13225,0,2.510069," ","integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(5 \, c d^{2} e^{2} - 3 \, b d e^{3} + a e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e + b^{2} d^{3} e^{2} + 2 \, a c d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} \sqrt{d}} - \frac{2 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - b^{7} c^{3} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 11 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 12 \, a b^{5} c^{4} + 3 \, b^{6} c^{4} + 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 88 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 48 \, a^{2} b^{3} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 28 \, a b^{4} c^{5} + 5 \, b^{5} c^{5} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 176 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + 64 \, a^{3} b c^{6} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} + 80 \, a^{2} b^{2} c^{6} - 7 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} - 24 \, a b^{3} c^{6} - 11 \, b^{4} c^{6} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} - 64 \, a^{3} c^{7} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{7} + 16 \, a^{2} b c^{7} - 8 \, a b^{2} c^{7} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{8} + 80 \, a^{2} c^{8} + 16 \, a b c^{8} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + \sqrt{b^{2} - 4 \, a c} b^{6} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 12 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} - 5 \, \sqrt{b^{2} - 4 \, a c} b^{5} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 48 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 40 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} + 7 \, \sqrt{b^{2} - 4 \, a c} b^{4} c^{5} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 64 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 80 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 56 \, \sqrt{b^{2} - 4 \, a c} a b^{2} c^{6} - 3 \, \sqrt{b^{2} - 4 \, a c} b^{3} c^{6} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{7} + 112 \, \sqrt{b^{2} - 4 \, a c} a^{2} c^{7} + 60 \, \sqrt{b^{2} - 4 \, a c} a b c^{7} - 24 \, \sqrt{b^{2} - 4 \, a c} a c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - 12 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6} + 48 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6} + 14 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{7}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{2} d^{4} - 2 \, b^{2} c d^{3} e + b^{3} d^{2} e^{2} + 2 \, a b c d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4} + \sqrt{{\left(b c^{2} d^{4} - 2 \, b^{2} c d^{3} e + b^{3} d^{2} e^{2} + 2 \, a b c d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)}^{2} - 4 \, {\left(a c^{2} d^{4} - 2 \, a b c d^{3} e + a b^{2} d^{2} e^{2} + 2 \, a^{2} c d^{2} e^{2} - 2 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right)}{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} - 2 \, b^{8} c^{2} + 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 60 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 7 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 16 \, a b^{6} c^{3} + 8 \, b^{7} c^{3} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 240 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 84 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 32 \, a b^{5} c^{4} - 6 \, b^{6} c^{4} + 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 336 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 256 \, a^{3} b^{2} c^{5} + 72 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 128 \, a^{2} b^{3} c^{5} - 24 \, a b^{4} c^{5} - 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 512 \, a^{4} c^{6} - 240 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + 512 \, a^{3} b c^{6} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} + 224 \, a^{2} b^{2} c^{6} + 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} - 128 \, a^{3} c^{7} - 16 \, a b^{2} c^{7} + 64 \, a^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 72 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 24 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 192 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} + 32 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 384 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 128 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} + 8 \, \sqrt{b^{2} - 4 \, a c} a b^{2} c^{6} + 96 \, \sqrt{b^{2} - 4 \, a c} a^{2} c^{7} - 16 \, \sqrt{b^{2} - 4 \, a c} a b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{2} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{3} + 96 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 64 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5} - 48 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} + 96 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6} + 64 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} d^{2} {\left| c \right|} + 4 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} + 4 \, a b^{7} c^{2} - 36 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 48 \, a^{2} b^{5} c^{3} - 10 \, a b^{6} c^{3} + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 192 \, a^{3} b^{3} c^{4} - \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 56 \, a^{2} b^{4} c^{4} + 8 \, a b^{5} c^{4} - 192 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 256 \, a^{4} b c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 32 \, a^{3} b^{2} c^{5} + 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 6 \, a b^{4} c^{5} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 384 \, a^{4} c^{6} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 128 \, a^{3} b c^{6} + 16 \, a^{2} b^{2} c^{6} + 8 \, a b^{3} c^{6} + 32 \, a^{3} c^{7} - 32 \, a^{2} b c^{7} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 4 \, \sqrt{b^{2} - 4 \, a c} a b^{6} c^{2} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 48 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{4} c^{3} - 10 \, \sqrt{b^{2} - 4 \, a c} a b^{5} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 192 \, \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 80 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} c^{4} + 16 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 256 \, \sqrt{b^{2} - 4 \, a c} a^{4} c^{5} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 160 \, \sqrt{b^{2} - 4 \, a c} a^{3} b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 96 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} - 18 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 128 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} + 40 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} + 8 \, \sqrt{b^{2} - 4 \, a c} a b^{2} c^{6} - 16 \, \sqrt{b^{2} - 4 \, a c} a^{2} c^{7} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6}\right)} d {\left| c \right|} e - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c + 6 \, a b^{8} c + 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 80 \, a^{2} b^{6} c^{2} - 12 \, a b^{7} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 384 \, a^{3} b^{4} c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 80 \, a^{2} b^{5} c^{3} + 10 \, a b^{6} c^{3} + 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 768 \, a^{4} b^{2} c^{4} + 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 64 \, a^{3} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 24 \, a^{2} b^{4} c^{4} - 12 \, a b^{5} c^{4} - 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 512 \, a^{5} c^{5} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 256 \, a^{4} b c^{5} - 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 32 \, a^{3} b^{2} c^{5} + 32 \, a^{2} b^{3} c^{5} + 16 \, a b^{4} c^{5} + 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 128 \, a^{4} c^{6} + 64 \, a^{3} b c^{6} - 80 \, a^{2} b^{2} c^{6} + 64 \, a^{3} c^{7} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 8 \, \sqrt{b^{2} - 4 \, a c} a b^{7} c + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 96 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{5} c^{2} - 20 \, \sqrt{b^{2} - 4 \, a c} a b^{6} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 384 \, \sqrt{b^{2} - 4 \, a c} a^{3} b^{3} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 136 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{4} c^{3} + 32 \, \sqrt{b^{2} - 4 \, a c} a b^{5} c^{3} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, \sqrt{b^{2} - 4 \, a c} a^{4} b c^{4} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 128 \, \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 160 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} c^{4} - 36 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 384 \, \sqrt{b^{2} - 4 \, a c} a^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 128 \, \sqrt{b^{2} - 4 \, a c} a^{3} b c^{5} + 88 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} + 16 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} + 96 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} - 48 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{2} + 96 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 96 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} {\left| c \right|} e^{2}} + \frac{2 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + b^{7} c^{3} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 11 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, a b^{5} c^{4} - 3 \, b^{6} c^{4} + 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 88 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 48 \, a^{2} b^{3} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 28 \, a b^{4} c^{5} - 5 \, b^{5} c^{5} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 176 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 64 \, a^{3} b c^{6} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 80 \, a^{2} b^{2} c^{6} - 7 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 24 \, a b^{3} c^{6} + 11 \, b^{4} c^{6} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} + 64 \, a^{3} c^{7} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{7} - 16 \, a^{2} b c^{7} + 8 \, a b^{2} c^{7} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{8} - 80 \, a^{2} c^{8} - 16 \, a b c^{8} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + \sqrt{b^{2} - 4 \, a c} b^{6} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 12 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} - 5 \, \sqrt{b^{2} - 4 \, a c} b^{5} c^{4} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 48 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 40 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} + 7 \, \sqrt{b^{2} - 4 \, a c} b^{4} c^{5} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 64 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 80 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 56 \, \sqrt{b^{2} - 4 \, a c} a b^{2} c^{6} - 3 \, \sqrt{b^{2} - 4 \, a c} b^{3} c^{6} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{7} + 112 \, \sqrt{b^{2} - 4 \, a c} a^{2} c^{7} + 60 \, \sqrt{b^{2} - 