1,1,491,0,1.419677," ","integrate(sin(x)^5/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \cos\left(x\right)^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \cos\left(x\right)^{2} - 3 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} + 2 \, b c \cos\left(x\right) + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\right) + 6 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 8 \, a c^{4} + 2 \, {\left(2 \, a^{2} - b^{2}\right)} c^{3}\right)} \cos\left(x\right) - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2}\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}, -\frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \cos\left(x\right)^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \cos\left(x\right)^{2} - 6 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 8 \, a c^{4} + 2 \, {\left(2 \, a^{2} - b^{2}\right)} c^{3}\right)} \cos\left(x\right) - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2}\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}\right]"," ",0,"[-1/6*(2*(b^2*c^3 - 4*a*c^4)*cos(x)^3 - 3*(b^3*c^2 - 4*a*b*c^3)*cos(x)^2 - 3*(b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2)*sqrt(b^2 - 4*a*c)*log(-(2*c^2*cos(x)^2 + 2*b*c*cos(x) + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*cos(x) + b))/(c*cos(x)^2 + b*cos(x) + a)) + 6*(b^4*c - 5*a*b^2*c^2 + 8*a*c^4 + 2*(2*a^2 - b^2)*c^3)*cos(x) - 3*(b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2)*log(c*cos(x)^2 + b*cos(x) + a))/(b^2*c^4 - 4*a*c^5), -1/6*(2*(b^2*c^3 - 4*a*c^4)*cos(x)^3 - 3*(b^3*c^2 - 4*a*b*c^3)*cos(x)^2 - 6*(b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*cos(x) + b)/(b^2 - 4*a*c)) + 6*(b^4*c - 5*a*b^2*c^2 + 8*a*c^4 + 2*(2*a^2 - b^2)*c^3)*cos(x) - 3*(b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2)*log(c*cos(x)^2 + b*cos(x) + a))/(b^2*c^4 - 4*a*c^5)]","A",0
2,1,258,0,2.261066," ","integrate(sin(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} + 2 \, b c \cos\left(x\right) + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \cos\left(x\right) + {\left(b^{3} - 4 \, a b c\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, -\frac{2 \, {\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \cos\left(x\right) + {\left(b^{3} - 4 \, a b c\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[-1/2*((b^2 - 2*a*c - 2*c^2)*sqrt(b^2 - 4*a*c)*log(-(2*c^2*cos(x)^2 + 2*b*c*cos(x) + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*cos(x) + b))/(c*cos(x)^2 + b*cos(x) + a)) - 2*(b^2*c - 4*a*c^2)*cos(x) + (b^3 - 4*a*b*c)*log(c*cos(x)^2 + b*cos(x) + a))/(b^2*c^2 - 4*a*c^3), -1/2*(2*(b^2 - 2*a*c - 2*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*cos(x) + b)/(b^2 - 4*a*c)) - 2*(b^2*c - 4*a*c^2)*cos(x) + (b^3 - 4*a*b*c)*log(c*cos(x)^2 + b*cos(x) + a))/(b^2*c^2 - 4*a*c^3)]","A",0
3,1,126,0,1.766784," ","integrate(sin(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} + 2 \, b c \cos\left(x\right) + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\right)}{\sqrt{b^{2} - 4 \, a c}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right)}{b^{2} - 4 \, a c}\right]"," ",0,"[log(-(2*c^2*cos(x)^2 + 2*b*c*cos(x) + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*cos(x) + b))/(c*cos(x)^2 + b*cos(x) + a))/sqrt(b^2 - 4*a*c), 2*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*cos(x) + b)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
4,1,470,0,3.288589," ","integrate(csc(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} + 2 \, b c \cos\left(x\right) + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right) + {\left(a b^{2} + b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)}}, -\frac{2 \, {\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right) + {\left(a b^{2} + b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)}}\right]"," ",0,"[-1/2*((b^2 - 2*a*c - 2*c^2)*sqrt(b^2 - 4*a*c)*log(-(2*c^2*cos(x)^2 + 2*b*c*cos(x) + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*cos(x) + b))/(c*cos(x)^2 + b*cos(x) + a)) - (b^3 - 4*a*b*c)*log(c*cos(x)^2 + b*cos(x) + a) + (a*b^2 + b^3 - 4*a*c^2 - (4*a^2 + 4*a*b - b^2)*c)*log(1/2*cos(x) + 1/2) - (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*log(-1/2*cos(x) + 1/2))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c), -1/2*(2*(b^2 - 2*a*c - 2*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*cos(x) + b)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*log(c*cos(x)^2 + b*cos(x) + a) + (a*b^2 + b^3 - 4*a*c^2 - (4*a^2 + 4*a*b - b^2)*c)*log(1/2*cos(x) + 1/2) - (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*log(-1/2*cos(x) + 1/2))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)]","A",0
