1,1,153,0,0.329900," ","integrate(sin(x)^5/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","-\frac{2 \, c^{2} \cos\left(x\right)^{3} - 3 \, b c \cos\left(x\right)^{2} + 6 \, b^{2} \cos\left(x\right) - 6 \, a c \cos\left(x\right) - 12 \, c^{2} \cos\left(x\right)}{6 \, c^{3}} + \frac{{\left(b^{3} - 2 \, a b c - 2 \, b c^{2}\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{2 \, c^{4}} - \frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2} - 2 \, b^{2} c^{2} + 4 \, a c^{3} + 2 \, c^{4}\right)} \arctan\left(\frac{2 \, c \cos\left(x\right) + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"-1/6*(2*c^2*cos(x)^3 - 3*b*c*cos(x)^2 + 6*b^2*cos(x) - 6*a*c*cos(x) - 12*c^2*cos(x))/c^3 + 1/2*(b^3 - 2*a*b*c - 2*b*c^2)*log(c*cos(x)^2 + b*cos(x) + a)/c^4 - (b^4 - 4*a*b^2*c + 2*a^2*c^2 - 2*b^2*c^2 + 4*a*c^3 + 2*c^4)*arctan((2*c*cos(x) + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
2,1,76,0,0.377001," ","integrate(sin(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\frac{\cos\left(x\right)}{c} - \frac{b \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{2 \, c^{2}} + \frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \arctan\left(\frac{2 \, c \cos\left(x\right) + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"cos(x)/c - 1/2*b*log(c*cos(x)^2 + b*cos(x) + a)/c^2 + (b^2 - 2*a*c - 2*c^2)*arctan((2*c*cos(x) + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
3,1,35,0,0.331689," ","integrate(sin(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{2 \, c \cos\left(x\right) + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"-2*arctan((2*c*cos(x) + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
4,1,130,0,0.274995," ","integrate(csc(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\frac{b \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{2 \, {\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)}} + \frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \arctan\left(\frac{2 \, c \cos\left(x\right) + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{\log\left(\cos\left(x\right) + 1\right)}{2 \, {\left(a - b + c\right)}} + \frac{\log\left(-\cos\left(x\right) + 1\right)}{2 \, {\left(a + b + c\right)}}"," ",0,"1/2*b*log(c*cos(x)^2 + b*cos(x) + a)/(a^2 - b^2 + 2*a*c + c^2) + (b^2 - 2*a*c - 2*c^2)*arctan((2*c*cos(x) + b)/sqrt(-b^2 + 4*a*c))/((a^2 - b^2 + 2*a*c + c^2)*sqrt(-b^2 + 4*a*c)) - 1/2*log(cos(x) + 1)/(a - b + c) + 1/2*log(-cos(x) + 1)/(a + b + c)","A",0
5,1,378,0,0.345444," ","integrate(csc(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","-\frac{{\left(b^{3} - 2 \, a b c - 2 \, b c^{2}\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} + 4 \, a^{3} c - 4 \, a b^{2} c + 6 \, a^{2} c^{2} - 2 \, b^{2} c^{2} + 4 \, a c^{3} + c^{4}\right)}} - \frac{{\left(a - 2 \, b + 3 \, c\right)} \log\left(\cos\left(x\right) + 1\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, a c - 2 \, b c + c^{2}\right)}} + \frac{{\left(a + 2 \, b + 3 \, c\right)} \log\left(-\cos\left(x\right) + 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2} + 2 \, a c + 2 \, b c + c^{2}\right)}} - \frac{{\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2} - 2 \, b^{2} c^{2} + 4 \, a c^{3} + 2 \, c^{4}\right)} \arctan\left(\frac{2 \, c \cos\left(x\right) + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} + 4 \, a^{3} c - 4 \, a b^{2} c + 6 \, a^{2} c^{2} - 2 \, b^{2} c^{2} + 4 \, a c^{3} + c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{a^{2} b - b^{3} + 2 \, a b c + b c^{2} - {\left(a^{3} - a b^{2} + 3 \, a^{2} c - b^{2} c + 3 \, a c^{2} + c^{3}\right)} \cos\left(x\right)}{2 \, {\left(a + b + c\right)}^{2} {\left(a - b + c\right)}^{2} {\left(\cos\left(x\right) + 1\right)} {\left(\cos\left(x\right) - 1\right)}}"," ",0,"-1/2*(b^3 - 2*a*b*c - 2*b*c^2)*log(c*cos(x)^2 + b*cos(x) + a)/(a^4 - 2*a^2*b^2 + b^4 + 4*a^3*c - 4*a*b^2*c + 6*a^2*c^2 - 2*b^2*c^2 + 4*a*c^3 + c^4) - 1/4*(a - 2*b + 3*c)*log(cos(x) + 1)/(a^2 - 2*a*b + b^2 + 2*a*c - 2*b*c + c^2) + 1/4*(a + 2*b + 3*c)*log(-cos(x) + 1)/(a^2 + 2*a*b + b^2 + 2*a*c + 2*b*c + c^2) - (b^4 - 4*a*b^2*c + 2*a^2*c^2 - 2*b^2*c^2 + 4*a*c^3 + 2*c^4)*arctan((2*c*cos(x) + b)/sqrt(-b^2 + 4*a*c))/((a^4 - 2*a^2*b^2 + b^4 + 4*a^3*c - 4*a*b^2*c + 6*a^2*c^2 - 2*b^2*c^2 + 4*a*c^3 + c^4)*sqrt(-b^2 + 4*a*c)) - 1/2*(a^2*b - b^3 + 2*a*b*c + b*c^2 - (a^3 - a*b^2 + 3*a^2*c - b^2*c + 3*a*c^2 + c^3)*cos(x))/((a + b + c)^2*(a - b + c)^2*(cos(x) + 1)*(cos(x) - 1))","A",0
6,-1,0,0,0.000000," ","integrate(sin(x)^4/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,1,6564,0,177.349330," ","integrate(sin(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","-\frac{x}{c} - \frac{{\left({\left(2 \, a^{2} b^{4} - 4 \, a b^{5} + 2 \, b^{6} - 16 \, a^{3} b^{2} c + 32 \, a^{2} b^{3} c - 12 \, a b^{4} c - 4 \, b^{5} c + 32 \, a^{4} c^{2} - 64 \, a^{3} b c^{2} + 32 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + 64 \, a^{3} c^{3} - 64 \, a^{2} b c^{3} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c + 8 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c + 34 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{2} - 24 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} c^{2} {\left| a - b + c \right|} + {\left(4 \, a^{2} b^{4} c - 4 \, b^{6} c - 32 \, a^{3} b^{2} c^{2} + 40 \, a b^{4} c^{2} + 64 \, a^{4} c^{3} - 128 \, a^{2} b^{2} c^{3} + 4 \, b^{4} c^{3} + 128 \, a^{3} c^{4} - 32 \, a b^{2} c^{4} + 64 \, a^{2} c^{5} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b^{2} c - \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{3} c + 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{4} c + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{5} c + 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} c^{2} + 4 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b c^{2} - 45 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} c^{2} - 38 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} c^{2} - \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} c^{2} + 68 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c^{3} + 72 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c^{3} - \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c^{3} + 36 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{4} + 4 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{4} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{4} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left| a - b + c \right|} {\left| c \right|} + {\left(2 \, a^{3} b^{3} c^{2} - 4 \, a^{2} b^{4} c^{2} + 2 \, a b^{5} c^{2} - 8 \, a^{4} b c^{3} + 20 \, a^{3} b^{2} c^{3} - 14 \, a^{2} b^{3} c^{3} + 4 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} - 