4 \, a c} a b c^{7} - 24 \, \sqrt{b^{2} - 4 \, a c} a c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} + 12 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6} - 48 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6} - 14 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{7}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{2} d^{4} - 2 \, b^{2} c d^{3} e + b^{3} d^{2} e^{2} + 2 \, a b c d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4} - \sqrt{{\left(b c^{2} d^{4} - 2 \, b^{2} c d^{3} e + b^{3} d^{2} e^{2} + 2 \, a b c d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)}^{2} - 4 \, {\left(a c^{2} d^{4} - 2 \, a b c d^{3} e + a b^{2} d^{2} e^{2} + 2 \, a^{2} c d^{2} e^{2} - 2 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right)}{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 2 \, b^{8} c^{2} + 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 60 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 7 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 16 \, a b^{6} c^{3} - 8 \, b^{7} c^{3} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 240 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 84 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 32 \, a b^{5} c^{4} + 6 \, b^{6} c^{4} + 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 336 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 256 \, a^{3} b^{2} c^{5} + 72 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 128 \, a^{2} b^{3} c^{5} + 24 \, a b^{4} c^{5} - 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 512 \, a^{4} c^{6} - 240 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 512 \, a^{3} b c^{6} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 224 \, a^{2} b^{2} c^{6} + 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} + 128 \, a^{3} c^{7} + 16 \, a b^{2} c^{7} - 64 \, a^{2} c^{8} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 72 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 24 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 192 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} + 32 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 384 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 128 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} + 8 \, \sqrt{b^{2} - 4 \, a c} a b^{2} c^{6} + 96 \, \sqrt{b^{2} - 4 \, a c} a^{2} c^{7} - 16 \, \sqrt{b^{2} - 4 \, a c} a b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{2} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 64 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5} + 48 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6} - 64 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} d^{2} {\left| c \right|} + 4 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 4 \, a b^{7} c^{2} - 36 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 48 \, a^{2} b^{5} c^{3} + 10 \, a b^{6} c^{3} + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 192 \, a^{3} b^{3} c^{4} - \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 56 \, a^{2} b^{4} c^{4} - 8 \, a b^{5} c^{4} - 192 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 256 \, a^{4} b c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 32 \, a^{3} b^{2} c^{5} + 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 6 \, a b^{4} c^{5} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 384 \, a^{4} c^{6} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + 128 \, a^{3} b c^{6} - 16 \, a^{2} b^{2} c^{6} - 8 \, a b^{3} c^{6} - 32 \, a^{3} c^{7} + 32 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 4 \, \sqrt{b^{2} - 4 \, a c} a b^{6} c^{2} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 48 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{4} c^{3} - 10 \, \sqrt{b^{2} - 4 \, a c} a b^{5} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 192 \, \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 80 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} c^{4} + 16 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 256 \, \sqrt{b^{2} - 4 \, a c} a^{4} c^{5} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 160 \, \sqrt{b^{2} - 4 \, a c} a^{3} b c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 96 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} - 18 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 128 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} + 40 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} + 8 \, \sqrt{b^{2} - 4 \, a c} a b^{2} c^{6} - 16 \, \sqrt{b^{2} - 4 \, a c} a^{2} c^{7} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6}\right)} d {\left| c \right|} e - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c - 6 \, a b^{8} c + 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} + 80 \, a^{2} b^{6} c^{2} + 12 \, a b^{7} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 384 \, a^{3} b^{4} c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 80 \, a^{2} b^{5} c^{3} - 10 \, a b^{6} c^{3} + 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 768 \, a^{4} b^{2} c^{4} + 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 64 \, a^{3} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 24 \, a^{2} b^{4} c^{4} + 12 \, a b^{5} c^{4} - 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 512 \, a^{5} c^{5} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 256 \, a^{4} b c^{5} - 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 32 \, a^{3} b^{2} c^{5} - 32 \, a^{2} b^{3} c^{5} - 16 \, a b^{4} c^{5} + 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 128 \, a^{4} c^{6} - 64 \, a^{3} b c^{6} + 80 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 8 \, \sqrt{b^{2} - 4 \, a c} a b^{7} c - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 96 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{5} c^{2} - 20 \, \sqrt{b^{2} - 4 \, a c} a b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 384 \, \sqrt{b^{2} - 4 \, a c} a^{3} b^{3} c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 136 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{4} c^{3} + 32 \, \sqrt{b^{2} - 4 \, a c} a b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, \sqrt{b^{2} - 4 \, a c} a^{4} b c^{4} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 128 \, \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 160 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} c^{4} - 36 \, \sqrt{b^{2} - 4 \, a c} a b^{4} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 384 \, \sqrt{b^{2} - 4 \, a c} a^{4} c^{5} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 128 \, \sqrt{b^{2} - 4 \, a c} a^{3} b c^{5} + 88 \, \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{5} + 16 \, \sqrt{b^{2} - 4 \, a c} a b^{3} c^{5} + 96 \, \sqrt{b^{2} - 4 \, a c} a^{3} c^{6} - 48 \, \sqrt{b^{2} - 4 \, a c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{2} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} {\left| c \right|} e^{2}} + \frac{x e^{2}}{2 \, {\left(c d^{3} - b d^{2} e + a d e^{2}\right)} {\left(x^{2} e + d\right)}}"," ",0,"1/2*(5*c*d^2*e^2 - 3*b*d*e^3 + a*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/((c^2*d^5 - 2*b*c*d^4*e + b^2*d^3*e^2 + 2*a*c*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*sqrt(d)) - 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - b^7*c^3 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 11*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 12*a*b^5*c^4 + 3*b^6*c^4 + 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 88*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 48*a^2*b^3*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 28*a*b^4*c^5 + 5*b^5*c^5 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 176*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 64*a^3*b*c^6 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 80*a^2*b^2*c^6 - 7*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 - 24*a*b^3*c^6 - 11*b^4*c^6 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 - 64*a^3*c^7 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^7 + 16*a^2*b*c^7 - 8*a*b^2*c^7 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^8 + 80*a^2*c^8 + 16*a*b*c^8 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + sqrt(b^2 - 4*a*c)*b^6*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 12*sqrt(b^2 - 4*a*c)*a*b^4*c^4 - 5*sqrt(b^2 - 4*a*c)*b^5*c^4 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 48*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 40*sqrt(b^2 - 4*a*c)*a*b^3*c^5 + 7*sqrt(b^2 - 4*a*c)*b^4*c^5 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 64*sqrt(b^2 - 4*a*c)*a^3*c^6 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 80*sqrt(b^2 - 4*a*c)*a^2*b*c^6 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 56*sqrt(b^2 - 4*a*c)*a*b^2*c^6 - 3*sqrt(b^2 - 4*a*c)*b^3*c^6 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^7 + 112*sqrt(b^2 - 4*a*c)*a^2*c^7 + 60*sqrt(b^2 - 4*a*c)*a*b*c^7 - 24*sqrt(b^2 - 4*a*c)*a*c^8 + 2*(b^2 - 4*a*c)*b^4*c^4 - 16*(b^2 - 4*a*c)*a*b^2*c^5 - 12*(b^2 - 4*a*c)*b^3*c^5 + 32*(b^2 - 4*a*c)*a^2*c^6 + 48*(b^2 - 4*a*c)*a*b*c^6 + 14*(b^2 - 4*a*c)*b^2*c^6 + 8*(b^2 - 4*a*c)*a*c^7)*arctan(2*sqrt(1/2)*x/sqrt((b*c^2*d^4 - 2*b^2*c*d^3*e + b^3*d^2*e^2 + 2*a*b*c*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4 + sqrt((b*c^2*d^4 - 2*b^2*c*d^3*e + b^3*d^2*e^2 + 2*a*b*c*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4)^2 - 4*(a*c^2*d^4 - 2*a*b*c*d^3*e + a*b^2*d^2*e^2 + 2*a^2*c*d^2*e^2 - 2*a^2*b*d*e^3 + a^3*e^4)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^2 - 2*b^8*c^2 + 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 60*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 7*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 16*a*b^6*c^3 + 8*b^7*c^3 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 240*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 84*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 32*a*b^5*c^4 - 6*b^6*c^4 + 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 + 320*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 336*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 256*a^3*b^2*c^5 + 72*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 128*a^2*b^3*c^5 - 24*a*b^4*c^5 - 448*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 512*a^4*c^6 - 240*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 512*a^3*b*c^6 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 224*a^2*b^2*c^6 + 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 - 128*a^3*c^7 - 16*a*b^2*c^7 + 64*a^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 72*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 24*sqrt(b^2 - 4*a*c)*a*b^4*c^4 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 192*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 + 32*sqrt(b^2 - 4*a*c)*a*b^3*c^5 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 384*sqrt(b^2 - 4*a*c)*a^3*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 128*sqrt(b^2 - 4*a*c)*a^2*b*c^6 + 8*sqrt(b^2 - 4*a*c)*a*b^2*c^6 + 96*sqrt(b^2 - 4*a*c)*a^2*c^7 - 16*sqrt(b^2 - 4*a*c)*a*b*c^7 + 2*(b^2 - 4*a*c)*b^6*c^2 - 24*(b^2 - 4*a*c)*a*b^4*c^3 - 8*(b^2 - 4*a*c)*b^5*c^3 + 96*(b^2 - 4*a*c)*a^2*b^2*c^4 + 64*(b^2 - 4*a*c)*a*b^3*c^4 + 6*(b^2 - 4*a*c)*b^4*c^4 - 128*(b^2 - 4*a*c)*a^3*c^5 - 128*(b^2 - 4*a*c)*a^2*b*c^5 - 48*(b^2 - 4*a*c)*a*b^2*c^5 + 96*(b^2 - 4*a*c)*a^2*c^6 + 64*(b^2 - 4*a*c)*a*b*c^6)*d^2*abs(c) + 4*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 + 4*a*b^7*c^2 - 36*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 48*a^2*b^5*c^3 - 10*a*b^6*c^3 + 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + 192*a^3*b^3*c^4 - sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 56*a^2*b^4*c^4 + 8*a*b^5*c^4 - 192*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 256*a^4*b*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 32*a^3*b^2*c^5 + 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 6*a*b^4*c^5 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 384*a^4*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 128*a^3*b*c^6 + 16*a^2*b^2*c^6 + 8*a*b^3*c^6 + 32*a^3*c^7 - 32*a^2*b*c^7 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 4*sqrt(b^2 - 4*a*c)*a*b^6*c^2 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 48*sqrt(b^2 - 4*a*c)*a^2*b^4*c^3 - 10*sqrt(b^2 - 4*a*c)*a*b^5*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 192*sqrt(b^2 - 4*a*c)*a^3*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 80*sqrt(b^2 - 4*a*c)*a^2*b^3*c^4 + 16*sqrt(b^2 - 4*a*c)*a*b^4*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 256*sqrt(b^2 - 4*a*c)*a^4*c^5 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 160*sqrt(b^2 - 4*a*c)*a^3*b*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 96*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 - 18*sqrt(b^2 - 4*a*c)*a*b^3*c^5 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 128*sqrt(b^2 - 4*a*c)*a^3*c^6 + 40*sqrt(b^2 - 4*a*c)*a^2*b*c^6 + 8*sqrt(b^2 - 4*a*c)*a*b^2*c^6 - 16*sqrt(b^2 - 4*a*c)*a^2*c^7 + 8*(b^2 - 4*a*c)*a*b^3*c^4 - 32*(b^2 - 4*a*c)*a^2*b*c^5 - 12*(b^2 - 4*a*c)*a*b^2*c^5 - 16*(b^2 - 4*a*c)*a^2*c^6)*d*abs(c)*e - (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c + 6*a*b^8*c + 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 80*a^2*b^6*c^2 - 12*a*b^7*c^2 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 384*a^3*b^4*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 80*a^2*b^5*c^3 + 10*a*b^6*c^3 + 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^4 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 768*a^4*b^2*c^4 + 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 64*a^3*b^3*c^4 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 24*a^2*b^4*c^4 - 12*a*b^5*c^4 - 448*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 + 512*a^5*c^5 - 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 256*a^4*b*c^5 - 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 32*a^3*b^2*c^5 + 32*a^2*b^3*c^5 + 16*a*b^4*c^5 + 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 128*a^4*c^6 + 64*a^3*b*c^6 - 80*a^2*b^2*c^6 + 64*a^3*c^7 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 8*sqrt(b^2 - 4*a*c)*a*b^7*c + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 96*sqrt(b^2 - 4*a*c)*a^2*b^5*c^2 - 20*sqrt(b^2 - 4*a*c)*a*b^6*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 384*sqrt(b^2 - 4*a*c)*a^3*b^3*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 136*sqrt(b^2 - 4*a*c)*a^2*b^4*c^3 + 32*sqrt(b^2 - 4*a*c)*a*b^5*c^3 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 512*sqrt(b^2 - 4*a*c)*a^4*b*c^4 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 128*sqrt(b^2 - 4*a*c)*a^3*b^2*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 160*sqrt(b^2 - 4*a*c)*a^2*b^3*c^4 - 36*sqrt(b^2 - 4*a*c)*a*b^4*c^4 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 384*sqrt(b^2 - 4*a*c)*a^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 128*sqrt(b^2 - 4*a*c)*a^3*b*c^5 + 88*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 + 16*sqrt(b^2 - 4*a*c)*a*b^3*c^5 + 96*sqrt(b^2 - 4*a*c)*a^3*c^6 - 48*sqrt(b^2 - 4*a*c)*a^2*b*c^6 + 2*(b^2 - 4*a*c)*a*b^6*c - 24*(b^2 - 4*a*c)*a^2*b^4*c^2 - 8*(b^2 - 4*a*c)*a*b^5*c^2 + 96*(b^2 - 4*a*c)*a^3*b^2*c^3 + 64*(b^2 - 4*a*c)*a^2*b^3*c^3 + 22*(b^2 - 4*a*c)*a*b^4*c^3 - 128*(b^2 - 4*a*c)*a^4*c^4 - 128*(b^2 - 4*a*c)*a^3*b*c^4 - 112*(b^2 - 4*a*c)*a^2*b^2*c^4 - 24*(b^2 - 4*a*c)*a*b^3*c^4 + 96*(b^2 - 4*a*c)*a^3*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^5)*abs(c)*e^2) + 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + b^7*c^3 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 11*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*a*b^5*c^4 - 3*b^6*c^4 + 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 88*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 48*a^2*b^3*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 28*a*b^4*c^5 - 5*b^5*c^5 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 176*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 64*a^3*b*c^6 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 80*a^2*b^2*c^6 - 7*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 24*a*b^3*c^6 + 11*b^4*c^6 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 64*a^3*c^7 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 - 16*a^2*b*c^7 + 8*a*b^2*c^7 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^8 - 80*a^2*c^8 - 16*a*b*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + sqrt(b^2 - 4*a*c)*b^6*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 12*sqrt(b^2 - 4*a*c)*a*b^4*c^4 - 5*sqrt(b^2 - 4*a*c)*b^5*c^4 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 48*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 40*sqrt(b^2 - 4*a*c)*a*b^3*c^5 + 7*sqrt(b^2 - 4*a*c)*b^4*c^5 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 64*sqrt(b^2 - 4*a*c)*a^3*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 80*sqrt(b^2 - 4*a*c)*a^2*b*c^6 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 56*sqrt(b^2 - 4*a*c)*a*b^2*c^6 - 3*sqrt(b^2 - 4*a*c)*b^3*c^6 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^7 + 112*sqrt(b^2 - 4*a*c)*a^2*c^7 + 60*sqrt(b^2 - 4*a*c)*a*b*c^7 - 24*sqrt(b^2 - 4*a*c)*a*c^8 - 2*(b^2 - 4*a*c)*b^4*c^4 + 16*(b^2 - 4*a*c)*a*b^2*c^5 + 12*(b^2 - 4*a*c)*b^3*c^5 - 32*(b^2 - 4*a*c)*a^2*c^6 - 48*(b^2 - 4*a*c)*a*b*c^6 - 14*(b^2 - 4*a*c)*b^2*c^6 - 8*(b^2 - 4*a*c)*a*c^7)*arctan(2*sqrt(1/2)*x/sqrt((b*c^2*d^4 - 2*b^2*c*d^3*e + b^3*d^2*e^2 + 2*a*b*c*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4 - sqrt((b*c^2*d^4 - 2*b^2*c*d^3*e + b^3*d^2*e^2 + 2*a*b*c*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4)^2 - 4*(a*c^2*d^4 - 2*a*b*c*d^3*e + a*b^2*d^2*e^2 + 2*a^2*c*d^2*e^2 - 2*a^2*b*d*e^3 + a^3*e^4)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 2*b^8*c^2 + 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 60*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 7*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 16*a*b^6*c^3 - 8*b^7*c^3 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 240*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 84*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 32*a*b^5*c^4 + 6*b^6*c^4 + 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 + 320*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 336*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 256*a^3*b^2*c^5 + 72*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 128*a^2*b^3*c^5 + 24*a*b^4*c^5 - 448*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 512*a^4*c^6 - 240*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 512*a^3*b*c^6 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 224*a^2*b^2*c^6 + 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 128*a^3*c^7 + 16*a*b^2*c^7 - 64*a^2*c^8 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 72*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 24*sqrt(b^2 - 4*a*c)*a*b^4*c^4 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 192*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 + 32*sqrt(b^2 - 4*a*c)*a*b^3*c^5 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 - 384*sqrt(b^2 - 4*a*c)*a^3*c^6 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 128*sqrt(b^2 - 4*a*c)*a^2*b*c^6 + 8*sqrt(b^2 - 4*a*c)*a*b^2*c^6 + 96*sqrt(b^2 - 4*a*c)*a^2*c^7 - 16*sqrt(b^2 - 4*a*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^6*c^2 + 24*(b^2 - 4*a*c)*a*b^4*c^3 + 8*(b^2 - 4*a*c)*b^5*c^3 - 96*(b^2 - 4*a*c)*a^2*b^2*c^4 - 64*(b^2 - 4*a*c)*a*b^3*c^4 - 6*(b^2 - 4*a*c)*b^4*c^4 + 128*(b^2 - 4*a*c)*a^3*c^5 + 128*(b^2 - 4*a*c)*a^2*b*c^5 + 48*(b^2 - 4*a*c)*a*b^2*c^5 - 96*(b^2 - 4*a*c)*a^2*c^6 - 64*(b^2 - 4*a*c)*a*b*c^6)*d^2*abs(c) + 4*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 4*a*b^7*c^2 - 36*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 48*a^2*b^5*c^3 + 10*a*b^6*c^3 + 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 192*a^3*b^3*c^4 - sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 56*a^2*b^4*c^4 - 8*a*b^5*c^4 - 192*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 256*a^4*b*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 32*a^3*b^2*c^5 + 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 6*a*b^4*c^5 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 384*a^4*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 128*a^3*b*c^6 - 16*a^2*b^2*c^6 - 8*a*b^3*c^6 - 32*a^3*c^7 + 32*a^2*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 4*sqrt(b^2 - 4*a*c)*a*b^6*c^2 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 48*sqrt(b^2 - 4*a*c)*a^2*b^4*c^3 - 10*sqrt(b^2 - 4*a*c)*a*b^5*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 192*sqrt(b^2 - 4*a*c)*a^3*b^2*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 80*sqrt(b^2 - 4*a*c)*a^2*b^3*c^4 + 16*sqrt(b^2 - 4*a*c)*a*b^4*c^4 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 256*sqrt(b^2 - 4*a*c)*a^4*c^5 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 160*sqrt(b^2 - 4*a*c)*a^3*b*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 96*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 - 18*sqrt(b^2 - 4*a*c)*a*b^3*c^5 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 128*sqrt(b^2 - 4*a*c)*a^3*c^6 + 40*sqrt(b^2 - 4*a*c)*a^2*b*c^6 + 8*sqrt(b^2 - 4*a*c)*a*b^2*c^6 - 16*sqrt(b^2 - 4*a*c)*a^2*c^7 - 8*(b^2 - 4*a*c)*a*b^3*c^4 + 32*(b^2 - 4*a*c)*a^2*b*c^5 + 12*(b^2 - 4*a*c)*a*b^2*c^5 + 16*(b^2 - 4*a*c)*a^2*c^6)*d*abs(c)*e - (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c - 6*a*b^8*c + 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 + 80*a^2*b^6*c^2 + 12*a*b^7*c^2 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 384*a^3*b^4*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 80*a^2*b^5*c^3 - 10*a*b^6*c^3 + 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^4 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 768*a^4*b^2*c^4 + 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + 64*a^3*b^3*c^4 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 24*a^2*b^4*c^4 + 12*a*b^5*c^4 - 448*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 512*a^5*c^5 - 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 256*a^4*b*c^5 - 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 32*a^3*b^2*c^5 - 32*a^2*b^3*c^5 - 16*a*b^4*c^5 + 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 128*a^4*c^6 - 64*a^3*b*c^6 + 80*a^2*b^2*c^6 - 64*a^3*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 8*sqrt(b^2 - 4*a*c)*a*b^7*c - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 96*sqrt(b^2 - 4*a*c)*a^2*b^5*c^2 - 20*sqrt(b^2 - 4*a*c)*a*b^6*c^2 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 384*sqrt(b^2 - 4*a*c)*a^3*b^3*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 136*sqrt(b^2 - 4*a*c)*a^2*b^4*c^3 + 32*sqrt(b^2 - 4*a*c)*a*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 512*sqrt(b^2 - 4*a*c)*a^4*b*c^4 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 128*sqrt(b^2 - 4*a*c)*a^3*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 160*sqrt(b^2 - 4*a*c)*a^2*b^3*c^4 - 36*sqrt(b^2 - 4*a*c)*a*b^4*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 384*sqrt(b^2 - 4*a*c)*a^4*c^5 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 128*sqrt(b^2 - 4*a*c)*a^3*b*c^5 + 88*sqrt(b^2 - 4*a*c)*a^2*b^2*c^5 + 16*sqrt(b^2 - 4*a*c)*a*b^3*c^5 + 96*sqrt(b^2 - 4*a*c)*a^3*c^6 - 48*sqrt(b^2 - 4*a*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*a*b^6*c + 24*(b^2 - 4*a*c)*a^2*b^4*c^2 + 8*(b^2 - 4*a*c)*a*b^5*c^2 - 96*(b^2 - 4*a*c)*a^3*b^2*c^3 - 64*(b^2 - 4*a*c)*a^2*b^3*c^3 - 22*(b^2 - 4*a*c)*a*b^4*c^3 + 128*(b^2 - 4*a*c)*a^4*c^4 + 128*(b^2 - 4*a*c)*a^3*b*c^4 + 112*(b^2 - 4*a*c)*a^2*b^2*c^4 + 24*(b^2 - 4*a*c)*a*b^3*c^4 - 96*(b^2 - 4*a*c)*a^3*c^5 - 32*(b^2 - 4*a*c)*a^2*b*c^5)*abs(c)*e^2) + 1/2*x*e^2/((c*d^3 - b*d^2*e + a*d*e^2)*(x^2*e + d))","B",0