5,1,1991,0,18.117183," ","integrate(csc(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a b c^{3} - 2 \, {\left(8 \, a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2} - {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} + 2 \, b c \cos\left(x\right) + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\right) - 4 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c - 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a c^{4} - {\left(12 \, a^{2} - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 7 \, a b^{2}\right)} c^{2} - {\left(4 \, a^{4} - 7 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(x\right) - 2 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2}\right)} \cos\left(x\right)^{2}\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right) - {\left(a^{3} b^{2} - 3 \, a b^{4} - 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} + 16 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 3 \, a b^{4} - 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} + 16 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} c\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(a^{3} b^{2} - 3 \, a b^{4} + 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} - 16 \, a^{2} b - 11 \, a b^{2} + 4 \, b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 3 \, a b^{4} + 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} - 16 \, a^{2} b - 11 \, a b^{2} + 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} + 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} + 12 \, a b^{3} + b^{4}\right)} c\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c\right)} \cos\left(x\right)^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c\right)}}, \frac{2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a b c^{3} - 2 \, {\left(8 \, a^{2} b - b^{3}\right)} c^{2} + 4 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2} - {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \cos\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c - 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a c^{4} - {\left(12 \, a^{2} - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 7 \, a b^{2}\right)} c^{2} - {\left(4 \, a^{4} - 7 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(x\right) - 2 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2}\right)} \cos\left(x\right)^{2}\right)} \log\left(c \cos\left(x\right)^{2} + b \cos\left(x\right) + a\right) - {\left(a^{3} b^{2} - 3 \, a b^{4} - 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} + 16 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 3 \, a b^{4} - 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} + 16 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} c\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(a^{3} b^{2} - 3 \, a b^{4} + 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} - 16 \, a^{2} b - 11 \, a b^{2} + 4 \, b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 3 \, a b^{4} + 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} - 16 \, a^{2} b - 11 \, a b^{2} + 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} + 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} + 12 \, a b^{3} + b^{4}\right)} c\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c\right)} \cos\left(x\right)^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c\right)}}\right]"," ",0,"[1/4*(2*a^2*b^3 - 2*b^5 - 8*a*b*c^3 - 2*(8*a^2*b - b^3)*c^2 + 2*(b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2 - (b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2)*cos(x)^2)*sqrt(b^2 - 4*a*c)*log(-(2*c^2*cos(x)^2 + 2*b*c*cos(x) + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*cos(x) + b))/(c*cos(x)^2 + b*cos(x) + a)) - 4*(2*a^3*b - 3*a*b^3)*c - 2*(a^3*b^2 - a*b^4 - 4*a*c^4 - (12*a^2 - b^2)*c^3 - (12*a^3 - 7*a*b^2)*c^2 - (4*a^4 - 7*a^2*b^2 + b^4)*c)*cos(x) - 2*(b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2 - (b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2)*cos(x)^2)*log(c*cos(x)^2 + b*cos(x) + a) - (a^3*b^2 - 3*a*b^4 - 2*b^5 - 12*a*c^4 - (28*a^2 + 16*a*b - 3*b^2)*c^3 - (20*a^3 + 16*a^2*b - 11*a*b^2 - 4*b^3)*c^2 - (a^3*b^2 - 3*a*b^4 - 2*b^5 - 12*a*c^4 - (28*a^2 + 16*a*b - 3*b^2)*c^3 - (20*a^3 + 16*a^2*b - 11*a*b^2 - 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 - 12*a*b^3 + b^4)*c)*cos(x)^2 - (4*a^4 - 17*a^2*b^2 - 12*a*b^3 + b^4)*c)*log(1/2*cos(x) + 1/2) + (a^3*b^2 - 3*a*b^4 + 2*b^5 - 12*a*c^4 - (28*a^2 - 16*a*b - 3*b^2)*c^3 - (20*a^3 - 16*a^2*b - 11*a*b^2 + 4*b^3)*c^2 - (a^3*b^2 - 3*a*b^4 + 2*b^5 - 12*a*c^4 - (28*a^2 - 16*a*b - 3*b^2)*c^3 - (20*a^3 - 16*a^2*b - 11*a*b^2 + 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 + 12*a*b^3 + b^4)*c)*cos(x)^2 - (4*a^4 - 17*a^2*b^2 + 12*a*b^3 + b^4)*c)*log(-1/2*cos(x) + 1/2))/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - (a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)*cos(x)^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c), 