16 \, a^{4} c^{4} + 24 \, a^{3} b c^{4} - 12 \, a^{2} b^{2} c^{4} + 6 \, a b^{3} c^{4} - 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} - 4 \, a b^{2} c^{5} + 6 \, b^{3} c^{5} + 16 \, a^{2} c^{6} - 24 \, a b c^{6} - 4 \, b^{2} c^{6} + 16 \, a c^{7} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 22 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} + 4 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c^{4} - 38 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{5} - 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b c^{5} + 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} c^{6}\right)} {\left| a - b + c \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a c - 2 \, c^{2} + \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} {\left(a c - b c + c^{2}\right)} + 4 \, {\left(a c - c^{2}\right)}^{2}}}{a c - b c + c^{2}}}}\right)\right)}}{{\left(3 \, a^{5} b^{2} c^{2} - 5 \, a^{4} b^{3} c^{2} - 6 \, a^{3} b^{4} c^{2} + 10 \, a^{2} b^{5} c^{2} + 3 \, a b^{6} c^{2} - 5 \, b^{7} c^{2} - 12 \, a^{6} c^{3} + 20 \, a^{5} b c^{3} + 47 \, a^{4} b^{2} c^{3} - 60 \, a^{3} b^{3} c^{3} - 46 \, a^{2} b^{4} c^{3} + 40 \, a b^{5} c^{3} + 11 \, b^{6} c^{3} - 92 \, a^{5} c^{4} + 80 \, a^{4} b c^{4} + 182 \, a^{3} b^{2} c^{4} - 94 \, a^{2} b^{3} c^{4} - 78 \, a b^{4} c^{4} - 6 \, b^{5} c^{4} - 184 \, a^{4} c^{5} + 56 \, a^{3} b c^{5} + 166 \, a^{2} b^{2} c^{5} + 36 \, a b^{3} c^{5} - 6 \, b^{4} c^{5} - 120 \, a^{3} c^{6} - 48 \, a^{2} b c^{6} + 23 \, a b^{2} c^{6} + 11 \, b^{3} c^{6} + 4 \, a^{2} c^{7} - 44 \, a b c^{7} - 5 \, b^{2} c^{7} + 20 \, a c^{8}\right)} {\left| c \right|}} + \frac{{\left({\left(2 \, a^{2} b^{4} - 4 \, a b^{5} + 2 \, b^{6} - 16 \, a^{3} b^{2} c + 32 \, a^{2} b^{3} c - 12 \, a b^{4} c - 4 \, b^{5} c + 32 \, a^{4} c^{2} - 64 \, a^{3} b c^{2} + 32 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + 64 \, a^{3} c^{3} - 64 \, a^{2} b c^{3} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c + 8 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c + 34 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{2} - 24 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} c^{2} {\left| a - b + c \right|} + {\left(4 \, a^{2} b^{4} c - 4 \, b^{6} c - 32 \, a^{3} b^{2} c^{2} + 40 \, a b^{4} c^{2} + 64 \, a^{4} c^{3} - 128 \, a^{2} b^{2} c^{3} + 4 \, b^{4} c^{3} + 128 \, a^{3} c^{4} - 32 \, a b^{2} c^{4} + 64 \, a^{2} c^{5} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b^{2} c + \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{3} c - 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{4} c - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{5} c - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} c^{2} - 4 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b c^{2} + 45 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} c^{2} + 38 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} c^{2} + \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} c^{2} - 68 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c^{3} - 72 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c^{3} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c^{3} + \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c^{3} - 36 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{4} - 4 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{4} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{4} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left| a - b + c \right|} {\left| c \right|} + {\left(2 \, a^{3} b^{3} c^{2} - 4 \, a^{2} b^{4} c^{2} + 2 \, a b^{5} c^{2} - 8 \, a^{4} b c^{3} + 20 \, a^{3} b^{2} c^{3} - 14 \, a^{2} b^{3} c^{3} + 4 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} - 16 \, a^{4} c^{4} + 24 \, a^{3} b c^{4} - 12 \, a^{2} b^{2} c^{4} + 6 \, a b^{3} c^{4} - 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} - 4 \, a b^{2} c^{5} + 6 \, b^{3} c^{5} + 16 \, a^{2} c^{6} - 24 \, a b c^{6} - 4 \, b^{2} c^{6} + 16 \, a c^{7} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 22 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} + 4 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c^{4} - 38 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{5} - 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b c^{5} + 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} c^{6}\right)} {\left| a - b + c \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a c - 2 \, c^{2} - \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} {\left(a c - b c + c^{2}\right)} + 4 \, {\left(a c - c^{2}\right)}^{2}}}{a c - b c + c^{2}}}}\right)\right)}}{{\left(3 \, a^{5} b^{2} c^{2} - 5 \, a^{4} b^{3} c^{2} - 6 \, a^{3} b^{4} c^{2} + 10 \, a^{2} b^{5} c^{2} + 3 \, a b^{6} c^{2} - 5 \, b^{7} c^{2} - 12 \, a^{6} c^{3} + 20 \, a^{5} b c^{3} + 47 \, a^{4} b^{2} c^{3} - 60 \, a^{3} b^{3} c^{3} - 46 \, a^{2} b^{4} c^{3} + 40 \, a b^{5} c^{3} + 11 \, b^{6} c^{3} - 92 \, a^{5} c^{4} + 80 \, a^{4} b c^{4} + 182 \, a^{3} b^{2} c^{4} - 94 \, a^{2} b^{3} c^{4} - 78 \, a b^{4} c^{4} - 6 \, b^{5} c^{4} - 184 \, a^{4} c^{5} + 56 \, a^{3} b c^{5} + 166 \, a^{2} b^{2} c^{5} + 36 \, a b^{3} c^{5} - 6 \, b^{4} c^{5} - 120 \, a^{3} c^{6} - 48 \, a^{2} b c^{6} + 23 \, a b^{2} c^{6} + 11 \, b^{3} c^{6} + 4 \, a^{2} c^{7} - 44 \, a b c^{7} - 5 \, b^{2} c^{7} + 20 \, a c^{8}\right)} {\left| c \right|}}"," ",0,"-x/c - ((2*a^2*b^4 - 4*a*b^5 + 2*b^6 - 16*a^3*b^2*c + 32*a^2*b^3*c - 12*a*b^4*c - 4*b^5*c + 32*a^4*c^2 - 64*a^3*b*c^2 + 32*a*b^3*c^2 + 2*b^4*c^2 + 64*a^3*c^3 - 64*a^2*b*c^3 - 16*a*b^2*c^3 + 32*a^2*c^4 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2 - 2*(b^2 - 4*a*c)*a^2*b^2 - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3 + 4*(b^2 - 4*a*c)*a*b^3 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^4 - 2*(b^2 - 4*a*c)*b^4 - 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c + 8*(b^2 - 4*a*c)*a^3*c + 8*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c - 16*(b^2 - 4*a*c)*a^2*b*c + 34*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c + 4*(b^2 - 4*a*c)*a*b^2*c + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c + 4*(b^2 - 4*a*c)*b^3*c - 56*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^2 + 16*(b^2 - 4*a*c)*a^2*c^2 - 24*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^2 - 16*(b^2 - 4*a*c)*a*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c^2 - 2*(b^2 - 4*a*c)*b^2*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^3 + 8*(b^2 - 4*a*c)*a*c^3)*c^2*abs(a - b + c) + (4*a^2*b^4*c - 4*b^6*c - 32*a^3*b^2*c^2 + 40*a*b^4*c^2 + 64*a^4*c^3 - 128*a^2*b^2*c^3 + 4*b^4*c^3 + 128*a^3*c^4 - 32*a*b^2*c^4 + 64*a^2*c^5 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b^2*c - sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^3*c + 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^4*c + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^5*c + 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*c^2 + 4*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b*c^2 - 45*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2*c^2 - 38*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3*c^2 - sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^4*c^2 + 68*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c^3 + 72*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c^3 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c^3 - sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c^3 + 36*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^4 + 4*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^4 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^4 - 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^5 - 4*(b^2 - 4*a*c)*a^2*b^2*c + 4*(b^2 - 4*a*c)*b^4*c + 16*(b^2 - 4*a*c)*a^3*c^2 - 24*(b^2 - 4*a*c)*a*b^2*c^2 + 32*(b^2 - 4*a*c)*a^2*c^3 - 4*(b^2 - 4*a*c)*b^2*c^3 + 16*(b^2 - 4*a*c)*a*c^4)*abs(a - b + c)*abs(c) + (2*a^3*b^3*c^2 - 4*a^2*b^4*c^2 + 2*a*b^5*c^2 - 8*a^4*b*c^3 + 20*a^3*b^2*c^3 - 14*a^2*b^3*c^3 + 4*a*b^4*c^3 - 2*b^5*c^3 - 16*a^4*c^4 + 24*a^3*b*c^4 - 12*a^2*b^2*c^4 + 6*a*b^3*c^4 - 16*a^3*c^5 + 8*a^2*b*c^5 - 4*a*b^2*c^5 + 6*b^3*c^5 + 16*a^2*c^6 - 24*a*b*c^6 - 4*b^2*c^6 + 16*a*c^7 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2 - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2*c^2 + 4*(b^2 - 4*a*c)*a^2*b^2*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c^3 - 4*(b^2 - 4*a*c)*a^3*c^3 + 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c^3 + 6*(b^2 - 4*a*c)*a^2*b*c^3 - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c^3 - 4*(b^2 - 4*a*c)*a*b^2*c^3 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c^3 + 2*(b^2 - 4*a*c)*b^3*c^3 + 22*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^4 - 4*(b^2 - 4*a*c)*a^2*c^4 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^4 + 2*(b^2 - 4*a*c)*a*b*c^4 + 4*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c^4 - 38*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^5 + 4*(b^2 - 4*a*c)*a*c^5 - 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^5 - 6*(b^2 - 4*a*c)*b*c^5 + 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*c^6 + 4*(b^2 - 4*a*c)*c^6)*abs(a - b + c))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a*c - 2*c^2 + sqrt(-4*(a*c + b*c + c^2)*(a*c - b*c + c^2) + 4*(a*c - c^2)^2))/(a*c - b*c + c^2))))/((3*a^5*b^2*c^2 - 5*a^4*b^3*c^2 - 6*a^3*b^4*c^2 + 10*a^2*b^5*c^2 + 3*a*b^6*c^2 - 5*b^7*c^2 - 12*a^6*c^3 + 20*a^5*b*c^3 + 47*a^4*b^2*c^3 - 60*a^3*b^3*c^3 - 46*a^2*b^4*c^3 + 40*a*b^5*c^3 + 11*b^6*c^3 - 92*a^5*c^4 + 80*a^4*b*c^4 + 182*a^3*b^2*c^4 - 94*a^2*b^3*c^4 - 78*a*b^4*c^4 - 6*b^5*c^4 - 184*a^4*c^5 + 56*a^3*b*c^5 + 166*a^2*b^2*c^5 + 36*a*b^3*c^5 - 6*b^4*c^5 - 120*a^3*c^6 - 48*a^2*b*c^6 + 23*a*b^2*c^6 + 11*b^3*c^6 + 4*a^2*c^7 - 44*a*b*c^7 - 5*b^2*c^7 + 20*a*c^8)*abs(c)) + ((2*a^2*b^4 - 4*a*b^5 + 2*b^6 - 16*a^3*b^2*c + 32*a^2*b^3*c - 12*a*b^4*c - 4*b^5*c + 32*a^4*c^2 - 64*a^3*b*c^2 + 32*a*b^3*c^2 + 2*b^4*c^2 + 64*a^3*c^3 - 64*a^2*b*c^3 - 16*a*b^2*c^3 + 32*a^2*c^4 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2 - 2*(b^2 - 4*a*c)*a^2*b^2 - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3 + 4*(b^2 - 4*a*c)*a*b^3 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^4 - 2*(b^2 - 4*a*c)*b^4 - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c + 8*(b^2 - 4*a*c)*a^3*c + 8*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c - 16*(b^2 - 4*a*c)*a^2*b*c + 34*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c + 4*(b^2 - 4*a*c)*a*b^2*c + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c + 4*(b^2 - 4*a*c)*b^3*c - 56*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^2 + 16*(b^2 - 4*a*c)*a^2*c^2 - 24*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^2 - 16*(b^2 - 4*a*c)*a*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c^2 - 2*(b^2 - 4*a*c)*b^2*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^3 + 8*(b^2 - 4*a*c)*a*c^3)*c^2*abs(a - b + c) + (4*a^2*b^4*c - 4*b^6*c - 32*a^3*b^2*c^2 + 40*a*b^4*c^2 + 64*a^4*c^3 - 128*a^2*b^2*c^3 + 4*b^4*c^3 + 128*a^3*c^4 - 32*a*b^2*c^4 + 64*a^2*c^5 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b^2*c + sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^3*c - 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^4*c - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^5*c - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*c^2 - 4*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b*c^2 + 45*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2*c^2 + 38*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3*c^2 + sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^4*c^2 - 68*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c^3 - 72*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c^3 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c^3 + sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c^3 - 36*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^4 - 4*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^4 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^4 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^5 - 4*(b^2 - 4*a*c)*a^2*b^2*c + 4*(b^2 - 4*a*c)*b^4*c + 16*(b^2 - 4*a*c)*a^3*c^2 - 24*(b^2 - 4*a*c)*a*b^2*c^2 + 32*(b^2 - 4*a*c)*a^2*c^3 - 4*(b^2 - 4*a*c)*b^2*c^3 + 16*(b^2 - 4*a*c)*a*c^4)*abs(a - b + c)*abs(c) + (2*a^3*b^3*c^2 - 4*a^2*b^4*c^2 + 2*a*b^5*c^2 - 8*a^4*b*c^3 + 20*a^3*b^2*c^3 - 14*a^2*b^3*c^3 + 4*a*b^4*c^3 - 2*b^5*c^3 - 16*a^4*c^4 + 24*a^3*b*c^4 - 12*a^2*b^2*c^4 + 6*a*b^3*c^4 - 16*a^3*c^5 + 8*a^2*b*c^5 - 4*a*b^2*c^5 + 6*b^3*c^5 + 16*a^2*c^6 - 24*a*b*c^6 - 4*b^2*c^6 + 16*a*c^7 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2 - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2*c^2 + 4*(b^2 - 4*a*c)*a^2*b^2*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c^3 - 4*(b^2 - 4*a*c)*a^3*c^3 + 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c^3 + 6*(b^2 - 4*a*c)*a^2*b*c^3 - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c^3 - 4*(b^2 - 4*a*c)*a*b^2*c^3 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c^3 + 2*(b^2 - 4*a*c)*b^3*c^3 + 22*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^4 - 4*(b^2 - 4*a*c)*a^2*c^4 - 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^4 + 2*(b^2 - 4*a*c)*a*b*c^4 + 4*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c^4 - 38*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^5 + 4*(b^2 - 4*a*c)*a*c^5 - 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^5 - 6*(b^2 - 4*a*c)*b*c^5 + 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*c^6 + 4*(b^2 - 4*a*c)*c^6)*abs(a - b + c))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a*c - 2*c^2 - sqrt(-4*(a*c + b*c + c^2)*(a*c - b*c + c^2) + 4*(a*c - c^2)^2))/(a*c - b*c + c^2))))/((3*a^5*b^2*c^2 - 5*a^4*b^3*c^2 - 6*a^3*b^4*c^2 + 10*a^2*b^5*c^2 + 3*a*b^6*c^2 - 5*b^7*c^2 - 12*a^6*c^3 + 20*a^5*b*c^3 + 47*a^4*b^2*c^3 - 60*a^3*b^3*c^3 - 46*a^2*b^4*c^3 + 40*a*b^5*c^3 + 11*b^6*c^3 - 92*a^5*c^4 + 80*a^4*b*c^4 + 182*a^3*b^2*c^4 - 94*a^2*b^3*c^4 - 78*a*b^4*c^4 - 6*b^5*c^4 - 184*a^4*c^5 + 56*a^3*b*c^5 + 166*a^2*b^2*c^5 + 36*a*b^3*c^5 - 6*b^4*c^5 - 120*a^3*c^6 - 48*a^2*b*c^6 + 23*a*b^2*c^6 + 11*b^3*c^6 + 4*a^2*c^7 - 44*a*b*c^7 - 5*b^2*c^7 + 20*a*c^8)*abs(c))","B",0
