1,-2,0,0,0.000000," ","integrate(sin(x)^5/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
2,-2,0,0,0.000000," ","integrate(sin(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
3,-2,0,0,0.000000," ","integrate(sin(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
4,-2,0,0,0.000000," ","integrate(csc(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
5,-2,0,0,0.000000," ","integrate(csc(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
6,0,0,0,0.000000," ","integrate(sin(x)^4/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\frac{-8 \, c^{3} \int \frac{2 \, {\left(b^{4} - 2 \, a b^{2} c - 2 \, b^{2} c^{2}\right)} \cos\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a^{2} b^{2} - 5 \, a^{2} c^{2} - 4 \, a c^{3} - c^{4} - {\left(2 \, a^{3} - a b^{2}\right)} c\right)} \cos\left(2 \, x\right)^{2} + 2 \, {\left(b^{4} - 2 \, a b^{2} c - 2 \, b^{2} c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{4} - 2 \, a b^{2} c - 2 \, b^{2} c^{2}\right)} \sin\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a^{2} b^{2} - 5 \, a^{2} c^{2} - 4 \, a c^{3} - c^{4} - {\left(2 \, a^{3} - a b^{2}\right)} c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a b^{3} - 10 \, a b c^{2} - 4 \, b c^{3} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(b^{4} - 2 \, a b^{2} c - 2 \, b^{2} c^{2}\right)} \sin\left(x\right)^{2} + {\left({\left(b^{3} c - 2 \, a b c^{2} - 2 \, b c^{3}\right)} \cos\left(3 \, x\right) + 2 \, {\left(a b^{2} c - a^{2} c^{2} - 2 \, a c^{3} - c^{4}\right)} \cos\left(2 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2} - 2 \, b c^{3}\right)} \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2} - 2 \, b c^{3} + 2 \, {\left(4 \, a b^{3} - 10 \, a b c^{2} - 4 \, b c^{3} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(2 \, x\right) + 4 \, {\left(b^{4} - 2 \, a b^{2} c - 2 \, b^{2} c^{2}\right)} \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(a b^{2} c - a^{2} c^{2} - 2 \, a c^{3} - c^{4} + {\left(4 \, a b^{3} - 10 \, a b c^{2} - 4 \, b c^{3} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2} - 2 \, b c^{3}\right)} \cos\left(x\right) + {\left({\left(b^{3} c - 2 \, a b c^{2} - 2 \, b c^{3}\right)} \sin\left(3 \, x\right) + 2 \, {\left(a b^{2} c - a^{2} c^{2} - 2 \, a c^{3} - c^{4}\right)} \sin\left(2 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2} - 2 \, b c^{3}\right)} \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left({\left(4 \, a b^{3} - 10 \, a b c^{2} - 4 \, b c^{3} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right) + 2 \, {\left(b^{4} - 2 \, a b^{2} c - 2 \, b^{2} c^{2}\right)} \sin\left(x\right)\right)} \sin\left(3 \, x\right)}{c^{5} \cos\left(4 \, x\right)^{2} + 4 \, b^{2} c^{3} \cos\left(3 \, x\right)^{2} + 4 \, b^{2} c^{3} \cos\left(x\right)^{2} + c^{5} \sin\left(4 \, x\right)^{2} + 4 \, b^{2} c^{3} \sin\left(3 \, x\right)^{2} + 4 \, b^{2} c^{3} \sin\left(x\right)^{2} + 