270,1,8983,0,2.459476," ","integrate((e*x^2+d)^3/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c^{2} d^{3} x^{3} - 6 \, a c^{2} d^{2} x^{3} e + 3 \, a b c d x^{3} e^{2} + b^{2} c d^{3} x - 2 \, a c^{2} d^{3} x - a b^{2} x^{3} e^{3} + 2 \, a^{2} c x^{3} e^{3} - 3 \, a b c d^{2} x e + 6 \, a^{2} c d x e^{2} - a^{2} b x e^{3}}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}} + \frac{{\left({\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d^{3} - 6 \, {\left(2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 2 \, a b^{6} c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 28 \, a^{2} b^{4} c^{5} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 128 \, a^{3} b^{2} c^{6} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 192 \, a^{4} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} d^{3} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} + 3 \, {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d e^{2} + 6 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 2 \, a^{2} b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 16 \, a^{3} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, a^{4} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} d^{2} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e + {\left(2 \, a^{2} b^{7} c^{6} - 40 \, a^{3} b^{5} c^{7} + 224 \, a^{4} b^{3} c^{8} - 384 \, a^{5} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{6} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{7} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{8}\right)} d^{3} + {\left(2 \, a b^{4} c^{2} - 20 \, a^{2} b^{2} c^{3} + 48 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} e^{3} - 12 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 2 \, a^{3} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 16 \, a^{4} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 32 \, a^{5} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{5}\right)} d {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e^{2} + 12 \, {\left(2 \, a^{3} b^{6} c^{6} - 16 \, a^{4} b^{4} c^{7} + 32 \, a^{5} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{7}\right)} d^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 2 \, a^{3} b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 16 \, a^{4} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 32 \, a^{5} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e^{3} - 3 \, {\left(2 \, a^{3} b^{7} c^{5} - 8 \, a^{4} b^{5} c^{6} - 32 \, a^{5} b^{3} c^{7} + 128 \, a^{6} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{7}\right)} d e^{2} - {\left(2 \, a^{3} b^{8} c^{4} - 32 \, a^{4} b^{6} c^{5} + 160 \, a^{5} b^{4} c^{6} - 256 \, a^{6} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{6}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} c - 4 \, a^{2} b c^{2} + \sqrt{{\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}\right)}{16 \, {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} - 2 \, a^{3} b^{5} c^{4} + 48 \, a^{5} b^{2} c^{5} + 16 \, a^{4} b^{3} c^{5} + a^{3} b^{4} c^{5} - 64 \, a^{6} c^{6} - 32 \, a^{5} b c^{6} - 8 \, a^{4} b^{2} c^{6} + 16 \, a^{5} c^{7}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d^{3} - 6 \, {\left(2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, a b^{6} c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 28 \, a^{2} b^{4} c^{5} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 128 \, a^{3} b^{2} c^{6} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} - 192 \, a^{4} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} d^{3} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} + 3 \, {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d e^{2} - 6 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 2 \, a^{2} b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 16 \, a^{3} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 32 \, a^{4} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} d^{2} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e + {\left(2 \, a^{2} b^{7} c^{6} - 40 \, a^{3} b^{5} c^{7} + 224 \, a^{4} b^{3} c^{8} - 384 \, a^{5} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{6} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{7} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{8}\right)} d^{3} + {\left(2 \, a b^{4} c^{2} - 20 \, a^{2} b^{2} c^{3} + 48 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} e^{3} + 12 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 2 \, a^{3} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 16 \, a^{4} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} + 32 \, a^{5} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{5}\right)} d {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e^{2} + 12 \, {\left(2 \, a^{3} b^{6} c^{6} - 16 \, a^{4} b^{4} c^{7} + 32 \, a^{5} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{7}\right)} d^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 2 \, a^{3} b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 16 \, a^{4} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 32 \, a^{5} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e^{3} - 3 \, {\left(2 \, a^{3} b^{7} c^{5} - 8 \, a^{4} b^{5} c^{6} - 32 \, a^{5} b^{3} c^{7} + 128 \, a^{6} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{7}\right)} d e^{2} - {\left(2 \, a^{3} b^{8} c^{4} - 32 \, a^{4} b^{6} c^{5} + 160 \, a^{5} b^{4} c^{6} - 256 \, a^{6} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{6}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} c - 4 \, a^{2} b c^{2} - \sqrt{{\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}\right)}{16 \, {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} - 2 \, a^{3} b^{5} c^{4} + 48 \, a^{5} b^{2} c^{5} + 16 \, a^{4} b^{3} c^{5} + a^{3} b^{4} c^{5} - 64 \, a^{6} c^{6} - 32 \, a^{5} b c^{6} - 8 \, a^{4} b^{2} c^{6} + 16 \, a^{5} c^{7}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} {\left| c \right|}}"," ",0,"1/2*(b*c^2*d^3*x^3 - 6*a*c^2*d^2*x^3*e + 3*a*b*c*d*x^3*e^2 + b^2*c*d^3*x - 2*a*c^2*d^3*x - a*b^2*x^3*e^3 + 2*a^2*c*x^3*e^3 - 3*a*b*c*d^2*x*e + 6*a^2*c*d*x*e^2 - a^2*b*x*e^3)/((c*x^4 + b*x^2 + a)*(a*b^2*c - 4*a^2*c^2)) + 1/16*((2*b^3*c^4 - 8*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(a*b^2*c - 4*a^2*c^2)^2*d^3 - 6*(2*a*b^2*c^4 - 8*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*a*c^4)*(a*b^2*c - 4*a^2*c^2)^2*d^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 2*a*b^6*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 28*a^2*b^4*c^5 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 128*a^3*b^2*c^6 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 192*a^4*c^7 + 2*(b^2 - 4*a*c)*a*b^4*c^4 - 20*(b^2 - 4*a*c)*a^2*b^2*c^5 + 48*(b^2 - 4*a*c)*a^3*c^6)*d^3*abs(a*b^2*c - 4*a^2*c^2) + 3*(2*a*b^3*c^3 - 8*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*(a*b^2*c - 4*a^2*c^2)^2*d*e^2 + 6*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 2*a^2*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 16*a^3*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*a^4*b*c^6 + 2*(b^2 - 4*a*c)*a^2*b^3*c^4 - 8*(b^2 - 4*a*c)*a^3*b*c^5)*d^2*abs(a*b^2*c - 4*a^2*c^2)*e + (2*a^2*b^7*c^6 - 40*a^3*b^5*c^7 + 224*a^4*b^3*c^8 - 384*a^5*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 2*(b^2 - 4*a*c)*a^2*b^5*c^6 + 32*(b^2 - 4*a*c)*a^3*b^3*c^7 - 96*(b^2 - 4*a*c)*a^4*b*c^8)*d^3 + (2*a*b^4*c^2 - 20*a^2*b^2*c^3 + 48*a^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 12*(b^2 - 4*a*c)*a^2*c^3)*(a*b^2*c - 4*a^2*c^2)^2*e^3 - 12*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 2*a^3*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 16*a^4*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 32*a^5*c^6 + 2*(b^2 - 4*a*c)*a^3*b^2*c^4 - 8*(b^2 - 4*a*c)*a^4*c^5)*d*abs(a*b^2*c - 4*a^2*c^2)*e^2 + 12*(2*a^3*b^6*c^6 - 16*a^4*b^4*c^7 + 32*a^5*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 - 2*(b^2 - 4*a*c)*a^3*b^4*c^6 + 8*(b^2 - 4*a*c)*a^4*b^2*c^7)*d^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 2*a^3*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 16*a^4*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 32*a^5*b*c^5 + 2*(b^2 - 4*a*c)*a^3*b^3*c^3 - 8*(b^2 - 4*a*c)*a^4*b*c^4)*abs(a*b^2*c - 4*a^2*c^2)*e^3 - 3*(2*a^3*b^7*c^5 - 8*a^4*b^5*c^6 - 32*a^5*b^3*c^7 + 128*a^6*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 - 2*(b^2 - 4*a*c)*a^3*b^5*c^5 + 32*(b^2 - 4*a*c)*a^5*b*c^7)*d*e^2 - (2*a^3*b^8*c^4 - 32*a^4*b^6*c^5 + 160*a^5*b^4*c^6 - 256*a^6*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 2*(b^2 - 4*a*c)*a^3*b^6*c^4 + 24*(b^2 - 4*a*c)*a^4*b^4*c^5 - 64*(b^2 - 4*a*c)*a^5*b^2*c^6)*e^3)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3*c - 4*a^2*b*c^2 + sqrt((a*b^3*c - 4*a^2*b*c^2)^2 - 4*(a^2*b^2*c - 4*a^3*c^2)*(a*b^2*c^2 - 4*a^2*c^3)))/(a*b^2*c^2 - 4*a^2*c^3)))/((a^3*b^6*c^3 - 12*a^4*b^4*c^4 - 2*a^3*b^5*c^4 + 48*a^5*b^2*c^5 + 16*a^4*b^3*c^5 + a^3*b^4*c^5 - 64*a^6*c^6 - 32*a^5*b*c^6 - 8*a^4*b^2*c^6 + 16*a^5*c^7)*abs(a*b^2*c - 4*a^2*c^2)*abs(c)) - 1/16*((2*b^3*c^4 - 8*a*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(a*b^2*c - 4*a^2*c^2)^2*d^3 - 6*(2*a*b^2*c^4 - 8*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*a*c^4)*(a*b^2*c - 4*a^2*c^2)^2*d^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*a*b^6*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 28*a^2*b^4*c^5 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 128*a^3*b^2*c^6 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 192*a^4*c^7 - 2*(b^2 - 4*a*c)*a*b^4*c^4 + 20*(b^2 - 4*a*c)*a^2*b^2*c^5 - 48*(b^2 - 