1/4*(2*a^2*b^3 - 2*b^5 - 8*a*b*c^3 - 2*(8*a^2*b - b^3)*c^2 + 4*(b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2 - (b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2)*cos(x)^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*cos(x) + b)/(b^2 - 4*a*c)) - 4*(2*a^3*b - 3*a*b^3)*c - 2*(a^3*b^2 - a*b^4 - 4*a*c^4 - (12*a^2 - b^2)*c^3 - (12*a^3 - 7*a*b^2)*c^2 - (4*a^4 - 7*a^2*b^2 + b^4)*c)*cos(x) - 2*(b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2 - (b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2)*cos(x)^2)*log(c*cos(x)^2 + b*cos(x) + a) - (a^3*b^2 - 3*a*b^4 - 2*b^5 - 12*a*c^4 - (28*a^2 + 16*a*b - 3*b^2)*c^3 - (20*a^3 + 16*a^2*b - 11*a*b^2 - 4*b^3)*c^2 - (a^3*b^2 - 3*a*b^4 - 2*b^5 - 12*a*c^4 - (28*a^2 + 16*a*b - 3*b^2)*c^3 - (20*a^3 + 16*a^2*b - 11*a*b^2 - 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 - 12*a*b^3 + b^4)*c)*cos(x)^2 - (4*a^4 - 17*a^2*b^2 - 12*a*b^3 + b^4)*c)*log(1/2*cos(x) + 1/2) + (a^3*b^2 - 3*a*b^4 + 2*b^5 - 12*a*c^4 - (28*a^2 - 16*a*b - 3*b^2)*c^3 - (20*a^3 - 16*a^2*b - 11*a*b^2 + 4*b^3)*c^2 - (a^3*b^2 - 3*a*b^4 + 2*b^5 - 12*a*c^4 - (28*a^2 - 16*a*b - 3*b^2)*c^3 - (20*a^3 - 16*a^2*b - 11*a*b^2 + 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 + 12*a*b^3 + b^4)*c)*cos(x)^2 - (4*a^4 - 17*a^2*b^2 + 12*a*b^3 + b^4)*c)*log(-1/2*cos(x) + 1/2))/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - (a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)*cos(x)^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)]","B",0
6,1,5045,0,3.579255," ","integrate(sin(x)^4/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} c^{3} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} \log\left(24 \, a b c^{6} + 6 \, b c^{7} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{5} + 8 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{4} + 2 \, {\left(3 \, a^{4} b - 14 \, a^{2} b^{3} + 4 \, b^{5}\right)} c^{3} - 4 \, {\left(2 \, a^{3} b^{3} - 3 \, a b^{5}\right)} c^{2} - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \cos\left(x\right) + 2 \, {\left(a^{2} b^{5} - b^{7}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(b^{4} c^{7} - 6 \, a b^{2} c^{8} + 8 \, a c^{10} + 2 \, {\left(4 \, a^{2} - b^{2}\right)} c^{9}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \sin\left(x\right) - {\left(b^{8} c - 8 \, a b^{6} c^{2} - 12 \, a b^{2} c^{6} - 3 \, {\left(8 \, a^{2} b^{2} - b^{4}\right)} c^{5} - 6 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{4} + {\left(19 \, a^{2} b^{4} - 3 \, b^{6}\right)} c^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(a^{2} b^{6} - b^{8} + 12 \, a b^{2} c^{5} + 3 \, b^{2} c^{6} + 6 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{4} + 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c^{3} + {\left(3 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c\right)} \cos\left(x\right)\right) - \sqrt{2} c^{3} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} \log\left(24 \, a b c^{6} + 6 \, b c^{7} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{5} + 8 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{4} + 2 \, {\left(3 \, a^{4} b - 14 \, a^{2} b^{3} + 4 \, b^{5}\right)} c^{3} - 4 \, {\left(2 \, a^{3} b^{3} - 3 \, a b^{5}\right)} c^{2} - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \cos\left(x\right) + 2 \, {\left(a^{2} b^{5} - b^{7}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(b^{4} c^{7} - 6 \, a b^{2} c^{8} + 8 \, a c^{10} + 2 \, {\left(4 \, a^{2} - b^{2}\right)} c^{9}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \sin\left(x\right) - {\left(b^{8} c - 8 \, a b^{6} c^{2} - 12 \, a b^{2} c^{6} - 3 \, {\left(8 \, a^{2} b^{2} - b^{4}\right)} c^{5} - 6 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{4} + {\left(19 \, a^{2} b^{4} - 3 \, b^{6}\right)} c^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} + {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(a^{2} b^{6} - b^{8} + 12 \, a b^{2} c^{5} + 3 \, b^{2} c^{6} + 6 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{4} + 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c^{3} + {\left(3 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c\right)} \cos\left(x\right)\right) + \sqrt{2} c^{3} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} - {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} \log\left(-24 \, a b c^{6} - 6 \, b c^{7} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{5} - 8 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{4} - 2 \, {\left(3 \, a^{4} b - 14 \, a^{2} b^{3} + 4 \, b^{5}\right)} c^{3} + 4 \, {\left(2 \, a^{3} b^{3} - 3 \, a b^{5}\right)} c^{2} - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \cos\left(x\right) - 