4 \, b c^{4} \cos\left(x\right) + c^{5} + 4 \, {\left(4 \, a^{2} c^{3} + 4 \, a c^{4} + c^{5}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{2} c^{3} + 4 \, a c^{4} + c^{5}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a b c^{3} + b c^{4}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, b c^{4} \cos\left(3 \, x\right) + 2 \, b c^{4} \cos\left(x\right) + c^{5} + 2 \, {\left(2 \, a c^{4} + c^{5}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, b^{2} c^{3} \cos\left(x\right) + b c^{4} + 2 \, {\left(2 \, a b c^{3} + b c^{4}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a c^{4} + c^{5} + 2 \, {\left(2 \, a b c^{3} + b c^{4}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(b c^{4} \sin\left(3 \, x\right) + b c^{4} \sin\left(x\right) + {\left(2 \, a c^{4} + c^{5}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(b^{2} c^{3} \sin\left(x\right) + {\left(2 \, a b c^{3} + b c^{4}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} + c^{2} \sin\left(2 \, x\right) - 4 \, b c \sin\left(x\right) + 2 \, {\left(2 \, b^{2} - 2 \, a c - 3 \, c^{2}\right)} x}{4 \, c^{3}}"," ",0,"1/4*(4*c^3*integrate(-2*(2*(b^4 - 2*a*b^2*c - 2*b^2*c^2)*cos(3*x)^2 + 4*(2*a^2*b^2 - 5*a^2*c^2 - 4*a*c^3 - c^4 - (2*a^3 - a*b^2)*c)*cos(2*x)^2 + 2*(b^4 - 2*a*b^2*c - 2*b^2*c^2)*cos(x)^2 + 2*(b^4 - 2*a*b^2*c - 2*b^2*c^2)*sin(3*x)^2 + 4*(2*a^2*b^2 - 5*a^2*c^2 - 4*a*c^3 - c^4 - (2*a^3 - a*b^2)*c)*sin(2*x)^2 + 2*(4*a*b^3 - 10*a*b*c^2 - 4*b*c^3 - (6*a^2*b - b^3)*c)*sin(2*x)*sin(x) + 2*(b^4 - 2*a*b^2*c - 2*b^2*c^2)*sin(x)^2 + ((b^3*c - 2*a*b*c^2 - 2*b*c^3)*cos(3*x) + 2*(a*b^2*c - a^2*c^2 - 2*a*c^3 - c^4)*cos(2*x) + (b^3*c - 2*a*b*c^2 - 2*b*c^3)*cos(x))*cos(4*x) + (b^3*c - 2*a*b*c^2 - 2*b*c^3 + 2*(4*a*b^3 - 10*a*b*c^2 - 4*b*c^3 - (6*a^2*b - b^3)*c)*cos(2*x) + 4*(b^4 - 2*a*b^2*c - 2*b^2*c^2)*cos(x))*cos(3*x) + 2*(a*b^2*c - a^2*c^2 - 2*a*c^3 - c^4 + (4*a*b^3 - 10*a*b*c^2 - 4*b*c^3 - (6*a^2*b - b^3)*c)*cos(x))*cos(2*x) + (b^3*c - 2*a*b*c^2 - 2*b*c^3)*cos(x) + ((b^3*c - 2*a*b*c^2 - 2*b*c^3)*sin(3*x) + 2*(a*b^2*c - a^2*c^2 - 2*a*c^3 - c^4)*sin(2*x) + (b^3*c - 2*a*b*c^2 - 2*b*c^3)*sin(x))*sin(4*x) + 2*((4*a*b^3 - 10*a*b*c^2 - 4*b*c^3 - (6*a^2*b - b^3)*c)*sin(2*x) + 2*(b^4 - 2*a*b^2*c - 2*b^2*c^2)*sin(x))*sin(3*x))/(c^5*cos(4*x)^2 + 4*b^2*c^3*cos(3*x)^2 + 4*b^2*c^3*cos(x)^2 + c^5*sin(4*x)^2 + 4*b^2*c^3*sin(3*x)^2 + 4*b^2*c^3*sin(x)^2 + 4*b*c^4*cos(x) + c^5 + 4*(4*a^2*c^3 + 4*a*c^4 + c^5)*cos(2*x)^2 + 4*(4*a^2*c^3 + 4*a*c^4 + c^5)*sin(2*x)^2 + 8*(2*a*b*c^3 + b*c^4)*sin(2*x)*sin(x) + 2*(2*b*c^4*cos(3*x) + 2*b*c^4*cos(x) + c^5 + 2*(2*a*c^4 + c^5)*cos(2*x))*cos(4*x) + 4*(2*b^2*c^3*cos(x) + b*c^4 + 2*(2*a*b*c^3 + b*c^4)*cos(2*x))*cos(3*x) + 4*(2*a*c^4 + c^5 + 2*(2*a*b*c^3 + b*c^4)*cos(x))*cos(2*x) + 4*(b*c^4*sin(3*x) + b*c^4*sin(x) + (2*a*c^4 + c^5)*sin(2*x))*sin(4*x) + 8*(b^2*c^3*sin(x) + (2*a*b*c^3 + b*c^4)*sin(2*x))*sin(3*x)), x) + c^2*sin(2*x) - 4*b*c*sin(x) + 2*(2*b^2 - 2*a*c - 3*c^2)*x)/c^3","F",0