4*a*c)*a^3*c^6)*d^3*abs(a*b^2*c - 4*a^2*c^2) + 3*(2*a*b^3*c^3 - 8*a^2*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*(a*b^2*c - 4*a^2*c^2)^2*d*e^2 - 6*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 2*a^2*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 16*a^3*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 32*a^4*b*c^6 - 2*(b^2 - 4*a*c)*a^2*b^3*c^4 + 8*(b^2 - 4*a*c)*a^3*b*c^5)*d^2*abs(a*b^2*c - 4*a^2*c^2)*e + (2*a^2*b^7*c^6 - 40*a^3*b^5*c^7 + 224*a^4*b^3*c^8 - 384*a^5*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 2*(b^2 - 4*a*c)*a^2*b^5*c^6 + 32*(b^2 - 4*a*c)*a^3*b^3*c^7 - 96*(b^2 - 4*a*c)*a^4*b*c^8)*d^3 + (2*a*b^4*c^2 - 20*a^2*b^2*c^3 + 48*a^3*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 12*(b^2 - 4*a*c)*a^2*c^3)*(a*b^2*c - 4*a^2*c^2)^2*e^3 + 12*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 2*a^3*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 16*a^4*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 + 32*a^5*c^6 - 2*(b^2 - 4*a*c)*a^3*b^2*c^4 + 8*(b^2 - 4*a*c)*a^4*c^5)*d*abs(a*b^2*c - 4*a^2*c^2)*e^2 + 12*(2*a^3*b^6*c^6 - 16*a^4*b^4*c^7 + 32*a^5*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 - 2*(b^2 - 4*a*c)*a^3*b^4*c^6 + 8*(b^2 - 4*a*c)*a^4*b^2*c^7)*d^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 2*a^3*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 16*a^4*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 32*a^5*b*c^5 - 2*(b^2 - 4*a*c)*a^3*b^3*c^3 + 8*(b^2 - 4*a*c)*a^4*b*c^4)*abs(a*b^2*c - 4*a^2*c^2)*e^3 - 3*(2*a^3*b^7*c^5 - 8*a^4*b^5*c^6 - 32*a^5*b^3*c^7 + 128*a^6*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 - 2*(b^2 - 4*a*c)*a^3*b^5*c^5 + 32*(b^2 - 4*a*c)*a^5*b*c^7)*d*e^2 - (2*a^3*b^8*c^4 - 32*a^4*b^6*c^5 + 160*a^5*b^4*c^6 - 256*a^6*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 2*(b^2 - 4*a*c)*a^3*b^6*c^4 + 24*(b^2 - 4*a*c)*a^4*b^4*c^5 - 64*(b^2 - 4*a*c)*a^5*b^2*c^6)*e^3)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3*c - 4*a^2*b*c^2 - sqrt((a*b^3*c - 4*a^2*b*c^2)^2 - 4*(a^2*b^2*c - 4*a^3*c^2)*(a*b^2*c^2 - 4*a^2*c^3)))/(a*b^2*c^2 - 4*a^2*c^3)))/((a^3*b^6*c^3 - 12*a^4*b^4*c^4 - 2*a^3*b^5*c^4 + 48*a^5*b^2*c^5 + 16*a^4*b^3*c^5 + a^3*b^4*c^5 - 64*a^6*c^6 - 32*a^5*b*c^6 - 8*a^4*b^2*c^6 + 16*a^5*c^7)*abs(a*b^2*c - 4*a^2*c^2)*abs(c))","B",0
271,1,6390,0,1.846396," ","integrate((e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c d^{2} x^{3} - 4 \, a c d x^{3} e + a b x^{3} e^{2} + b^{2} d^{2} x - 2 \, a c d^{2} x - 2 \, a b d x e + 2 \, a^{2} x e^{2}}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{{\left({\left(2 \, b^{3} c^{3} - 8 \, a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d^{2} - 4 \, {\left(2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 2 \, a b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 28 \, a^{2} b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 128 \, a^{3} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 192 \, a^{4} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} d^{2} {\left| a b^{2} - 4 \, a^{2} c \right|} + {\left(2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} e^{2} + 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, a^{2} b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 16 \, a^{3} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 32 \, a^{4} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} d {\left| a b^{2} - 4 \, a^{2} c \right|} e + {\left(2 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 224 \, a^{4} b^{3} c^{5} - 384 \, a^{5} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} d^{2} - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, a^{3} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 16 \, a^{4} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 32 \, a^{5} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} e^{2} + 8 \, {\left(2 \, a^{3} b^{6} c^{3} - 16 \, a^{4} b^{4} c^{4} + 32 \, a^{5} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{4}\right)} d e - {\left(2 \, a^{3} b^{7} c^{2} - 8 \, a^{4} b^{5} c^{3} - 32 \, a^{5} b^{3} c^{4} + 128 \, a^{6} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{4}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} - 2 \, a^{3} b^{5} c^{2} + 48 \, a^{5} b^{2} c^{3} + 16 \, a^{4} b^{3} c^{3} + a^{3} b^{4} c^{3} - 64 \, a^{6} c^{4} - 32 \, a^{5} b c^{4} - 8 \, a^{4} b^{2} c^{4} + 16 \, a^{5} c^{5}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{3} - 8 \, a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d^{2} - 4 \, {\left(2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 2 \, a b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 28 \, a^{2} b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 128 \, a^{3} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 192 \, a^{4} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} d^{2} {\left| a b^{2} - 4 \, a^{2} c \right|} + {\left(2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} e^{2} - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 2 \, a^{2} b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 16 \, a^{3} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 32 \, a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} d {\left| a b^{2} - 4 \, a^{2} c \right|} e + {\left(2 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 224 \, a^{4} b^{3} c^{5} - 384 \, a^{5} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} d^{2} + 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, a^{3} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 16 \, a^{4} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 32 \, a^{5} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} e^{2} + 8 \, {\left(2 \, a^{3} b^{6} c^{3} - 16 \, a^{4} b^{4} c^{4} + 32 \, a^{5} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{4}\right)} d e - {\left(2 \, a^{3} b^{7} c^{2} - 8 \, a^{4} b^{5} c^{3} - 32 \, a^{5} b^{3} c^{4} + 128 \, a^{6} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{4}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} - 2 \, a^{3} b^{5} c^{2} + 48 \, a^{5} b^{2} c^{3} + 16 \, a^{4} b^{3} c^{3} + a^{3} b^{4} c^{3} - 64 \, a^{6} c^{4} - 32 \, a^{5} b c^{4} - 8 \, a^{4} b^{2} c^{4} + 16 \, a^{5} c^{5}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}}"," ",0,"1/2*(b*c*d^2*x^3 - 4*a*c*d*x^3*e + a*b*x^3*e^2 + b^2*d^2*x - 2*a*c*d^2*x - 2*a*b*d*x*e + 2*a^2*x*e^2)/((c*x^4 + b*x^2 + a)*(a*b^2 - 4*a^2*c)) + 1/16*((2*b^3*c^3 - 8*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^3 - 2*(b^2 - 4*a*c)*b*c^3)*(a*b^2 - 4*a^2*c)^2*d^2 - 4*(2*a*b^2*c^3 - 8*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*a*c^3)*(a*b^2 - 4*a^2*c)^2*d*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 2*a*b^6*c^2 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 28*a^2*b^4*c^3 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 128*a^3*b^2*c^4 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 192*a^4*c^5 + 2*(b^2 - 4*a*c)*a*b^4*c^2 - 20*(b^2 - 4*a*c)*a^2*b^2*c^3 + 48*(b^2 - 4*a*c)*a^3*c^4)*d^2*abs(a*b^2 - 4*a^2*c) + (2*a*b^3*c^2 - 8*a^2*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a*b^2 - 4*a^2*c)^2*e^2 + 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 2*a^2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 16*a^3*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 32*a^4*b*c^4 + 2*(b^2 - 4*a*c)*a^2*b^3*c^2 - 8*(b^2 - 4*a*c)*a^3*b*c^3)*d*abs(a*b^2 - 4*a^2*c)*e + (2*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 224*a^4*b^3*c^5 - 384*a^5*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2*(b^2 - 4*a*c)*a^2*b^5*c^3 + 32*(b^2 - 4*a*c)*a^3*b^3*c^4 - 96*(b^2 - 4*a*c)*a^4*b*c^5)*d^2 - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 2*a^3*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 16*a^4*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 32*a^5*c^4 + 2*(b^2 - 4*a*c)*a^3*b^2*c^2 - 8*(b^2 - 4*a*c)*a^4*c^3)*abs(a*b^2 - 4*a^2*c)*e^2 + 8*(2*a^3*b^6*c^3 - 16*a^4*b^4*c^4 + 32*a^5*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*(b^2 - 4*a*c)*a^3*b^4*c^3 + 8*(b^2 - 4*a*c)*a^4*b^2*c^4)*d*e - (2*a^3*b^7*c^2 - 8*a^4*b^5*c^3 - 32*a^5*b^3*c^4 + 128*a^6*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 2*(b^2 - 4*a*c)*a^3*b^5*c^2 + 32*(b^2 - 4*a*c)*a^5*b*c^4)*e^2)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6*c - 12*a^4*b^4*c^2 - 2*a^3*b^5*c^2 + 48*a^5*b^2*c^3 + 16*a^4*b^3*c^3 + a^3*b^4*c^3 - 64*a^6*c^4 - 32*a^5*b*c^4 - 8*a^4*b^2*c^4 + 16*a^5*c^5)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/16*((2*b^3*c^3 - 8*a*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^3 - 2*(b^2 - 4*a*c)*b*c^3)*(a*b^2 - 4*a^2*c)^2*d^2 - 4*(2*a*b^2*c^3 - 8*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*a*c^3)*(a*b^2 - 4*a^2*c)^2*d*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 2*a*b^6*c^2 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 28*a^2*b^4*c^3 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 128*a^3*b^2*c^4 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 192*a^4*c^5 - 2*(b^2 - 4*a*c)*a*b^4*c^2 + 20*(b^2 - 4*a*c)*a^2*b^2*c^3 - 48*(b^2 - 4*a*c)*a^3*c^4)*d^2*abs(a*b^2 - 4*a^2*c) + (2*a*b^3*c^2 - 8*a^2*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a*b^2 - 4*a^2*c)^2*e^2 - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 2*a^2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 16*a^3*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 32*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^3*c^2 + 8*(b^2 - 4*a*c)*a^3*b*c^3)*d*abs(a*b^2 - 4*a^2*c)*e + (2*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 224*a^4*b^3*c^5 - 384*a^5*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2*(b^2 - 4*a*c)*a^2*b^5*c^3 + 32*(b^2 - 4*a*c)*a^3*b^3*c^4 - 96*(b^2 - 4*a*c)*a^4*b*c^5)*d^2 + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 2*a^3*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 16*a^4*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 32*a^5*c^4 - 2*(b^2 - 4*a*c)*a^3*b^2*c^2 + 8*(b^2 - 4*a*c)*a^4*c^3)*abs(a*b^2 - 4*a^2*c)*e^2 + 8*(2*a^3*b^6*c^3 - 16*a^4*b^4*c^4 + 32*a^5*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*(b^2 - 4*a*c)*a^3*b^4*c^3 + 8*(b^2 - 4*a*c)*a^4*b^2*c^4)*d*e - (2*a^3*b^7*c^2 - 8*a^4*b^5*c^3 - 32*a^5*b^3*c^4 + 128*a^6*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 2*(b^2 - 4*a*c)*a^3*b^5*c^2 + 32*(b^2 - 4*a*c)*a^5*b*c^4)*e^2)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6*c - 12*a^4*b^4*c^2 - 2*a^3*b^5*c^2 + 48*a^5*b^2*c^3 + 16*a^4*b^3*c^3 + a^3*b^4*c^3 - 64*a^6*c^4 - 32*a^5*b*c^4 - 8*a^4*b^2*c^4 + 16*a^5*c^5)*abs(a*b^2 - 4*a^2*c)*abs(c))","B",0