2 \, {\left(a^{2} b^{5} - b^{7}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(b^{4} c^{7} - 6 \, a b^{2} c^{8} + 8 \, a c^{10} + 2 \, {\left(4 \, a^{2} - b^{2}\right)} c^{9}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \sin\left(x\right) + {\left(b^{8} c - 8 \, a b^{6} c^{2} - 12 \, a b^{2} c^{6} - 3 \, {\left(8 \, a^{2} b^{2} - b^{4}\right)} c^{5} - 6 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{4} + {\left(19 \, a^{2} b^{4} - 3 \, b^{6}\right)} c^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} - {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} - {\left(a^{2} b^{6} - b^{8} + 12 \, a b^{2} c^{5} + 3 \, b^{2} c^{6} + 6 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{4} + 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c^{3} + {\left(3 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c\right)} \cos\left(x\right)\right) - \sqrt{2} c^{3} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} - {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} \log\left(-24 \, a b c^{6} - 6 \, b c^{7} - 12 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{5} - 8 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} c^{4} - 2 \, {\left(3 \, a^{4} b - 14 \, a^{2} b^{3} + 4 \, b^{5}\right)} c^{3} + 4 \, {\left(2 \, a^{3} b^{3} - 3 \, a b^{5}\right)} c^{2} - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \cos\left(x\right) - 2 \, {\left(a^{2} b^{5} - b^{7}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(b^{4} c^{7} - 6 \, a b^{2} c^{8} + 8 \, a c^{10} + 2 \, {\left(4 \, a^{2} - b^{2}\right)} c^{9}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}} \sin\left(x\right) + {\left(b^{8} c - 8 \, a b^{6} c^{2} - 12 \, a b^{2} c^{6} - 3 \, {\left(8 \, a^{2} b^{2} - b^{4}\right)} c^{5} - 6 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{4} + {\left(19 \, a^{2} b^{4} - 3 \, b^{6}\right)} c^{3}\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{6} - 6 \, a b^{4} c - 6 \, a c^{5} - 2 \, c^{6} - 3 \, {\left(2 \, a^{2} - b^{2}\right)} c^{4} - 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{2} - {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{\frac{b^{10} - 8 \, a b^{8} c + 36 \, a b^{2} c^{7} + 9 \, b^{2} c^{8} + 18 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{6} + 12 \, {\left(3 \, a^{3} b^{2} - 5 \, a b^{4}\right)} c^{5} + 3 \, {\left(3 \, a^{4} b^{2} - 22 \, a^{2} b^{4} + 5 \, b^{6}\right)} c^{4} - 12 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c^{3} + 2 \, {\left(11 \, a^{2} b^{6} - 3 \, b^{8}\right)} c^{2}}{b^{2} c^{12} - 4 \, a c^{13}}}}{b^{2} c^{6} - 4 \, a c^{7}}} - {\left(a^{2} b^{6} - b^{8} + 12 \, a b^{2} c^{5} + 3 \, b^{2} c^{6} + 6 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} c^{4} + 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c^{3} + {\left(3 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{4} - 3 \, a b^{6}\right)} c\right)} \cos\left(x\right)\right) + 2 \, {\left(2 \, b^{2} - 2 \, a c - 3 \, c^{2}\right)} x + 2 \, {\left(c^{2} \cos\left(x\right) - 2 \, b c\right)} \sin\left(x\right)}{4 \, c^{3}}"," ",0,"1/4*(sqrt(2)*c^3*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 + (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7))*log(24*a*b*c^6 + 6*b*c^7 + 12*(3*a^2*b - b^3)*c^5 + 8*(3*a^3*b - 4*a*b^3)*c^4 + 2*(3*a^4*b - 14*a^2*b^3 + 4*b^5)*c^3 - 4*(2*a^3*b^3 - 3*a*b^5)*c^2 - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*cos(x) + 2*(a^2*b^5 - b^7)*c + 1/2*sqrt(2)*((b^4*c^7 - 6*a*b^2*c^8 + 8*a*c^10 + 2*(4*a^2 - b^2)*c^9)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*sin(x) - (b^8*c - 8*a*b^6*c^2 - 12*a*b^2*c^6 - 3*(8*a^2*b^2 - b^4)*c^5 - 6*(2*a^3*b^2 - 3*a*b^4)*c^4 + (19*a^2*b^4 - 3*b^6)*c^3)*sin(x))*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 + (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7)) + (a^2*b^6 - b^8 + 12*a*b^2*c^5 + 3*b^2*c^6 + 6*(3*a^2*b^2 - b^4)*c^4 + 4*(3*a^3*b^2 - 4*a*b^4)*c^3 + (3*a^4*b^2 - 14*a^2*b^4 + 4*b^6)*c^2 - 2*(2*a^3*b^4 - 3*a*b^6)*c)*cos(x)) - sqrt(2)*c^3*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 + (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7))*log(24*a*b*c^6 + 6*b*c^7 + 12*(3*a^2*b - b^3)*c^5 + 8*(3*a^3*b - 4*a*b^3)*c^4 + 2*(3*a^4*b - 14*a^2*b^3 + 4*b^5)*c^3 - 4*(2*a^3*b^3 - 3*a*b^5)*c^2 - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*cos(x) + 2*(a^2*b^5 - b^7)*c - 1/2*sqrt(2)*((b^4*c^7 - 6*a*b^2*c^8 + 8*a*c^10 + 2*(4*a^2 - b^2)*c^9)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*sin(x) - (b^8*c - 8*a*b^6*c^2 - 12*a*b^2*c^6 - 3*(8*a^2*b^2 - b^4)*c^5 - 6*(2*a^3*b^2 - 3*a*b^4)*c^4 + (19*a^2*b^4 - 3*b^6)*c^3)*sin(x))*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 + (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7)) + (a^2*b^6 - b^8 + 12*a*b^2*c^5 + 3*b^2*c^6 + 6*(3*a^2*b^2 - b^4)*c^4 + 4*(3*a^3*b^2 - 4*a*b^4)*c^3 + (3*a^4*b^2 - 14*a^2*b^4 + 4*b^6)*c^2 - 2*(2*a^3*b^4 - 3*a*b^6)*c)*cos(x)) + sqrt(2)*c^3*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 - (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7))*log(-24*a*b*c^6 - 6*b*c^7 - 12*(3*a^2*b - b^3)*c^5 - 8*(3*a^3*b - 4*a*b^3)*c^4 - 2*(3*a^4*b - 14*a^2*b^3 + 4*b^5)*c^3 + 4*(2*a^3*b^3 - 3*a*b^5)*c^2 - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*cos(x) - 2*(a^2*b^5 - b^7)*c + 1/2*sqrt(2)*((b^4*c^7 - 6*a*b^2*c^8 + 8*a*c^10 + 2*(4*a^2 - b^2)*c^9)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*sin(x) + (b^8*c - 8*a*b^6*c^2 - 12*a*b^2*c^6 - 3*(8*a^2*b^2 - b^4)*c^5 - 6*(2*a^3*b^2 - 3*a*b^4)*c^4 + (19*a^2*b^4 - 3*b^6)*c^3)*sin(x))*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 - (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7)) - (a^2*b^6 - b^8 + 12*a*b^2*c^5 + 3*b^2*c^6 + 6*(3*a^2*b^2 - b^4)*c^4 + 4*(3*a^3*b^2 - 4*a*b^4)*c^3 + (3*a^4*b^2 - 14*a^2*b^4 + 4*b^6)*c^2 - 2*(2*a^3*b^4 - 3*a*b^6)*c)*cos(x)) - sqrt(2)*c^3*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 - (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7))*log(-24*a*b*c^6 - 6*b*c^7 - 12*(3*a^2*b - b^3)*c^5 - 8*(3*a^3*b - 4*a*b^3)*c^4 - 2*(3*a^4*b - 14*a^2*b^3 + 4*b^5)*c^3 + 4*(2*a^3*b^3 - 3*a*b^5)*c^2 - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*cos(x) - 2*(a^2*b^5 - b^7)*c - 1/2*sqrt(2)*((b^4*c^7 - 6*a*b^2*c^8 + 8*a*c^10 + 2*(4*a^2 - b^2)*c^9)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13))*sin(x) + (b^8*c - 8*a*b^6*c^2 - 12*a*b^2*c^6 - 3*(8*a^2*b^2 - b^4)*c^5 - 6*(2*a^3*b^2 - 3*a*b^4)*c^4 + (19*a^2*b^4 - 3*b^6)*c^3)*sin(x))*sqrt(-(b^6 - 6*a*b^4*c - 6*a*c^5 - 2*c^6 - 3*(2*a^2 - b^2)*c^4 - 2*(a^3 - 6*a*b^2)*c^3 + 3*(3*a^2*b^2 - b^4)*c^2 - (b^2*c^6 - 4*a*c^7)*sqrt((b^10 - 8*a*b^8*c + 36*a*b^2*c^7 + 9*b^2*c^8 + 18*(3*a^2*b^2 - b^4)*c^6 + 12*(3*a^3*b^2 - 5*a*b^4)*c^5 + 3*(3*a^4*b^2 - 22*a^2*b^4 + 5*b^6)*c^4 - 12*(2*a^3*b^4 - 3*a*b^6)*c^3 + 2*(11*a^2*b^6 - 3*b^8)*c^2)/(b^2*c^12 - 4*a*c^13)))/(b^2*c^6 - 4*a*c^7)) - (a^2*b^6 - b^8 + 12*a*b^2*c^5 + 3*b^2*c^6 + 6*(3*a^2*b^2 - b^4)*c^4 + 4*(3*a^3*b^2 - 4*a*b^4)*c^3 + (3*a^4*b^2 - 14*a^2*b^4 + 4*b^6)*c^2 - 2*(2*a^3*b^4 - 3*a*b^6)*c)*cos(x)) + 2*(2*b^2 - 2*a*c - 3*c^2)*x + 2*(c^2*cos(x) - 2*b*c)*sin(x))/c^3","B",0
7,1,971,0,1.114386," ","integrate(sin(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \sin\left(x\right) + b^{2} \cos\left(x\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \cos\left(x\right) + 2 \, b c\right) - \sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \sin\left(x\right) + b^{2} \cos\left(x\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \cos\left(x\right) + 2 \, b c\right) + \sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \sin\left(x\right) - b^{2} \cos\left(x\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \cos\left(x\right) - 2 \, b c\right) - \sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \sin\left(x\right) - b^{2} \cos\left(x\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \cos\left(x\right) - 2 \, b c\right) + 4 \, x}{4 \, c}"," ",0,"-1/4*(sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*sin(x) + b^2*cos(x) + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*cos(x) + 2*b*c) - sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*sin(x) + b^2*cos(x) + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*cos(x) + 2*b*c) + sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*sin(x) - b^2*cos(x) + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*cos(x) - 2*b*c) - sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*sin(x) - b^2*cos(x) + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*cos(x) - 2*b*c) + 4*x)/c","B",0
8,-1,0,0,0.000000," ","integrate(csc(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,17,0,0.582496," ","integrate(sin(x)/(-2+cos(x)+cos(x)^2),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(\cos\left(x\right) + 2\right) - \frac{1}{3} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"1/3*log(cos(x) + 2) - 1/3*log(-1/2*cos(x) + 1/2)","A",0
10,1,19,0,0.484656," ","integrate(sin(x)/(4-5*cos(x)+cos(x)^2),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - \frac{1}{3} \, \log\left(-\cos\left(x\right) + 4\right)"," ",0,"1/3*log(-1/2*cos(x) + 1/2) - 1/3*log(-cos(x) + 4)","A",0
11,1,19,0,0.758064," ","integrate(sin(x)/(3-2*cos(x)+cos(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*cos(x) - 1/2*sqrt(2))","A",0