8,-1,0,0,0.000000," ","integrate(csc(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,17,0,0.297652," ","integrate(sin(x)/(-2+cos(x)+cos(x)^2),x, algorithm=""giac"")","\frac{1}{3} \, \log\left(\cos\left(x\right) + 2\right) - \frac{1}{3} \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"1/3*log(cos(x) + 2) - 1/3*log(-cos(x) + 1)","A",0
10,1,19,0,0.419412," ","integrate(sin(x)/(4-5*cos(x)+cos(x)^2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(-\cos\left(x\right) + 4\right) + \frac{1}{3} \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"-1/3*log(-cos(x) + 4) + 1/3*log(-cos(x) + 1)","A",0
11,1,15,0,0.599405," ","integrate(sin(x)/(3-2*cos(x)+cos(x)^2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\cos\left(x\right) - 1\right)}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*(cos(x) - 1))","A",0
12,1,28,0,0.483840," ","integrate(sin(x)/(13-4*cos(x)+cos(x)^2)^2,x, algorithm=""giac"")","-\frac{\cos\left(x\right) - 2}{18 \, {\left(\cos\left(x\right)^{2} - 4 \, \cos\left(x\right) + 13\right)}} - \frac{1}{54} \, \arctan\left(\frac{1}{3} \, \cos\left(x\right) - \frac{2}{3}\right)"," ",0,"-1/18*(cos(x) - 2)/(cos(x)^2 - 4*cos(x) + 13) - 1/54*arctan(1/3*cos(x) - 2/3)","A",0
13,-1,0,0,0.000000," ","integrate(cos(x)^4/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,-1,0,0,0.000000," ","integrate(cos(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,1,9028,0,165.932653," ","integrate(cos(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\frac{x}{c} + \frac{{\left({\left(2 \, a^{3} b^{4} - 6 \, a^{2} b^{5} + 6 \, a b^{6} - 2 \, b^{7} - 16 \, a^{4} b^{2} c + 48 \, a^{3} b^{3} c - 44 \, a^{2} b^{4} c + 8 \, a b^{5} c + 4 \, b^{6} c + 32 \, a^{5} c^{2} - 96 \, a^{4} b c^{2} + 64 \, a^{3} b^{2} c^{2} + 32 \, a^{2} b^{3} c^{2} - 30 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 64 \, a^{4} c^{3} - 128 \, a^{3} b c^{3} + 48 \, a^{2} b^{2} c^{3} + 16 \, a b^{3} c^{3} + 32 \, a^{3} c^{4} - 32 \, a^{2} b c^{4} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{4} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c + 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b c - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c + 26 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c - 28 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} c - 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{4} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} + 32 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 19 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{2} + 14 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} {\left| a - b + c \right|} + {\left(4 \, a^{3} b^{4} c - 4 \, a^{2} b^{5} c - 4 \, a b^{6} c + 4 \, b^{7} c - 32 \, a^{4} b^{2} c^{2} + 32 \, a^{3} b^{3} c^{2} + 40 \, a^{2} b^{4} c^{2} - 32 \, a b^{5} c^{2} - 8 \, b^{6} c^{2} + 64 \, a^{5} c^{3} - 64 \, a^{4} b c^{3} - 128 \, a^{3} b^{2} c^{3} + 64 \, a^{2} b^{3} c^{3} + 68 \, a b^{4} c^{3} + 4 \, b^{5} c^{3} + 128 \, a^{4} c^{4} - 160 \, a^{2} b^{2} c^{4} - 32 \, a b^{3} c^{4} + 64 \, a^{3} c^{5} + 64 \, a^{2} b c^{5} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} b^{2} c + 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b^{3} c + 8 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{4} c - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{5} c - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{6} c + 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{5} c^{2} - 8 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} b c^{2} - 49 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b^{2} c^{2} + \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{3} c^{2} + 41 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{4} c^{2} + 11 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{5} c^{2} + 68 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} c^{3} + 28 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b c^{3} - 93 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} c^{3} - 64 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} c^{3} - 11 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} c^{3} + 36 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c^{4} + 80 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c^{4} + 49 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c^{4} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c^{4} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{5} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} {\left| a - b + c \right|} {\left| c \right|} + {\left(2 \, a^{4} b^{3} c^{2} - 6 \, a^{3} b^{4} c^{2} + 6 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 8 \, a^{5} b c^{3} + 28 \, a^{4} b^{2} c^{3} - 30 \, a^{3} b^{3} c^{3} + 10 \, a^{2} b^{4} c^{3} - 2 \, a b^{5} c^{3} + 2 \, b^{6} c^{3} - 16 \, a^{5} c^{4} + 24 \, a^{4} b c^{4} - 4 \, a^{3} b^{2} c^{4} + 6 \, a^{2} b^{3} c^{4} - 6 \, a b^{4} c^{4} - 4 \, b^{5} c^{4} - 16 \, a^{4} c^{5} + 8 \, a^{3} b c^{5} - 12 \, a^{2} b^{2} c^{5} + 22 \, a b^{3} c^{5} + 2 \, b^{4} c^{5} + 16 \, a^{3} c^{6} - 24 \, a^{2} b c^{6} - 12 \, a b^{2} c^{6} + 16 \, a^{2} c^{7} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{4} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{4} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 13 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{4} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 22 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4} + 23 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} - 38 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5} - 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{6}\right)} {\left| a - b + c \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a c - 2 \, c^{2} + \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} {\left(a c - b c + c^{2}\right)} + 4 \, {\left(a c - c^{2}\right)}^{2}}}{a c - b c + c^{2}}}}\right)\right)}}{{\left(3 \, a^{6} b^{2} c^{2} - 8 \, a^{5} b^{3} c^{2} - a^{4} b^{4} c^{2} + 16 \, a^{3} b^{5} c^{2} - 7 \, a^{2} b^{6} c^{2} - 8 \, a b^{7} c^{2} + 5 \, b^{8} c^{2} - 12 \, a^{7} c^{3} + 32 \, a^{6} b c^{3} + 30 \, a^{5} b^{2} c^{3} - 112 \, a^{4} b^{3} c^{3} + 8 \, a^{3} b^{4} c^{3} + 96 \, a^{2} b^{5} c^{3} - 26 \, a b^{6} c^{3} - 16 \, b^{7} c^{3} - 104 \, a^{6} c^{4} + 192 \, a^{5} b c^{4} + 149 \, a^{4} b^{2} c^{4} - 336 \, a^{3} b^{3} c^{4} - 30 \, a^{2} b^{4} c^{4} + 112 \, a b^{5} c^{4} + 17 \, b^{6} c^{4} - 276 \, a^{5} c^{5} + 320 \, a^{4} b c^{5} + 292 \, a^{3} b^{2} c^{5} - 224 \, a^{2} b^{3} c^{5} - 120 \, a b^{4} c^{5} - 304 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 237 \, a^{2} b^{2} c^{6} + 24 \, a b^{3} c^{6} - 17 \, b^{4} c^{6} - 116 \, a^{3} c^{7} - 96 \, a^{2} b c^{7} + 62 \, a b^{2} c^{7} + 16 \, b^{3} c^{7} + 24 \, a^{2} c^{8} - 64 \, a b c^{8} - 5 \, b^{2} c^{8} + 20 \, a c^{9}\right)} {\left| c \right|}} - \frac{{\left({\left(2 \, a^{3} b^{4} - 6 \, a^{2} b^{5} + 6 \, a b^{6} - 2 \, b^{7} - 16 \, a^{4} b^{2} c + 48 \, a^{3} b^{3} c - 44 \, a^{2} b^{4} c + 8 \, a b^{5} c + 4 \, b^{6} c + 32 \, a^{5} c^{2} - 96 \, a^{4} b c^{2} + 64 \, a^{3} b^{2} c^{2} + 32 \, a^{2} b^{3} c^{2} - 30 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 64 \, a^{4} c^{3} - 128 \, a^{3} b c^{3} + 48 \, a^{2} b^{2} c^{3} + 16 \, a b^{3} c^{3} + 32 \, a^{3} c^{4} - 32 \, a^{2} b c^{4} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{4} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b c - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c + 26 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c - 28 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} c - 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{4} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} + 32 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 19 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{2} + 14 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} {\left| a - b + c \right|} + {\left(4 \, a^{3} b^{4} c - 4 \, a^{2} b^{5} c - 4 \, a b^{6} c + 4 \, b^{7} c - 32 \, a^{4} b^{2} c^{2} + 32 \, a^{3} b^{3} c^{2} + 40 \, a^{2} b^{4} c^{2} - 32 \, a b^{5} c^{2} - 8 \, b^{6} c^{2} + 64 \, a^{5} c^{3} - 64 \, a^{4} b c^{3} - 128 \, a^{3} b^{2} c^{3} + 64 \, a^{2} b^{3} c^{3} + 68 \, a b^{4} c^{3} + 4 \, b^{5} c^{3} + 128 \, a^{4} c^{4} - 160 \, a^{2} b^{2} c^{4} - 32 \, a b^{3} c^{4} + 64 \, a^{3} c^{5} + 64 \, a^{2} b c^{5} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} b^{2} c - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b^{3} c - 8 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{4} c + 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{5} c + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{6} c - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{5} c^{2} + 8 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} b c^{2} + 49 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b^{2} c^{2} - \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{3} c^{2} - 41 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{4} c^{2} - 11 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{5} c^{2} - 68 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{4} c^{3} - 28 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} b c^{3} + 93 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} c^{3} + 64 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} c^{3} + 11 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} c^{3} - 36 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c^{4} - 80 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c^{4} - 49 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c^{4} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c^{4} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{5} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} {\left| a - b + c \right|} {\left| c \right|} + {\left(2 \, a^{4} b^{3} c^{2} - 6 \, a^{3} b^{4} c^{2} + 6 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 8 \, a^{5} b c^{3} + 28 \, a^{4} b^{2} c^{3} - 30 \, a^{3} b^{3} c^{3} + 10 \, a^{2} b^{4} c^{3} - 2 \, a b^{5} c^{3} + 2 \, b^{6} c^{3} - 16 \, a^{5} c^{4} + 24 \, a^{4} b c^{4} - 4 \, a^{3} b^{2} c^{4} + 6 \, a^{2} b^{3} c^{4} - 6 \, a b^{4} c^{4} - 4 \, b^{5} c^{4} - 16 \, a^{4} c^{5} + 8 \, a^{3} b c^{5} - 12 \, a^{2} b^{2} c^{5} + 22 \, a b^{3} c^{5} + 2 \, b^{4} c^{5} + 16 \, a^{3} c^{6} - 24 \, a^{2} b c^{6} - 12 \, a b^{2} c^{6} + 16 \, a^{2} c^{7} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{4} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{4} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} b c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 13 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{4} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 22 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4} + 23 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} - 38 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5} - 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{6}\right)} {\left| a - b + c \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a c - 2 \, c^{2} - \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} {\left(a c - b c + c^{2}\right)} + 4 \, {\left(a c - c^{2}\right)}^{2}}}{a c - b c + c^{2}}}}\right)\right)}}{{\left(3 \, a^{6} b^{2} c^{2} - 8 \, a^{5} b^{3} c^{2} - a^{4} b^{4} c^{2} + 16 \, a^{3} b^{5} c^{2} - 7 \, a^{2} b^{6} c^{2} - 8 \, a b^{7} c^{2} + 5 \, b^{8} c^{2} - 12 \, a^{7} c^{3} + 32 \, a^{6} b c^{3} + 30 \, a^{5} b^{2} c^{3} - 112 \, a^{4} b^{3} c^{3} + 8 \, a^{3} b^{4} c^{3} + 96 \, a^{2} b^{5} c^{3} - 26 \, a b^{6} c^{3} - 16 \, b^{7} c^{3} - 104 \, a^{6} c^{4} + 192 \, a^{5} b c^{4} + 149 \, a^{4} b^{2} c^{4} - 336 \, a^{3} b^{3} c^{4} - 30 \, a^{2} b^{4} c^{4} + 112 \, a b^{5} c^{4} + 17 \, b^{6} c^{4} - 276 \, a^{5} c^{5} + 320 \, a^{4} b c^{5} + 292 \, a^{3} b^{2} c^{5} - 224 \, a^{2} b^{3} c^{5} - 120 \, a b^{4} c^{5} - 304 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 237 \, a^{2} b^{2} c^{6} + 24 \, a b^{3} c^{6} - 17 \, b^{4} c^{6} - 116 \, a^{3} c^{7} - 96 \, a^{2} b c^{7} + 62 \, a b^{2} c^{7} + 16 \, b^{3} c^{7} + 24 \, a^{2} c^{8} - 64 \, a b c^{8} - 5 \, b^{2} c^{8} + 20 \, a c^{9}\right)} {\left| c \right|}}"," ",0,"x/c + ((2*a^3*b^4 - 6*a^2*b^5 + 6*a*b^6 - 2*b^7 - 16*a^4*b^2*c + 48*a^3*b^3*c - 44*a^2*b^4*c + 8*a*b^5*c + 4*b^6*c + 32*a^5*c^2 - 96*a^4*b*c^2 + 64*a^3*b^2*c^2 + 32*a^2*b^3*c^2 - 30*a*b^4*c^2 - 2*b^5*c^2 + 64*a^4*c^3 - 128*a^3*b*c^3 + 