272,1,4433,0,1.763613," ","integrate((e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c d x^{3} - 2 \, a c x^{3} e + b^{2} d x - 2 \, a c d x - a b x e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 192 \, a^{4} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} d {\left| a b^{2} - 4 \, a^{2} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 16 \, a^{3} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, a^{4} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} e + {\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} d + 4 \, {\left(2 \, a^{3} b^{6} c^{2} - 16 \, a^{4} b^{4} c^{3} + 32 \, a^{5} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 192 \, a^{4} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} d {\left| a b^{2} - 4 \, a^{2} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 16 \, a^{3} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 32 \, a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} e + {\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} d + 4 \, {\left(2 \, a^{3} b^{6} c^{2} - 16 \, a^{4} b^{4} c^{3} + 32 \, a^{5} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}}"," ",0,"1/2*(b*c*d*x^3 - 2*a*c*x^3*e + b^2*d*x - 2*a*c*d*x - a*b*x*e)/((c*x^4 + b*x^2 + a)*(a*b^2 - 4*a^2*c)) + 1/16*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2*d - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*(a*b^2 - 4*a^2*c)^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 192*a^4*c^4 + 2*(b^2 - 4*a*c)*a*b^4*c - 20*(b^2 - 4*a*c)*a^2*b^2*c^2 + 48*(b^2 - 4*a*c)*a^3*c^3)*d*abs(a*b^2 - 4*a^2*c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*a^2*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 16*a^3*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*a^4*b*c^3 + 2*(b^2 - 4*a*c)*a^2*b^3*c - 8*(b^2 - 4*a*c)*a^3*b*c^2)*abs(a*b^2 - 4*a^2*c)*e + (2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4)*d + 4*(2*a^3*b^6*c^2 - 16*a^4*b^4*c^3 + 32*a^5*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 8*(b^2 - 4*a*c)*a^4*b^2*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/16*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2*d - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*(a*b^2 - 4*a^2*c)^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 192*a^4*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c + 20*(b^2 - 4*a*c)*a^2*b^2*c^2 - 48*(b^2 - 4*a*c)*a^3*c^3)*d*abs(a*b^2 - 4*a^2*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*a^2*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 16*a^3*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 32*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^2*b^3*c + 8*(b^2 - 4*a*c)*a^3*b*c^2)*abs(a*b^2 - 4*a^2*c)*e + (2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4)*d + 4*(2*a^3*b^6*c^2 - 16*a^4*b^4*c^3 + 32*a^5*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 8*(b^2 - 4*a*c)*a^4*b^2*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c))","B",0
273,1,2682,0,0.601623," ","integrate(1/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c x^{3} + b^{2} x - 2 \, a c x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{{\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4} + {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 192 \, a^{4} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4} + {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 28 \, a^{2} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 128 \, a^{3} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 192 \, a^{4} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}}"," ",0,"1/2*(b*c*x^3 + b^2*x - 2*a*c*x)/((c*x^4 + b*x^2 + a)*(a*b^2 - 4*a^2*c)) + 1/16*(2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4 + (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 192*a^4*c^4 + 2*(b^2 - 4*a*c)*a*b^4*c - 20*(b^2 - 4*a*c)*a^2*b^2*c^2 + 48*(b^2 - 4*a*c)*a^3*c^3)*abs(a*b^2 - 4*a^2*c))*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/16*(2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4 + (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*a*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 28*a^2*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 128*a^3*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 192*a^4*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c + 20*(b^2 - 4*a*c)*a^2*b^2*c^2 - 48*(b^2 - 4*a*c)*a^3*c^3)*abs(a*b^2 - 4*a^2*c))*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c))","B",0
274,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,1,180,0,0.225827," ","integrate((e*x^2+d)^(5/2)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{1}{256} \, {\left(3 \, c d^{5} - 10 \, b d^{4} e + 80 \, a d^{3} e^{2}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -x e^{\frac{1}{2}} + \sqrt{x^{2} e + d} \right|}\right) + \frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, c x^{2} e^{2} + {\left(21 \, c d e^{9} + 10 \, b e^{10}\right)} e^{\left(-8\right)}\right)} x^{2} + {\left(93 \, c d^{2} e^{8} + 170 \, b d e^{9} + 80 \, a e^{10}\right)} e^{\left(-8\right)}\right)} x^{2} + 5 \, {\left(3 \, c d^{3} e^{7} + 118 \, b d^{2} e^{8} + 208 \, a d e^{9}\right)} e^{\left(-8\right)}\right)} x^{2} - 15 \, {\left(3 \, c d^{4} e^{6} - 10 \, b d^{3} e^{7} - 176 \, a d^{2} e^{8}\right)} e^{\left(-8\right)}\right)} \sqrt{x^{2} e + d} x"," ",0,"-1/256*(3*c*d^5 - 10*b*d^4*e + 80*a*d^3*e^2)*e^(-5/2)*log(abs(-x*e^(1/2) + sqrt(x^2*e + d))) + 1/3840*(2*(4*(6*(8*c*x^2*e^2 + (21*c*d*e^9 + 10*b*e^10)*e^(-8))*x^2 + (93*c*d^2*e^8 + 170*b*d*e^9 + 80*a*e^10)*e^(-8))*x^2 + 5*(3*c*d^3*e^7 + 118*b*d^2*e^8 + 208*a*d*e^9)*e^(-8))*x^2 - 15*(3*c*d^4*e^6 - 10*b*d^3*e^7 - 176*a*d^2*e^8)*e^(-8))*sqrt(x^2*e + d)*x","A",0
277,1,145,0,0.221546," ","integrate((e*x^2+d)^(3/2)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{1}{128} \, {\left(3 \, c d^{4} - 8 \, b d^{3} e + 48 \, a d^{2} e^{2}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -x e^{\frac{1}{2}} + \sqrt{x^{2} e + d} \right|}\right) + \frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, c x^{2} e + {\left(9 \, c d e^{6} + 8 \, b e^{7}\right)} e^{\left(-6\right)}\right)} x^{2} + {\left(3 \, c d^{2} e^{5} + 56 \, b d e^{6} + 48 \, a e^{7}\right)} e^{\left(-6\right)}\right)} x^{2} - 3 \, {\left(3 \, c d^{3} e^{4} - 8 \, b d^{2} e^{5} - 80 \, a d e^{6}\right)} e^{\left(-6\right)}\right)} \sqrt{x^{2} e + d} x"," ",0,"-1/128*(3*c*d^4 - 8*b*d^3*e + 48*a*d^2*e^2)*e^(-5/2)*log(abs(-x*e^(1/2) + sqrt(x^2*e + d))) + 1/384*(2*(4*(6*c*x^2*e + (9*c*d*e^6 + 8*b*e^7)*e^(-6))*x^2 + (3*c*d^2*e^5 + 56*b*d*e^6 + 48*a*e^7)*e^(-6))*x^2 - 3*(3*c*d^3*e^4 - 8*b*d^2*e^5 - 80*a*d*e^6)*e^(-6))*sqrt(x^2*e + d)*x","A",0
278,1,106,0,0.219159," ","integrate((e*x^2+d)^(1/2)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{1}{16} \, {\left(c d^{3} - 2 \, b d^{2} e + 8 \, a d e^{2}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -x e^{\frac{1}{2}} + \sqrt{x^{2} e + d} \right|}\right) + \frac{1}{48} \, {\left(2 \, {\left(4 \, c x^{2} + {\left(c d e^{3} + 6 \, b e^{4}\right)} e^{\left(-4\right)}\right)} x^{2} - 3 \, {\left(c d^{2} e^{2} - 2 \, b d e^{3} - 8 \, a e^{4}\right)} e^{\left(-4\right)}\right)} \sqrt{x^{2} e + d} x"," ",0,"-1/16*(c*d^3 - 2*b*d^2*e + 8*a*d*e^2)*e^(-5/2)*log(abs(-x*e^(1/2) + sqrt(x^2*e + d))) + 1/48*(2*(4*c*x^2 + (c*d*e^3 + 6*b*e^4)*e^(-4))*x^2 - 3*(c*d^2*e^2 - 2*b*d*e^3 - 8*a*e^4)*e^(-4))*sqrt(x^2*e + d)*x","A",0
279,1,79,0,0.192708," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","-\frac{1}{8} \, {\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -x e^{\frac{1}{2}} + \sqrt{x^{2} e + d} \right|}\right) + \frac{1}{8} \, {\left(2 \, c x^{2} e^{\left(-1\right)} - {\left(3 \, c d e - 4 \, b e^{2}\right)} e^{\left(-3\right)}\right)} \sqrt{x^{2} e + d} x"," ",0,"-1/8*(3*c*d^2 - 4*b*d*e + 8*a*e^2)*e^(-5/2)*log(abs(-x*e^(1/2) + sqrt(x^2*e + d))) + 1/8*(2*c*x^2*e^(-1) - (3*c*d*e - 4*b*e^2)*e^(-3))*sqrt(x^2*e + d)*x","A",0
280,1,80,0,0.204869," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(3 \, c d - 2 \, b e\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -x e^{\frac{1}{2}} + \sqrt{x^{2} e + d} \right|}\right) + \frac{{\left(c x^{2} e^{\left(-1\right)} + \frac{{\left(3 \, c d^{2} e - 2 \, b d e^{2} + 2 \, a e^{3}\right)} e^{\left(-3\right)}}{d}\right)} x}{2 \, \sqrt{x^{2} e + d}}"," ",0,"1/2*(3*c*d - 2*b*e)*e^(-5/2)*log(abs(-x*e^(1/2) + sqrt(x^2*e + d))) + 1/2*(c*x^2*e^(-1) + (3*c*d^2*e - 2*b*d*e^2 + 2*a*e^3)*e^(-3)/d)*x/sqrt(x^2*e + d)","A",0
281,1,88,0,0.225236," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(5/2),x, algorithm=""giac"")","-c e^{\left(-\frac{5}{2}\right)} \log\left({\left| -x e^{\frac{1}{2}} + \sqrt{x^{2} e + d} \right|}\right) - \frac{{\left(\frac{{\left(4 \, c d^{2} e^{2} - b d e^{3} - 2 \, a e^{4}\right)} x^{2} e^{\left(-3\right)}}{d^{2}} + \frac{3 \, {\left(c d^{3} e - a d e^{3}\right)} e^{\left(-3\right)}}{d^{2}}\right)} x}{3 \, {\left(x^{2} e + d\right)}^{\frac{3}{2}}}"," ",0,"-c*e^(-5/2)*log(abs(-x*e^(1/2) + sqrt(x^2*e + d))) - 1/3*((4*c*d^2*e^2 - b*d*e^3 - 2*a*e^4)*x^2*e^(-3)/d^2 + 3*(c*d^3*e - a*d*e^3)*e^(-3)/d^2)*x/(x^2*e + d)^(3/2)","A",0
282,1,75,0,0.210743," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(7/2),x, algorithm=""giac"")","\frac{{\left(x^{2} {\left(\frac{{\left(3 \, c d^{2} e^{2} + 2 \, b d e^{3} + 8 \, a e^{4}\right)} x^{2} e^{\left(-2\right)}}{d^{3}} + \frac{5 \, {\left(b d^{2} e^{2} + 4 \, a d e^{3}\right)} e^{\left(-2\right)}}{d^{3}}\right)} + \frac{15 \, a}{d}\right)} x}{15 \, {\left(x^{2} e + d\right)}^{\frac{5}{2}}}"," ",0,"1/15*(x^2*((3*c*d^2*e^2 + 2*b*d*e^3 + 8*a*e^4)*x^2*e^(-2)/d^3 + 5*(b*d^2*e^2 + 4*a*d*e^3)*e^(-2)/d^3) + 15*a/d)*x/(x^2*e + d)^(5/2)","A",0
283,1,113,0,0.270486," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{2 \, {\left(3 \, c d^{2} e^{4} + 4 \, b d e^{5} + 24 \, a e^{6}\right)} x^{2} e^{\left(-3\right)}}{d^{4}} + \frac{7 \, {\left(3 \, c d^{3} e^{3} + 4 \, b d^{2} e^{4} + 24 \, a d e^{5}\right)} e^{\left(-3\right)}}{d^{4}}\right)} + \frac{35 \, {\left(b d^{3} e^{3} + 6 \, a d^{2} e^{4}\right)} e^{\left(-3\right)}}{d^{4}}\right)} x^{2} + \frac{105 \, a}{d}\right)} x}{105 \, {\left(x^{2} e + d\right)}^{\frac{7}{2}}}"," ",0,"1/105*((x^2*(2*(3*c*d^2*e^4 + 4*b*d*e^5 + 24*a*e^6)*x^2*e^(-3)/d^4 + 7*(3*c*d^3*e^3 + 4*b*d^2*e^4 + 24*a*d*e^5)*e^(-3)/d^4) + 35*(b*d^3*e^3 + 6*a*d^2*e^4)*e^(-3)/d^4)*x^2 + 105*a/d)*x/(x^2*e + d)^(7/2)","A",0
284,1,148,0,0.228057," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(11/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(4 \, x^{2} {\left(\frac{2 \, {\left(c d^{2} e^{6} + 2 \, b d e^{7} + 16 \, a e^{8}\right)} x^{2} e^{\left(-4\right)}}{d^{5}} + \frac{9 \, {\left(c d^{3} e^{5} + 2 \, b d^{2} e^{6} + 16 \, a d e^{7}\right)} e^{\left(-4\right)}}{d^{5}}\right)} + \frac{63 \, {\left(c d^{4} e^{4} + 2 \, b d^{3} e^{5} + 16 \, a d^{2} e^{6}\right)} e^{\left(-4\right)}}{d^{5}}\right)} x^{2} + \frac{105 \, {\left(b d^{4} e^{4} + 8 \, a d^{3} e^{5}\right)} e^{\left(-4\right)}}{d^{5}}\right)} x^{2} + \frac{315 \, a}{d}\right)} x}{315 \, {\left(x^{2} e + d\right)}^{\frac{9}{2}}}"," ",0,"1/315*(((4*x^2*(2*(c*d^2*e^6 + 2*b*d*e^7 + 16*a*e^8)*x^2*e^(-4)/d^5 + 9*(c*d^3*e^5 + 2*b*d^2*e^6 + 16*a*d*e^7)*e^(-4)/d^5) + 63*(c*d^4*e^4 + 2*b*d^3*e^5 + 16*a*d^2*e^6)*e^(-4)/d^5)*x^2 + 105*(b*d^4*e^4 + 8*a*d^3*e^5)*e^(-4)/d^5)*x^2 + 315*a/d)*x/(x^2*e + d)^(9/2)","A",0