12,1,38,0,1.118888," ","integrate(sin(x)/(13-4*cos(x)+cos(x)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} - 4 \, \cos\left(x\right) + 13\right)} \arctan\left(\frac{1}{3} \, \cos\left(x\right) - \frac{2}{3}\right) + 3 \, \cos\left(x\right) - 6}{54 \, {\left(\cos\left(x\right)^{2} - 4 \, \cos\left(x\right) + 13\right)}}"," ",0,"-1/54*((cos(x)^2 - 4*cos(x) + 13)*arctan(1/3*cos(x) - 2/3) + 3*cos(x) - 6)/(cos(x)^2 - 4*cos(x) + 13)","A",0
13,1,8167,0,10.034483," ","integrate(cos(x)^4/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(8 \, a^{7} b c^{4} + 2 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} - {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) + 2 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) + {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} + {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \cos\left(x\right)\right) - \sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(8 \, a^{7} b c^{4} + 2 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} - {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) + 2 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) + {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} + {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \cos\left(x\right)\right) + \sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(-8 \, a^{7} b c^{4} - 2 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} + 4 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} - {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) - 2 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) - {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} - {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \cos\left(x\right)\right) - \sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(-8 \, a^{7} b c^{4} - 2 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} + 4 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} - {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) - 2 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) - {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} - {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \cos\left(x\right)\right) + 2 \, {\left(2 \, b^{2} - 2 \, a c + c^{2}\right)} x + 2 \, {\left(c^{2} \cos\left(x\right) - 2 \, b c\right)} \sin\left(x\right)}{4 \, c^{3}}"," ",0,"1/4*(sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(8*a^7*b*c^4 + 2*(3*a^8*b - 10*a^6*b^3)*c^3 - 4*(2*a^7*b^3 - 3*a^5*b^5)*c^2 - (4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) + 2*(a^6*b^5 - a^4*b^7)*c + 1/2*sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) + (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*sin(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) + (a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*cos(x)) - sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(8*a^7*b*c^4 + 2*(3*a^8*b - 10*a^6*b^3)*c^3 - 4*(2*a^7*b^3 - 3*a^5*b^5)*c^2 - (4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) + 2*(a^6*b^5 - a^4*b^7)*c - 1/2*sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) + (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*sin(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) + (a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*cos(x)) + sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(-8*a^7*b*c^4 - 2*(3*a^8*b - 10*a^6*b^3)*c^3 + 4*(2*a^7*b^3 - 3*a^5*b^5)*c^2 - (4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) - 2*(a^6*b^5 - a^4*b^7)*c + 1/2*sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) - (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*sin(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) - (a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*cos(x)) - sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(-8*a^7*b*c^4 - 2*(3*a^8*b - 10*a^6*b^3)*c^3 + 4*(2*a^7*b^3 - 3*a^5*b^5)*c^2 - (4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) - 2*(a^6*b^5 - a^4*b^7)*c - 1/2*sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) - (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*sin(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) - (a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*cos(x)) + 2*(2*b^2 - 2*a*c + c^2)*x + 2*(c^2*cos(x) - 2*b*c)*sin(x))/c^3","B",0