48*a^2*b^2*c^3 + 16*a*b^3*c^3 + 32*a^3*c^4 - 32*a^2*b*c^4 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b^2 - 2*(b^2 - 4*a*c)*a^3*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^3 + 6*(b^2 - 4*a*c)*a^2*b^3 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^4 - 6*(b^2 - 4*a*c)*a*b^4 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^5 + 2*(b^2 - 4*a*c)*b^5 - 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^4*c + 8*(b^2 - 4*a*c)*a^4*c + 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b*c - 24*(b^2 - 4*a*c)*a^3*b*c + 26*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2*c + 20*(b^2 - 4*a*c)*a^2*b^2*c - 28*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3*c - 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^4*c - 4*(b^2 - 4*a*c)*b^4*c - 56*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c^2 + 16*(b^2 - 4*a*c)*a^3*c^2 + 32*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c^2 - 32*(b^2 - 4*a*c)*a^2*b*c^2 + 19*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c^2 + 14*(b^2 - 4*a*c)*a*b^2*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c^2 + 2*(b^2 - 4*a*c)*b^3*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^3 - 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^3 - 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*abs(a - b + c) + (4*a^3*b^4*c - 4*a^2*b^5*c - 4*a*b^6*c + 4*b^7*c - 32*a^4*b^2*c^2 + 32*a^3*b^3*c^2 + 40*a^2*b^4*c^2 - 32*a*b^5*c^2 - 8*b^6*c^2 + 64*a^5*c^3 - 64*a^4*b*c^3 - 128*a^3*b^2*c^3 + 64*a^2*b^3*c^3 + 68*a*b^4*c^3 + 4*b^5*c^3 + 128*a^4*c^4 - 160*a^2*b^2*c^4 - 32*a*b^3*c^4 + 64*a^3*c^5 + 64*a^2*b*c^5 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*b^2*c + 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b^3*c + 8*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^4*c - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^5*c - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^6*c + 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^5*c^2 - 8*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*b*c^2 - 49*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b^2*c^2 + sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^3*c^2 + 41*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^4*c^2 + 11*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^5*c^2 + 68*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*c^3 + 28*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b*c^3 - 93*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2*c^3 - 64*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3*c^3 - 11*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^4*c^3 + 36*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c^4 + 80*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c^4 + 49*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c^4 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c^4 - 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^5 - 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^5 - 4*(b^2 - 4*a*c)*a^3*b^2*c + 4*(b^2 - 4*a*c)*a^2*b^3*c + 4*(b^2 - 4*a*c)*a*b^4*c - 4*(b^2 - 4*a*c)*b^5*c + 16*(b^2 - 4*a*c)*a^4*c^2 - 16*(b^2 - 4*a*c)*a^3*b*c^2 - 24*(b^2 - 4*a*c)*a^2*b^2*c^2 + 16*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*b^4*c^2 + 32*(b^2 - 4*a*c)*a^3*c^3 - 36*(b^2 - 4*a*c)*a*b^2*c^3 - 4*(b^2 - 4*a*c)*b^3*c^3 + 16*(b^2 - 4*a*c)*a^2*c^4 + 16*(b^2 - 4*a*c)*a*b*c^4)*abs(a - b + c)*abs(c) + (2*a^4*b^3*c^2 - 6*a^3*b^4*c^2 + 6*a^2*b^5*c^2 - 2*a*b^6*c^2 - 8*a^5*b*c^3 + 28*a^4*b^2*c^3 - 30*a^3*b^3*c^3 + 10*a^2*b^4*c^3 - 2*a*b^5*c^3 + 2*b^6*c^3 - 16*a^5*c^4 + 24*a^4*b*c^4 - 4*a^3*b^2*c^4 + 6*a^2*b^3*c^4 - 6*a*b^4*c^4 - 4*b^5*c^4 - 16*a^4*c^5 + 8*a^3*b*c^5 - 12*a^2*b^2*c^5 + 22*a*b^3*c^5 + 2*b^4*c^5 + 16*a^3*c^6 - 24*a^2*b*c^6 - 12*a*b^2*c^6 + 16*a^2*c^7 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^4*b*c^2 - 2*(b^2 - 4*a*c)*a^4*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b^2*c^2 + 6*(b^2 - 4*a*c)*a^3*b^2*c^2 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^3*c^2 - 6*(b^2 - 4*a*c)*a^2*b^3*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^4*c^2 + 2*(b^2 - 4*a*c)*a*b^4*c^2 + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^4*c^3 - 4*(b^2 - 4*a*c)*a^4*c^3 + 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b*c^3 + 6*(b^2 - 4*a*c)*a^3*b*c^3 - 13*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c^3 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^4*c^3 - 2*(b^2 - 4*a*c)*b^4*c^3 + 22*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c^4 - 4*(b^2 - 4*a*c)*a^3*c^4 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c^4 + 2*(b^2 - 4*a*c)*a^2*b*c^4 + 23*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c^4 - 2*(b^2 - 4*a*c)*a*b^2*c^4 + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*b^3*c^4 - 38*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^5 + 4*(b^2 - 4*a*c)*a^2*c^5 - 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^5 - 6*(b^2 - 4*a*c)*a*b*c^5 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5 + 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^6 + 4*(b^2 - 4*a*c)*a*c^6)*abs(a - b + c))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a*c - 2*c^2 + sqrt(-4*(a*c + b*c + c^2)*(a*c - b*c + c^2) + 4*(a*c - c^2)^2))/(a*c - b*c + c^2))))/((3*a^6*b^2*c^2 - 8*a^5*b^3*c^2 - a^4*b^4*c^2 + 16*a^3*b^5*c^2 - 7*a^2*b^6*c^2 - 8*a*b^7*c^2 + 5*b^8*c^2 - 12*a^7*c^3 + 32*a^6*b*c^3 + 30*a^5*b^2*c^3 - 112*a^4*b^3*c^3 + 8*a^3*b^4*c^3 + 96*a^2*b^5*c^3 - 26*a*b^6*c^3 - 16*b^7*c^3 - 104*a^6*c^4 + 192*a^5*b*c^4 + 149*a^4*b^2*c^4 - 336*a^3*b^3*c^4 - 30*a^2*b^4*c^4 + 112*a*b^5*c^4 + 17*b^6*c^4 - 276*a^5*c^5 + 320*a^4*b*c^5 + 292*a^3*b^2*c^5 - 224*a^2*b^3*c^5 - 120*a*b^4*c^5 - 304*a^4*c^6 + 128*a^3*b*c^6 + 237*a^2*b^2*c^6 + 24*a*b^3*c^6 - 17*b^4*c^6 - 116*a^3*c^7 - 96*a^2*b*c^7 + 62*a*b^2*c^7 + 16*b^3*c^7 + 24*a^2*c^8 - 64*a*b*c^8 - 5*b^2*c^8 + 20*a*c^9)*abs(c)) - ((2*a^3*b^4 - 6*a^2*b^5 + 6*a*b^6 - 2*b^7 - 16*a^4*b^2*c + 48*a^3*b^3*c - 44*a^2*b^4*c + 8*a*b^5*c + 4*b^6*c + 32*a^5*c^2 - 96*a^4*b*c^2 + 64*a^3*b^2*c^2 + 32*a^2*b^3*c^2 - 30*a*b^4*c^2 - 2*b^5*c^2 + 64*a^4*c^3 - 128*a^3*b*c^3 + 48*a^2*b^2*c^3 + 16*a*b^3*c^3 + 32*a^3*c^4 - 32*a^2*b*c^4 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b^2 - 2*(b^2 - 4*a*c)*a^3*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^3 + 6*(b^2 - 4*a*c)*a^2*b^3 - 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^4 - 6*(b^2 - 4*a*c)*a*b^4 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^5 + 2*(b^2 - 4*a*c)*b^5 - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^4*c + 8*(b^2 - 4*a*c)*a^4*c + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b*c - 24*(b^2 - 4*a*c)*a^3*b*c + 