285,1,189,0,0.234989," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(13/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(2 \, {\left(4 \, x^{2} {\left(\frac{2 \, {\left(3 \, c d^{2} e^{8} + 8 \, b d e^{9} + 80 \, a e^{10}\right)} x^{2} e^{\left(-5\right)}}{d^{6}} + \frac{11 \, {\left(3 \, c d^{3} e^{7} + 8 \, b d^{2} e^{8} + 80 \, a d e^{9}\right)} e^{\left(-5\right)}}{d^{6}}\right)} + \frac{99 \, {\left(3 \, c d^{4} e^{6} + 8 \, b d^{3} e^{7} + 80 \, a d^{2} e^{8}\right)} e^{\left(-5\right)}}{d^{6}}\right)} x^{2} + \frac{231 \, {\left(3 \, c d^{5} e^{5} + 8 \, b d^{4} e^{6} + 80 \, a d^{3} e^{7}\right)} e^{\left(-5\right)}}{d^{6}}\right)} x^{2} + \frac{1155 \, {\left(b d^{5} e^{5} + 10 \, a d^{4} e^{6}\right)} e^{\left(-5\right)}}{d^{6}}\right)} x^{2} + \frac{3465 \, a}{d}\right)} x}{3465 \, {\left(x^{2} e + d\right)}^{\frac{11}{2}}}"," ",0,"1/3465*(((2*(4*x^2*(2*(3*c*d^2*e^8 + 8*b*d*e^9 + 80*a*e^10)*x^2*e^(-5)/d^6 + 11*(3*c*d^3*e^7 + 8*b*d^2*e^8 + 80*a*d*e^9)*e^(-5)/d^6) + 99*(3*c*d^4*e^6 + 8*b*d^3*e^7 + 80*a*d^2*e^8)*e^(-5)/d^6)*x^2 + 231*(3*c*d^5*e^5 + 8*b*d^4*e^6 + 80*a*d^3*e^7)*e^(-5)/d^6)*x^2 + 1155*(b*d^5*e^5 + 10*a*d^4*e^6)*e^(-5)/d^6)*x^2 + 3465*a/d)*x/(x^2*e + d)^(11/2)","A",0
286,0,0,0,0.000000," ","integrate((5*x^2+7)^3*(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7)^3, x)","F",0
287,0,0,0,0.000000," ","integrate((5*x^2+7)^2*(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7)^2, x)","F",0
288,0,0,0,0.000000," ","integrate((5*x^2+7)*(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7), x)","F",0
289,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 2}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2), x)","F",0
290,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(1/2)/(5*x^2+7),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{5 \, x^{2} + 7}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2)/(5*x^2 + 7), x)","F",0
291,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{{\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2)/(5*x^2 + 7)^2, x)","F",0
292,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(1/2)/(5*x^2+7)^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{{\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 2)/(5*x^2 + 7)^3, x)","F",0
293,0,0,0,0.000000," ","integrate((5*x^2+7)^3*(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{3}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2)*(5*x^2 + 7)^3, x)","F",0
294,0,0,0,0.000000," ","integrate((5*x^2+7)^2*(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{2}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2)*(5*x^2 + 7)^2, x)","F",0
295,0,0,0,0.000000," ","integrate((5*x^2+7)*(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2)*(5*x^2 + 7), x)","F",0
296,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2), x)","F",0
297,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(3/2)/(5*x^2+7),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}{5 \, x^{2} + 7}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2)/(5*x^2 + 7), x)","F",0
298,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(3/2)/(5*x^2+7)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}{{\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2)/(5*x^2 + 7)^2, x)","F",0
299,0,0,0,0.000000," ","integrate((x^4+3*x^2+2)^(3/2)/(5*x^2+7)^3,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}{{\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(3/2)/(5*x^2 + 7)^3, x)","F",0
300,0,0,0,0.000000," ","integrate((5*x^2+7)^3/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{3}}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^3/sqrt(x^4 + 3*x^2 + 2), x)","F",0
301,0,0,0,0.000000," ","integrate((5*x^2+7)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{2}}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^2/sqrt(x^4 + 3*x^2 + 2), x)","F",0
302,0,0,0,0.000000," ","integrate((5*x^2+7)/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{5 \, x^{2} + 7}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate((5*x^2 + 7)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(x^4 + 3*x^2 + 2), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7)^2), x)","F",0
306,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7)^3), x)","F",0
307,0,0,0,0.000000," ","integrate((5*x^2+7)^5/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{5}}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^5/(x^4 + 3*x^2 + 2)^(3/2), x)","F",0
308,0,0,0,0.000000," ","integrate((5*x^2+7)^4/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{4}}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^4/(x^4 + 3*x^2 + 2)^(3/2), x)","F",0
309,0,0,0,0.000000," ","integrate((5*x^2+7)^3/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{3}}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^3/(x^4 + 3*x^2 + 2)^(3/2), x)","F",0
310,0,0,0,0.000000," ","integrate((5*x^2+7)^2/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{2}}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^2/(x^4 + 3*x^2 + 2)^(3/2), x)","F",0
311,0,0,0,0.000000," ","integrate((5*x^2+7)/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{5 \, x^{2} + 7}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)/(x^4 + 3*x^2 + 2)^(3/2), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 2)^(-3/2), x)","F",0
313,0,0,0,0.000000," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}}\,{d x}"," ",0,"integrate(1/((x^4 + 3*x^2 + 2)^(3/2)*(5*x^2 + 7)), x)","F",0
314,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(1/((x^4 + 3*x^2 + 2)^(3/2)*(5*x^2 + 7)^2), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(1/((x^4 + 3*x^2 + 2)^(3/2)*(5*x^2 + 7)^3), x)","F",0
316,0,0,0,0.000000," ","integrate((5*x^2+7)^4*(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)^4, x)","F",0
317,0,0,0,0.000000," ","integrate((5*x^2+7)^3*(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)^3, x)","F",0
318,0,0,0,0.000000," ","integrate((5*x^2+7)^2*(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)^2, x)","F",0
319,0,0,0,0.000000," ","integrate((5*x^2+7)*(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7), x)","F",0
320,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + x^{2} + 2}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2), x)","F",0
321,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(1/2)/(5*x^2+7),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} + x^{2} + 2}}{5 \, x^{2} + 7}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)/(5*x^2 + 7), x)","F",0
322,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(1/2)/(5*x^2+7)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} + x^{2} + 2}}{{\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)/(5*x^2 + 7)^2, x)","F",0
323,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(1/2)/(5*x^2+7)^3,x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} + x^{2} + 2}}{{\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-x^4 + x^2 + 2)/(5*x^2 + 7)^3, x)","F",0
324,0,0,0,0.000000," ","integrate((5*x^2+7)^4*(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{4}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7)^4, x)","F",0
325,0,0,0,0.000000," ","integrate((5*x^2+7)^3*(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{3}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7)^3, x)","F",0
326,0,0,0,0.000000," ","integrate((5*x^2+7)^2*(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{2}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7)^2, x)","F",0
327,0,0,0,0.000000," ","integrate((5*x^2+7)*(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7), x)","F",0
328,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2), x)","F",0
329,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(3/2)/(5*x^2+7),x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}{5 \, x^{2} + 7}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)/(5*x^2 + 7), x)","F",0
330,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(3/2)/(5*x^2+7)^2,x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}{{\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)/(5*x^2 + 7)^2, x)","F",0
331,0,0,0,0.000000," ","integrate((-x^4+x^2+2)^(3/2)/(5*x^2+7)^3,x, algorithm=""giac"")","\int \frac{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}{{\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(3/2)/(5*x^2 + 7)^3, x)","F",0
332,0,0,0,0.000000," ","integrate((5*x^2+7)^3/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{3}}{\sqrt{-x^{4} + x^{2} + 2}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^3/sqrt(-x^4 + x^2 + 2), x)","F",0
333,0,0,0,0.000000," ","integrate((5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{2}}{\sqrt{-x^{4} + x^{2} + 2}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^2/sqrt(-x^4 + x^2 + 2), x)","F",0
334,0,0,0,0.000000," ","integrate((5*x^2+7)/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{5 \, x^{2} + 7}{\sqrt{-x^{4} + x^{2} + 2}}\,{d x}"," ",0,"integrate((5*x^2 + 7)/sqrt(-x^4 + x^2 + 2), x)","F",0
335,0,0,0,0.000000," ","integrate(1/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + x^{2} + 2}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + x^2 + 2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(5*x^2+7)/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)^2), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^3/(-x^4+x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)^3), x)","F",0
339,0,0,0,0.000000," ","integrate((5*x^2+7)^5/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{5}}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^5/(-x^4 + x^2 + 2)^(3/2), x)","F",0
340,0,0,0,0.000000," ","integrate((5*x^2+7)^4/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{4}}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^4/(-x^4 + x^2 + 2)^(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{3}}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^3/(-x^4 + x^2 + 2)^(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate((5*x^2+7)^2/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{2}}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^2/(-x^4 + x^2 + 2)^(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate((5*x^2+7)/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{5 \, x^{2} + 7}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)/(-x^4 + x^2 + 2)^(3/2), x)","F",0
344,0,0,0,0.000000," ","integrate(1/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-x^4 + x^2 + 2)^(-3/2), x)","F",0
345,0,0,0,0.000000," ","integrate(1/(5*x^2+7)/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}}\,{d x}"," ",0,"integrate(1/((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7)), x)","F",0
346,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^2/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(1/((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7)^2), x)","F",0
347,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(1/((-x^4 + x^2 + 2)^(3/2)*(5*x^2 + 7)^3), x)","F",0
348,0,0,0,0.000000," ","integrate((5*x^2+7)^4*(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)^4, x)","F",0
349,0,0,0,0.000000," ","integrate((5*x^2+7)^3*(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)^3, x)","F",0
350,0,0,0,0.000000," ","integrate((5*x^2+7)^2*(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)^2, x)","F",0
351,0,0,0,0.000000," ","integrate((5*x^2+7)*(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7), x)","F",0