14,1,6529,0,3.216110," ","integrate(cos(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(6 \, a^{5} b c^{3} + 4 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} - {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) - 2 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) - {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} - {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \cos\left(x\right)\right) - \sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(6 \, a^{5} b c^{3} + 4 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} - {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) - 2 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) - {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} - {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \cos\left(x\right)\right) + \sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(-6 \, a^{5} b c^{3} - 4 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} - {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) + 2 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) + {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} + {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \cos\left(x\right)\right) - \sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(-6 \, a^{5} b c^{3} - 4 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} - {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) + 2 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) + {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} + {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \cos\left(x\right)\right) - 4 \, b x + 4 \, c \sin\left(x\right)}{4 \, c^{2}}"," ",0,"1/4*(sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(6*a^5*b*c^3 + 4*(a^6*b - 2*a^4*b^3)*c^2 - (4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) - 2*(a^5*b^3 - a^3*b^5)*c + 1/2*sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) - (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*sin(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) - (a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*cos(x)) - sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(6*a^5*b*c^3 + 4*(a^6*b - 2*a^4*b^3)*c^2 - (4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) - 2*(a^5*b^3 - a^3*b^5)*c - 1/2*sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) - (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*sin(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) - (a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*cos(x)) + sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(-6*a^5*b*c^3 - 4*(a^6*b - 2*a^4*b^3)*c^2 - (4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) + 2*(a^5*b^3 - a^3*b^5)*c + 1/2*sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) + (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*sin(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) + (a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*cos(x)) - sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(-6*a^5*b*c^3 - 4*(a^6*b - 2*a^4*b^3)*c^2 - (4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) + 2*(a^5*b^3 - a^3*b^5)*c - 1/2*sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) + (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*sin(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) + (a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*cos(x)) - 4*b*x + 4*c*sin(x))/c^2","B",0
15,1,4983,0,2.718520," ","integrate(cos(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(4 \, a^{3} b c^{2} - {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) + 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) + {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} + {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \cos\left(x\right)\right) - \sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(4 \, a^{3} b c^{2} - {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) + 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) + {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} + {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \cos\left(x\right)\right) + \sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(-4 \, a^{3} b c^{2} - {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} c + \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) - {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} - {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \cos\left(x\right)\right) - \sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(-4 \, a^{3} b c^{2} - {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} c - \frac{1}{2} \, \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) - {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} - {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \cos\left(x\right)\right) - 4 \, x}{4 \, c}"," ",0,"-1/4*(sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(4*a^3*b*c^2 - (4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) + 2*(a^4*b - a^2*b^3)*c + 1/2*sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) + (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*sin(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) + (a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*cos(x)) - sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(4*a^3*b*c^2 - (4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) + 2*(a^4*b - a^2*b^3)*c - 