26*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2*c + 20*(b^2 - 4*a*c)*a^2*b^2*c - 28*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3*c - 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^4*c - 4*(b^2 - 4*a*c)*b^4*c - 56*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c^2 + 16*(b^2 - 4*a*c)*a^3*c^2 + 32*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c^2 - 32*(b^2 - 4*a*c)*a^2*b*c^2 + 19*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c^2 + 14*(b^2 - 4*a*c)*a*b^2*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c^2 + 2*(b^2 - 4*a*c)*b^3*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^3 - 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^3 - 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*abs(a - b + c) + (4*a^3*b^4*c - 4*a^2*b^5*c - 4*a*b^6*c + 4*b^7*c - 32*a^4*b^2*c^2 + 32*a^3*b^3*c^2 + 40*a^2*b^4*c^2 - 32*a*b^5*c^2 - 8*b^6*c^2 + 64*a^5*c^3 - 64*a^4*b*c^3 - 128*a^3*b^2*c^3 + 64*a^2*b^3*c^3 + 68*a*b^4*c^3 + 4*b^5*c^3 + 128*a^4*c^4 - 160*a^2*b^2*c^4 - 32*a*b^3*c^4 + 64*a^3*c^5 + 64*a^2*b*c^5 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*b^2*c - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b^3*c - 8*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^4*c + 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^5*c + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^6*c - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^5*c^2 + 8*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*b*c^2 + 49*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b^2*c^2 - sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^3*c^2 - 41*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^4*c^2 - 11*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^5*c^2 - 68*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^4*c^3 - 28*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*b*c^3 + 93*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2*c^3 + 64*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3*c^3 + 11*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^4*c^3 - 36*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c^4 - 80*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c^4 - 49*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c^4 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c^4 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^5 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^5 - 4*(b^2 - 4*a*c)*a^3*b^2*c + 4*(b^2 - 4*a*c)*a^2*b^3*c + 4*(b^2 - 4*a*c)*a*b^4*c - 4*(b^2 - 4*a*c)*b^5*c + 16*(b^2 - 4*a*c)*a^4*c^2 - 16*(b^2 - 4*a*c)*a^3*b*c^2 - 24*(b^2 - 4*a*c)*a^2*b^2*c^2 + 16*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*b^4*c^2 + 32*(b^2 - 4*a*c)*a^3*c^3 - 36*(b^2 - 4*a*c)*a*b^2*c^3 - 4*(b^2 - 4*a*c)*b^3*c^3 + 16*(b^2 - 4*a*c)*a^2*c^4 + 16*(b^2 - 4*a*c)*a*b*c^4)*abs(a - b + c)*abs(c) + (2*a^4*b^3*c^2 - 6*a^3*b^4*c^2 + 6*a^2*b^5*c^2 - 2*a*b^6*c^2 - 8*a^5*b*c^3 + 28*a^4*b^2*c^3 - 30*a^3*b^3*c^3 + 10*a^2*b^4*c^3 - 2*a*b^5*c^3 + 2*b^6*c^3 - 16*a^5*c^4 + 24*a^4*b*c^4 - 4*a^3*b^2*c^4 + 6*a^2*b^3*c^4 - 6*a*b^4*c^4 - 4*b^5*c^4 - 16*a^4*c^5 + 8*a^3*b*c^5 - 12*a^2*b^2*c^5 + 22*a*b^3*c^5 + 2*b^4*c^5 + 16*a^3*c^6 - 24*a^2*b*c^6 - 12*a*b^2*c^6 + 16*a^2*c^7 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^4*b*c^2 - 2*(b^2 - 4*a*c)*a^4*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b^2*c^2 + 6*(b^2 - 4*a*c)*a^3*b^2*c^2 - 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^3*c^2 - 6*(b^2 - 4*a*c)*a^2*b^3*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^4*c^2 + 2*(b^2 - 4*a*c)*a*b^4*c^2 + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^4*c^3 - 4*(b^2 - 4*a*c)*a^4*c^3 + 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*b*c^3 + 6*(b^2 - 4*a*c)*a^3*b*c^3 - 13*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c^3 - 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^3*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c^3 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^4*c^3 - 2*(b^2 - 4*a*c)*b^4*c^3 + 22*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3*c^4 - 4*(b^2 - 4*a*c)*a^3*c^4 - 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b*c^4 + 2*(b^2 - 4*a*c)*a^2*b*c^4 + 23*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2*c^4 - 2*(b^2 - 4*a*c)*a*b^2*c^4 + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*b^3*c^4 - 38*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c^5 + 4*(b^2 - 4*a*c)*a^2*c^5 - 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c^5 - 6*(b^2 - 4*a*c)*a*b*c^5 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^5 + 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^6 + 4*(b^2 - 4*a*c)*a*c^6)*abs(a - b + c))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a*c - 2*c^2 - sqrt(-4*(a*c + b*c + c^2)*(a*c - b*c + c^2) + 4*(a*c - c^2)^2))/(a*c - b*c + c^2))))/((3*a^6*b^2*c^2 - 8*a^5*b^3*c^2 - a^4*b^4*c^2 + 16*a^3*b^5*c^2 - 7*a^2*b^6*c^2 - 8*a*b^7*c^2 + 5*b^8*c^2 - 12*a^7*c^3 + 32*a^6*b*c^3 + 30*a^5*b^2*c^3 - 112*a^4*b^3*c^3 + 8*a^3*b^4*c^3 + 96*a^2*b^5*c^3 - 26*a*b^6*c^3 - 16*b^7*c^3 - 104*a^6*c^4 + 192*a^5*b*c^4 + 149*a^4*b^2*c^4 - 336*a^3*b^3*c^4 - 30*a^2*b^4*c^4 + 112*a*b^5*c^4 + 17*b^6*c^4 - 276*a^5*c^5 + 320*a^4*b*c^5 + 292*a^3*b^2*c^5 - 224*a^2*b^3*c^5 - 120*a*b^4*c^5 - 304*a^4*c^6 + 128*a^3*b*c^6 + 237*a^2*b^2*c^6 + 24*a*b^3*c^6 - 17*b^4*c^6 - 116*a^3*c^7 - 96*a^2*b*c^7 + 62*a*b^2*c^7 + 16*b^3*c^7 + 24*a^2*c^8 - 64*a*b*c^8 - 5*b^2*c^8 + 20*a*c^9)*abs(c))","B",0
16,-1,0,0,0.000000," ","integrate(cos(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,1,2954,0,91.056690," ","integrate(1/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\frac{{\left(2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a^{3} b c - 12 \, a^{2} b^{2} c + 20 \, a b^{3} c + 4 \, b^{4} c + 48 \, a^{3} c^{2} - 48 \, a^{2} b c^{2} - 24 \, a b^{2} c^{2} - 6 \, b^{3} c^{2} + 32 \, a^{2} c^{3} + 24 \, a b c^{3} + 4 \, b^{2} c^{3} - 16 \, a c^{4} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c + 8 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c + 34 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{2} - 24 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{3} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c + 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c - 12 \, {\left(b^{2} - 4 \, a c\right)} a b c - 4 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 28 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} b c^{2} - 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a - 2 \, c + \sqrt{-4 \, {\left(a + b + c\right)} {\left(a - b + c\right)} + 4 \, {\left(a - c\right)}^{2}}}{a - b + c}}}\right)\right)} {\left| a - b + c \right|}}{3 \, a^{5} b^{2} - 5 \, a^{4} b^{3} - 6 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6} - 5 \, b^{7} - 12 \, a^{6} c + 20 \, a^{5} b c + 47 \, a^{4} b^{2} c - 60 \, a^{3} b^{3} c - 46 \, a^{2} b^{4} c + 40 \, a b^{5} c + 11 \, b^{6} c - 92 \, a^{5} c^{2} + 80 \, a^{4} b c^{2} + 182 \, a^{3} b^{2} c^{2} - 94 \, a^{2} b^{3} c^{2} - 78 \, a b^{4} c^{2} - 6 \, b^{5} c^{2} - 184 \, a^{4} c^{3} + 56 \, a^{3} b c^{3} + 166 \, a^{2} b^{2} c^{3} + 36 \, a b^{3} c^{3} - 6 \, b^{4} c^{3} - 120 \, a^{3} c^{4} - 48 \, a^{2} b c^{4} + 23 \, a b^{2} c^{4} + 11 \, b^{3} c^{4} + 4 \, a^{2} c^{5} - 44 \, a b c^{5} - 5 \, b^{2} c^{5} + 20 \, a c^{6}} - \frac{{\left(2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a^{3} b c - 12 \, a^{2} b^{2} c + 20 \, a b^{3} c + 4 \, b^{4} c + 48 \, a^{3} c^{2} - 48 \, a^{2} b c^{2} - 24 \, a b^{2} c^{2} - 6 \, b^{3} c^{2} + 32 \, a^{2} c^{3} + 24 \, a b c^{3} + 4 \, b^{2} c^{3} - 16 \, a c^{4} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} + 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} + 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c - 8 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c - 34 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c - 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c + 56 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{2} + 24 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{2} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{3} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c + 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c - 12 \, {\left(b^{2} - 4 \, a c\right)} a b c - 4 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 28 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} b c^{2} - 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a - 2 \, c - \sqrt{-4 \, {\left(a + b + c\right)} {\left(a - b + c\right)} + 4 \, {\left(a - c\right)}^{2}}}{a - b + c}}}\right)\right)} {\left| a - b + c \right|}}{3 \, a^{5} b^{2} - 5 \, a^{4} b^{3} - 6 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6} - 5 \, b^{7} - 12 \, a^{6} c + 20 \, a^{5} b c + 47 \, a^{4} b^{2} c - 60 \, a^{3} b^{3} c - 46 \, a^{2} b^{4} c + 40 \, a b^{5} c + 11 \, b^{6} c - 92 \, a^{5} c^{2} + 80 \, a^{4} b c^{2} + 182 \, a^{3} b^{2} c^{2} - 94 \, a^{2} b^{3} c^{2} - 78 \, a b^{4} c^{2} - 6 \, b^{5} c^{2} - 184 \, a^{4} c^{3} + 56 \, a^{3} b c^{3} + 166 \, a^{2} b^{2} c^{3} + 36 \, a b^{3} c^{3} - 6 \, b^{4} c^{3} - 120 \, a^{3} c^{4} - 48 \, a^{2} b c^{4} + 23 \, a b^{2} c^{4} + 11 \, b^{3} c^{4} + 4 \, a^{2} c^{5} - 44 \, a b c^{5} - 5 \, b^{2} c^{5} + 20 \, a c^{6}}"," ",0,"(2*a^2*b^3 - 2*b^5 - 8*a^3*b*c - 12*a^2*b^2*c + 20*a*b^3*c + 4*b^4*c + 48*a^3*c^2 - 48*a^2*b*c^2 - 24*a*b^2*c^2 - 6*b^3*c^2 + 32*a^2*c^3 + 24*a*b*c^3 + 4*b^2*c^3 - 16*a*c^4 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2 - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^4 - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c + 8*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c + 34*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c - 56*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^2 - 24*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^3 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b - 2*(b^2 - 4*a*c)*a^2*b - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3 + 2*(b^2 - 4*a*c)*b^3 + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c + 12*(b^2 - 4*a*c)*a^2*c + 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c - 12*(b^2 - 4*a*c)*a*b*c - 4*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c - 4*(b^2 - 4*a*c)*b^2*c + 28*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^2 + 8*(b^2 - 4*a*c)*a*c^2 + 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^2 + 6*(b^2 - 4*a*c)*b*c^2 - 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*c^3 - 4*(b^2 - 4*a*c)*c^3)*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a - 2*c + sqrt(-4*(a + b + c)*(a - b + c) + 4*(a - c)^2))/(a - b + c))))*abs(a - b + c)/(3*a^5*b^2 - 5*a^4*b^3 - 6*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6 - 5*b^7 - 12*a^6*c + 20*a^5*b*c + 47*a^4*b^2*c - 60*a^3*b^3*c - 46*a^2*b^4*c + 40*a*b^5*c + 11*b^6*c - 92*a^5*c^2 + 80*a^4*b*c^2 + 182*a^3*b^2*c^2 - 94*a^2*b^3*c^2 - 78*a*b^4*c^2 - 6*b^5*c^2 - 184*a^4*c^3 + 56*a^3*b*c^3 + 166*a^2*b^2*c^3 + 36*a*b^3*c^3 - 6*b^4*c^3 - 120*a^3*c^4 - 48*a^2*b*c^4 + 23*a*b^2*c^4 + 11*b^3*c^4 + 4*a^2*c^5 - 44*a*b*c^5 - 5*b^2*c^5 + 20*a*c^6) - (2*a^2*b^3 - 2*b^5 - 8*a^3*b*c - 12*a^2*b^2*c + 20*a*b^3*c + 4*b^4*c + 48*a^3*c^2 - 48*a^2*b*c^2 - 24*a*b^2*c^2 - 6*b^3*c^2 + 32*a^2*c^3 + 24*a*b*c^3 + 4*b^2*c^3 - 16*a*c^4 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2 + 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^4 + 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c - 8*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c - 34*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c - 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c + 56*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^2 + 24*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^2 - 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^3 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b - 2*(b^2 - 4*a*c)*a^2*b - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3 + 2*(b^2 - 4*a*c)*b^3 + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c + 12*(b^2 - 4*a*c)*a^2*c + 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c - 12*(b^2 - 4*a*c)*a*b*c - 4*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c - 4*(b^2 - 4*a*c)*b^2*c + 28*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^2 + 8*(b^2 - 4*a*c)*a*c^2 + 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^2 + 6*(b^2 - 4*a*c)*b*c^2 - 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*c^3 - 4*(b^2 - 4*a*c)*c^3)*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a - 2*c - sqrt(-4*(a + b + c)*(a - b + c) + 4*(a - c)^2))/(a - b + c))))*abs(a - b + c)/(3*a^5*b^2 - 5*a^4*b^3 - 6*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6 - 5*b^7 - 12*a^6*c + 20*a^5*b*c + 47*a^4*b^2*c - 60*a^3*b^3*c - 46*a^2*b^4*c + 40*a*b^5*c + 11*b^6*c - 92*a^5*c^2 + 80*a^4*b*c^2 + 182*a^3*b^2*c^2 - 94*a^2*b^3*c^2 - 78*a*b^4*c^2 - 6*b^5*c^2 - 184*a^4*c^3 + 56*a^3*b*c^3 + 166*a^2*b^2*c^3 + 36*a*b^3*c^3 - 6*b^4*c^3 - 120*a^3*c^4 - 48*a^2*b*c^4 + 23*a*b^2*c^4 + 11*b^3*c^4 + 4*a^2*c^5 - 44*a*b*c^5 - 5*b^2*c^5 + 20*a*c^6)","B",0
18,-1,0,0,0.000000," ","integrate(sec(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-1,0,0,0.000000," ","integrate(sec(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate(sec(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