352,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 3 \, x^{2} + 4}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4), x)","F",0
353,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(1/2)/(5*x^2+7),x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{5 \, x^{2} + 7}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)/(5*x^2 + 7), x)","F",0
354,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{{\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)/(5*x^2 + 7)^2, x)","F",0
355,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(1/2)/(5*x^2+7)^3,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{{\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 3*x^2 + 4)/(5*x^2 + 7)^3, x)","F",0
356,0,0,0,0.000000," ","integrate((5*x^2+7)^4*(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{4}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7)^4, x)","F",0
357,0,0,0,0.000000," ","integrate((5*x^2+7)^3*(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{3}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7)^3, x)","F",0
358,0,0,0,0.000000," ","integrate((5*x^2+7)^2*(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{2}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7)^2, x)","F",0
359,0,0,0,0.000000," ","integrate((5*x^2+7)*(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7), x)","F",0
360,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2), x)","F",0
361,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(3/2)/(5*x^2+7),x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}{5 \, x^{2} + 7}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)/(5*x^2 + 7), x)","F",0
362,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(3/2)/(5*x^2+7)^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}{{\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)/(5*x^2 + 7)^2, x)","F",0
363,0,0,0,0.000000," ","integrate((x^4+3*x^2+4)^(3/2)/(5*x^2+7)^3,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}{{\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(3/2)/(5*x^2 + 7)^3, x)","F",0
364,0,0,0,0.000000," ","integrate((5*x^2+7)^3/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{3}}{\sqrt{x^{4} + 3 \, x^{2} + 4}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^3/sqrt(x^4 + 3*x^2 + 4), x)","F",0
365,0,0,0,0.000000," ","integrate((5*x^2+7)^2/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{2}}{\sqrt{x^{4} + 3 \, x^{2} + 4}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^2/sqrt(x^4 + 3*x^2 + 4), x)","F",0
366,0,0,0,0.000000," ","integrate((5*x^2+7)/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{5 \, x^{2} + 7}{\sqrt{x^{4} + 3 \, x^{2} + 4}}\,{d x}"," ",0,"integrate((5*x^2 + 7)/sqrt(x^4 + 3*x^2 + 4), x)","F",0
367,0,0,0,0.000000," ","integrate(1/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 4}}\,{d x}"," ",0,"integrate(1/sqrt(x^4 + 3*x^2 + 4), x)","F",0
368,0,0,0,0.000000," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)), x)","F",0
369,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)^2), x)","F",0
370,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)^3), x)","F",0
371,0,0,0,0.000000," ","integrate((5*x^2+7)^5/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{5}}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^5/(x^4 + 3*x^2 + 4)^(3/2), x)","F",0
372,0,0,0,0.000000," ","integrate((5*x^2+7)^4/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{4}}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^4/(x^4 + 3*x^2 + 4)^(3/2), x)","F",0
373,0,0,0,0.000000," ","integrate((5*x^2+7)^3/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{3}}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^3/(x^4 + 3*x^2 + 4)^(3/2), x)","F",0
374,0,0,0,0.000000," ","integrate((5*x^2+7)^2/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(5 \, x^{2} + 7\right)}^{2}}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)^2/(x^4 + 3*x^2 + 4)^(3/2), x)","F",0
375,0,0,0,0.000000," ","integrate((5*x^2+7)/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{5 \, x^{2} + 7}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((5*x^2 + 7)/(x^4 + 3*x^2 + 4)^(3/2), x)","F",0
376,0,0,0,0.000000," ","integrate(1/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^4 + 3*x^2 + 4)^(-3/2), x)","F",0
377,0,0,0,0.000000," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}}\,{d x}"," ",0,"integrate(1/((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7)), x)","F",0
378,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{2}}\,{d x}"," ",0,"integrate(1/((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7)^2), x)","F",0
379,0,0,0,0.000000," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+4)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}} {\left(5 \, x^{2} + 7\right)}^{3}}\,{d x}"," ",0,"integrate(1/((x^4 + 3*x^2 + 4)^(3/2)*(5*x^2 + 7)^3), x)","F",0
380,0,0,0,0.000000," ","integrate((e*x^2+d)^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{3}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^3/sqrt(c*x^4 + b*x^2 + a), x)","F",0
381,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(c*x^4 + b*x^2 + a), x)","F",0
382,0,0,0,0.000000," ","integrate((e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
383,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)), x)","F",0
384,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)^2), x)","F",0
385,0,0,0,0.000000," ","integrate((e*x^2+d)^3/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{3}}{\sqrt{-c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^3/sqrt(-c*x^4 + b*x^2 + a), x)","F",0
386,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{-c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(-c*x^4 + b*x^2 + a), x)","F",0
387,0,0,0,0.000000," ","integrate((e*x^2+d)/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{-c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(-c*x^4 + b*x^2 + a), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + b*x^2 + a)*(e*x^2 + d)), x)","F",0
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390,0,0,0,0.000000," ","integrate((e*x^2+d)/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{c x^{4} + b x^{2} - a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(c*x^4 + b*x^2 - a), x)","F",0
391,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + b x^{2} - a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + b*x^2 - a)*(e*x^2 + d)), x)","F",0
392,0,0,0,0.000000," ","integrate((e*x^2+d)/(-c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{-c x^{4} + b x^{2} - a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(-c*x^4 + b*x^2 - a), x)","F",0
393,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c x^{4} + b x^{2} - a} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*x^4 + b*x^2 - a)*(e*x^2 + d)), x)","F",0
394,0,0,0,0.000000," ","integrate((e*x^2+d)^3/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{3}}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate((e*x^2 + d)^3/sqrt(x^4 + 3*x^2 + 2), x)","F",0
395,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(x^4 + 3*x^2 + 2), x)","F",0
396,0,0,0,0.000000," ","integrate((e*x^2+d)/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{x^{4} + 3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
397,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 2)*(e*x^2 + d)), x)","F",0
398,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^4 + 3*x^2 + 2)*(e*x^2 + d)^2), x)","F",0
399,0,0,0,0.000000," ","integrate((e*x^2+c)^q*(b*x^4+c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(b x^{4} + c x^{2} + a\right)}^{p} {\left(e x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q, x)","F",0
400,0,0,0,0.000000," ","integrate((e*x^2+c)^3*(b*x^4+c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + c\right)}^{3} {\left(b x^{4} + c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + c)^3*(b*x^4 + c*x^2 + a)^p, x)","F",0
401,0,0,0,0.000000," ","integrate((e*x^2+c)^2*(b*x^4+c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + c\right)}^{2} {\left(b x^{4} + c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + c)^2*(b*x^4 + c*x^2 + a)^p, x)","F",0
402,0,0,0,0.000000," ","integrate((e*x^2+c)*(b*x^4+c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x^{2} + c\right)} {\left(b x^{4} + c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^2 + c)*(b*x^4 + c*x^2 + a)^p, x)","F",0
403,0,0,0,0.000000," ","integrate((b*x^4+c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(b x^{4} + c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^4 + c*x^2 + a)^p, x)","F",0
404,0,0,0,0.000000," ","integrate((b*x^4+c*x^2+a)^p/(e*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + c x^{2} + a\right)}^{p}}{e x^{2} + c}\,{d x}"," ",0,"integrate((b*x^4 + c*x^2 + a)^p/(e*x^2 + c), x)","F",0
405,0,0,0,0.000000," ","integrate((b*x^4+c*x^2+a)^p/(e*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{4} + c x^{2} + a\right)}^{p}}{{\left(e x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^4 + c*x^2 + a)^p/(e*x^2 + c)^2, x)","F",0
406,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{g x + f}{\sqrt{c x^{4} + a} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate((g*x + f)/(sqrt(c*x^4 + a)*(e*x + d)), x)","F",0
407,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4-a)^(1/2),x, algorithm=""giac"")","\int \frac{g x + f}{\sqrt{c x^{4} - a} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate((g*x + f)/(sqrt(c*x^4 - a)*(e*x + d)), x)","F",0
408,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/(1+x+3^(1/2))/(-4+x^4+4*3^(1/2)*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{x^{4} + 4 \, \sqrt{3} x^{2} - 4} {\left(x + \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/(sqrt(x^4 + 4*sqrt(3)*x^2 - 4)*(x + sqrt(3) + 1)), x)","F",0
409,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/(1+x-3^(1/2))/(-4+x^4-4*3^(1/2)*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{x^{4} - 4 \, \sqrt{3} x^{2} - 4} {\left(x - \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/(sqrt(x^4 - 4*sqrt(3)*x^2 - 4)*(x - sqrt(3) + 1)), x)","F",0
410,0,0,0,0.000000," ","integrate((1+2*x-3^(1/2))/(1+2*x+3^(1/2))/(-1+4*x^4+4*3^(1/2)*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x - \sqrt{3} + 1}{\sqrt{4 \, x^{4} + 4 \, \sqrt{3} x^{2} - 1} {\left(2 \, x + \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate((2*x - sqrt(3) + 1)/(sqrt(4*x^4 + 4*sqrt(3)*x^2 - 1)*(2*x + sqrt(3) + 1)), x)","F",0
411,0,0,0,0.000000," ","integrate((1+2*x+3^(1/2))/(1+2*x-3^(1/2))/(-1+4*x^4-4*3^(1/2)*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{2 \, x + \sqrt{3} + 1}{\sqrt{4 \, x^{4} - 4 \, \sqrt{3} x^{2} - 1} {\left(2 \, x - \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate((2*x + sqrt(3) + 1)/(sqrt(4*x^4 - 4*sqrt(3)*x^2 - 1)*(2*x - sqrt(3) + 1)), x)","F",0
412,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{g x + f}{\sqrt{c x^{4} + b x^{2} + a} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate((g*x + f)/(sqrt(c*x^4 + b*x^2 + a)*(e*x + d)), x)","F",0
413,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{g x + f}{\sqrt{c x^{4} + b x^{2} - a} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate((g*x + f)/(sqrt(c*x^4 + b*x^2 - a)*(e*x + d)), x)","F",0