1/2*sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) + (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*sin(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) + (a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*cos(x)) + sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(-4*a^3*b*c^2 - (4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) - 2*(a^4*b - a^2*b^3)*c + 1/2*sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) - (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*sin(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) - (a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*cos(x)) - sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(-4*a^3*b*c^2 - (4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) - 2*(a^4*b - a^2*b^3)*c - 1/2*sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) - (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*sin(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) - (a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*cos(x)) - 4*x)/c","B",0
16,1,3513,0,1.961408," ","integrate(cos(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(a b^{2} \cos\left(x\right) + 2 \, a b c + {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(a b^{2} \cos\left(x\right) + 2 \, a b c + {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-a b^{2} \cos\left(x\right) - 2 \, a b c + {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-a b^{2} \cos\left(x\right) - 2 \, a b c + {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right)"," ",0,"-1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(a*b^2*cos(x) + 2*a*b*c + (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + 1/2*sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*sin(x))*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(a*b^2*cos(x) + 2*a*b*c + (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - 1/2*sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*sin(x))*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) - 1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-a*b^2*cos(x) - 2*a*b*c + (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + 1/2*sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*sin(x))*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-a*b^2*cos(x) - 2*a*b*c + (a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - 1/2*sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*sin(x))*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)))","B",0
17,1,3493,0,2.278784," ","integrate(1/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(b^{2} c \cos\left(x\right) + 2 \, b c^{2} - {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + {\left(b^{4} - 4 \, a b^{2} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(b^{2} c \cos\left(x\right) + 2 \, b c^{2} - {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) + {\left(b^{4} - 4 \, a b^{2} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-b^{2} c \cos\left(x\right) - 2 \, b c^{2} - {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - {\left(b^{4} - 4 \, a b^{2} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-b^{2} c \cos\left(x\right) - 2 \, b c^{2} - {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - \frac{1}{2} \, \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - {\left(b^{4} - 4 \, a b^{2} c\right)} \sin\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right)"," ",0,"1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(b^2*c*cos(x) + 2*b*c^2 - (4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + 1/2*sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + (b^4 - 4*a*b^2*c)*sin(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) - 1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(b^2*c*cos(x) + 2*b*c^2 - (4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - 1/2*sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) + (b^4 - 4*a*b^2*c)*sin(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-b^2*c*cos(x) - 2*b*c^2 - (4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + 1/2*sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - (b^4 - 4*a*b^2*c)*sin(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) - 1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-b^2*c*cos(x) - 2*b*c^2 - (4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - 1/2*sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - (b^4 - 4*a*b^2*c)*sin(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)))","B",0
18,-1,0,0,0.000000," ","integrate(sec(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""fricas"")","\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=""fricas"")","\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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