7,0,0,0,0.000000," ","integrate(sin(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\frac{2 \, c \int \frac{2 \, b^{2} \cos\left(3 \, x\right)^{2} + 2 \, b^{2} \cos\left(x\right)^{2} + 2 \, b^{2} \sin\left(3 \, x\right)^{2} + 2 \, b^{2} \sin\left(x\right)^{2} + 4 \, {\left(2 \, a^{2} + 3 \, a c + c^{2}\right)} \cos\left(2 \, x\right)^{2} + b c \cos\left(x\right) + 4 \, {\left(2 \, a^{2} + 3 \, a c + c^{2}\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a b + 3 \, b c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + {\left(b c \cos\left(3 \, x\right) + b c \cos\left(x\right) + 2 \, {\left(a c + c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + {\left(4 \, b^{2} \cos\left(x\right) + b c + 2 \, {\left(4 \, a b + 3 \, b c\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(a c + c^{2} + {\left(4 \, a b + 3 \, b c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b c \sin\left(3 \, x\right) + b c \sin\left(x\right) + 2 \, {\left(a c + c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(2 \, b^{2} \sin\left(x\right) + {\left(4 \, a b + 3 \, b c\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}{c^{3} \cos\left(4 \, x\right)^{2} + 4 \, b^{2} c \cos\left(3 \, x\right)^{2} + 4 \, b^{2} c \cos\left(x\right)^{2} + c^{3} \sin\left(4 \, x\right)^{2} + 4 \, b^{2} c \sin\left(3 \, x\right)^{2} + 4 \, b^{2} c \sin\left(x\right)^{2} + 4 \, b c^{2} \cos\left(x\right) + c^{3} + 4 \, {\left(4 \, a^{2} c + 4 \, a c^{2} + c^{3}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{2} c + 4 \, a c^{2} + c^{3}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a b c + b c^{2}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, b c^{2} \cos\left(3 \, x\right) + 2 \, b c^{2} \cos\left(x\right) + c^{3} + 2 \, {\left(2 \, a c^{2} + c^{3}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, b^{2} c \cos\left(x\right) + b c^{2} + 2 \, {\left(2 \, a b c + b c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a c^{2} + c^{3} + 2 \, {\left(2 \, a b c + b c^{2}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(b c^{2} \sin\left(3 \, x\right) + b c^{2} \sin\left(x\right) + {\left(2 \, a c^{2} + c^{3}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(b^{2} c \sin\left(x\right) + {\left(2 \, a b c + b c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} - x}{c}"," ",0,"(c*integrate(2*(2*b^2*cos(3*x)^2 + 2*b^2*cos(x)^2 + 2*b^2*sin(3*x)^2 + 2*b^2*sin(x)^2 + 4*(2*a^2 + 3*a*c + c^2)*cos(2*x)^2 + b*c*cos(x) + 4*(2*a^2 + 3*a*c + c^2)*sin(2*x)^2 + 2*(4*a*b + 3*b*c)*sin(2*x)*sin(x) + (b*c*cos(3*x) + b*c*cos(x) + 2*(a*c + c^2)*cos(2*x))*cos(4*x) + (4*b^2*cos(x) + b*c + 2*(4*a*b + 3*b*c)*cos(2*x))*cos(3*x) + 2*(a*c + c^2 + (4*a*b + 3*b*c)*cos(x))*cos(2*x) + (b*c*sin(3*x) + b*c*sin(x) + 2*(a*c + c^2)*sin(2*x))*sin(4*x) + 2*(2*b^2*sin(x) + (4*a*b + 3*b*c)*sin(2*x))*sin(3*x))/(c^3*cos(4*x)^2 + 4*b^2*c*cos(3*x)^2 + 4*b^2*c*cos(x)^2 + c^3*sin(4*x)^2 + 4*b^2*c*sin(3*x)^2 + 4*b^2*c*sin(x)^2 + 4*b*c^2*cos(x) + c^3 + 4*(4*a^2*c + 4*a*c^2 + c^3)*cos(2*x)^2 + 4*(4*a^2*c + 4*a*c^2 + c^3)*sin(2*x)^2 + 8*(2*a*b*c + b*c^2)*sin(2*x)*sin(x) + 2*(2*b*c^2*cos(3*x) + 2*b*c^2*cos(x) + c^3 + 2*(2*a*c^2 + c^3)*cos(2*x))*cos(4*x) + 4*(2*b^2*c*cos(x) + b*c^2 + 2*(2*a*b*c + b*c^2)*cos(2*x))*cos(3*x) + 4*(2*a*c^2 + c^3 + 2*(2*a*b*c + b*c^2)*cos(x))*cos(2*x) + 4*(b*c^2*sin(3*x) + b*c^2*sin(x) + (2*a*c^2 + c^3)*sin(2*x))*sin(4*x) + 8*(b^2*c*sin(x) + (2*a*b*c + b*c^2)*sin(2*x))*sin(3*x)), x) - x)/c","F",0
8,0,0,0,0.000000," ","integrate(csc(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","-\frac{2 \, b \cos\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left({\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \cos\left(2 \, x\right)^{2} + {\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \sin\left(2 \, x\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \cos\left(2 \, x\right)\right)} \int \frac{2 \, b^{2} c \cos\left(3 \, x\right)^{2} + 2 \, b^{2} c \cos\left(x\right)^{2} + 2 \, b^{2} c \sin\left(3 \, x\right)^{2} + 2 \, b^{2} c \sin\left(x\right)^{2} + b c^{2} \cos\left(x\right) + 4 \, {\left(2 \, a b^{2} - 3 \, a c^{2} - c^{3} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, a b^{2} - 3 \, a c^{2} - c^{3} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(2 \, b^{3} - b c^{2}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + {\left(b c^{2} \cos\left(3 \, x\right) + b c^{2} \cos\left(x\right) + 2 \, {\left(b^{2} c - a c^{2} - c^{3}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + {\left(4 \, b^{2} c \cos\left(x\right) + b c^{2} + 2 \, {\left(2 \, b^{3} - b c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(b^{2} c - a c^{2} - c^{3} + {\left(2 \, b^{3} - b c^{2}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b c^{2} \sin\left(3 \, x\right) + b c^{2} \sin\left(x\right) + 2 \, {\left(b^{2} c - a c^{2} - c^{3}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(2 \, b^{2} c \sin\left(x\right) + {\left(2 \, b^{3} - b c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}{2 \, a c^{3} + c^{4} + {\left(a^{2} - b^{2}\right)} c^{2} + {\left(2 \, a c^{3} + c^{4} + {\left(a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(4 \, x\right)^{2} + 4 \, {\left(a^{2} b^{2} - b^{4} + 2 \, a b^{2} c + b^{2} c^{2}\right)} \cos\left(3 \, x\right)^{2} + 4 \, {\left(4 \, a^{4} - 4 \, a^{2} b^{2} + 6 \, a c^{3} + c^{4} + {\left(13 \, a^{2} - b^{2}\right)} c^{2} + 4 \, {\left(3 \, a^{3} - a b^{2}\right)} c\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(a^{2} b^{2} - b^{4} + 2 \, a b^{2} c + b^{2} c^{2}\right)} \cos\left(x\right)^{2} + {\left(2 \, a c^{3} + c^{4} + {\left(a^{2} - b^{2}\right)} c^{2}\right)} \sin\left(4 \, x\right)^{2} + 4 \, {\left(a^{2} b^{2} - b^{4} + 2 \, a b^{2} c + b^{2} c^{2}\right)} \sin\left(3 \, x\right)^{2} + 4 \, {\left(4 \, a^{4} - 4 \, a^{2} b^{2} + 6 \, a c^{3} + c^{4} + {\left(13 \, a^{2} - b^{2}\right)} c^{2} + 4 \, {\left(3 \, a^{3} - a b^{2}\right)} c\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a^{3} b - 2 \, a b^{3} + 4 \, a b c^{2} + b c^{3} + {\left(5 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, {\left(a^{2} b^{2} - b^{4} + 2 \, a b^{2} c + b^{2} c^{2}\right)} \sin\left(x\right)^{2} + 2 \, {\left(2 \, a c^{3} + c^{4} + {\left(a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(2 \, a b c^{2} + b c^{3} + {\left(a^{2} b - b^{3}\right)} c\right)} \cos\left(3 \, x\right) + 2 \, {\left(4 \, a c^{3} + c^{4} + {\left(5 \, a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} \cos\left(2 \, x\right) + 2 \, {\left(2 \, a b c^{2} + b c^{3} + {\left(a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, a b c^{2} + b c^{3} + {\left(a^{2} b - b^{3}\right)} c + 2 \, {\left(2 \, a^{3} b - 2 \, a b^{3} + 4 \, a b c^{2} + b c^{3} + {\left(5 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(2 \, x\right) + 2 \, {\left(a^{2} b^{2} - b^{4} + 2 \, a b^{2} c + b^{2} c^{2}\right)} \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(4 \, a c^{3} + c^{4} + {\left(5 \, a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c + 2 \, {\left(2 \, a^{3} b - 2 \, a b^{3} + 4 \, a b c^{2} + b c^{3} + {\left(5 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(2 \, a b c^{2} + b c^{3} + {\left(a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right) + 4 \, {\left({\left(2 \, a b c^{2} + b c^{3} + {\left(a^{2} b - b^{3}\right)} c\right)} \sin\left(3 \, x\right) + {\left(4 \, a c^{3} + c^{4} + {\left(5 \, a^{2} - b^{2}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} \sin\left(2 \, x\right) + {\left(2 \, a b c^{2} + b c^{3} + {\left(a^{2} b - b^{3}\right)} c\right)} \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left({\left(2 \, a^{3} b - 2 \, a b^{3} + 4 \, a b c^{2} + b c^{3} + {\left(5 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right) + {\left(a^{2} b^{2} - b^{4} + 2 \, a b^{2} c + b^{2} c^{2}\right)} \sin\left(x\right)\right)} \sin\left(3 \, x\right)}\,{d x} - 2 \, {\left(b \cos\left(x\right) - a - c\right)} \sin\left(2 \, x\right) - 2 \, b \sin\left(x\right)}{{\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \cos\left(2 \, x\right)^{2} + {\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \sin\left(2 \, x\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - b^{2} + 2 \, a c + c^{2}\right)} \cos\left(2 \, x\right)}"," ",0,"-(2*b*cos(2*x)*sin(x) + ((a^2 - b^2 + 2*a*c + c^2)*cos(2*x)^2 + (a^2 - b^2 + 2*a*c + c^2)*sin(2*x)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - b^2 + 2*a*c + c^2)*cos(2*x))*integrate(2*(2*b^2*c*cos(3*x)^2 + 2*b^2*c*cos(x)^2 + 2*b^2*c*sin(3*x)^2 + 2*b^2*c*sin(x)^2 + b*c^2*cos(x) + 4*(2*a*b^2 - 3*a*c^2 - c^3 - (2*a^2 - b^2)*c)*cos(2*x)^2 + 4*(2*a*b^2 - 3*a*c^2 - c^3 - (2*a^2 - b^2)*c)*sin(2*x)^2 + 2*(2*b^3 - b*c^2)*sin(2*x)*sin(x) + (b*c^2*cos(3*x) + b*c^2*cos(x) + 2*(b^2*c - a*c^2 - c^3)*cos(2*x))*cos(4*x) + (4*b^2*c*cos(x) + b*c^2 + 2*(2*b^3 - b*c^2)*cos(2*x))*cos(3*x) + 2*(b^2*c - a*c^2 - c^3 + (2*b^3 - b*c^2)*cos(x))*cos(2*x) + (b*c^2*sin(3*x) + b*c^2*sin(x) + 2*(b^2*c - a*c^2 - c^3)*sin(2*x))*sin(4*x) + 2*(2*b^2*c*sin(x) + (2*b^3 - b*c^2)*sin(2*x))*sin(3*x))/(2*a*c^3 + c^4 + (a^2 - b^2)*c^2 + (2*a*c^3 + c^4 + (a^2 - b^2)*c^2)*cos(4*x)^2 + 4*(a^2*b^2 - b^4 + 2*a*b^2*c + b^2*c^2)*cos(3*x)^2 + 4*(4*a^4 - 4*a^2*b^2 + 6*a*c^3 + c^4 + (13*a^2 - b^2)*c^2 + 4*(3*a^3 - a*b^2)*c)*cos(2*x)^2 + 4*(a^2*b^2 - b^4 + 2*a*b^2*c + b^2*c^2)*cos(x)^2 + (2*a*c^3 + c^4 + (a^2 - b^2)*c^2)*sin(4*x)^2 + 4*(a^2*b^2 - b^4 + 2*a*b^2*c + b^2*c^2)*sin(3*x)^2 + 4*(4*a^4 - 4*a^2*b^2 + 6*a*c^3 + c^4 + (13*a^2 - b^2)*c^2 + 4*(3*a^3 - a*b^2)*c)*sin(2*x)^2 + 8*(2*a^3*b - 2*a*b^3 + 4*a*b*c^2 + b*c^3 + (5*a^2*b - b^3)*c)*sin(2*x)*sin(x) + 4*(a^2*b^2 - b^4 + 2*a*b^2*c + b^2*c^2)*sin(x)^2 + 2*(2*a*c^3 + c^4 + (a^2 - b^2)*c^2 + 2*(2*a*b*c^2 + b*c^3 + (a^2*b - b^3)*c)*cos(3*x) + 2*(4*a*c^3 + c^4 + (5*a^2 - b^2)*c^2 + 2*(a^3 - a*b^2)*c)*cos(2*x) + 2*(2*a*b*c^2 + b*c^3 + (a^2*b - b^3)*c)*cos(x))*cos(4*x) + 4*(2*a*b*c^2 + b*c^3 + (a^2*b - b^3)*c + 2*(2*a^3*b - 2*a*b^3 + 4*a*b*c^2 + b*c^3 + (5*a^2*b - b^3)*c)*cos(2*x) + 2*(a^2*b^2 - b^4 + 2*a*b^2*c + b^2*c^2)*cos(x))*cos(3*x) + 4*(4*a*c^3 + c^4 + (5*a^2 - b^2)*c^2 + 2*(a^3 - a*b^2)*c + 2*(2*a^3*b - 2*a*b^3 + 4*a*b*c^2 + b*c^3 + (5*a^2*b - b^3)*c)*cos(x))*cos(2*x) + 4*(2*a*b*c^2 + b*c^3 + (a^2*b - b^3)*c)*cos(x) + 4*((2*a*b*c^2 + b*c^3 + (a^2*b - b^3)*c)*sin(3*x) + (4*a*c^3 + c^4 + (5*a^2 - b^2)*c^2 + 2*(a^3 - a*b^2)*c)*sin(2*x) + (2*a*b*c^2 + b*c^3 + (a^2*b - b^3)*c)*sin(x))*sin(4*x) + 8*((2*a^3*b - 2*a*b^3 + 4*a*b*c^2 + b*c^3 + (5*a^2*b - b^3)*c)*sin(2*x) + (a^2*b^2 - b^4 + 2*a*b^2*c + b^2*c^2)*sin(x))*sin(3*x)), x) - 2*(b*cos(x) - a - c)*sin(2*x) - 2*b*sin(x))/((a^2 - b^2 + 2*a*c + c^2)*cos(2*x)^2 + (a^2 - b^2 + 2*a*c + c^2)*sin(2*x)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - b^2 + 2*a*c + c^2)*cos(2*x))","F",0
9,1,15,0,0.334848," ","integrate(sin(x)/(-2+cos(x)+cos(x)^2),x, algorithm=""maxima"")","\frac{1}{3} \, \log\left(\cos\left(x\right) + 2\right) - \frac{1}{3} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"1/3*log(cos(x) + 2) - 1/3*log(cos(x) - 1)","A",0
10,1,15,0,0.321866," ","integrate(sin(x)/(4-5*cos(x)+cos(x)^2),x, algorithm=""maxima"")","\frac{1}{3} \, \log\left(\cos\left(x\right) - 1\right) - \frac{1}{3} \, \log\left(\cos\left(x\right) - 4\right)"," ",0,"1/3*log(cos(x) - 1) - 1/3*log(cos(x) - 4)","A",0
11,1,15,0,0.854041," ","integrate(sin(x)/(3-2*cos(x)+cos(x)^2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\cos\left(x\right) - 1\right)}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*(cos(x) - 1))","A",0
12,1,28,0,0.897983," ","integrate(sin(x)/(13-4*cos(x)+cos(x)^2)^2,x, algorithm=""maxima"")","-\frac{\cos\left(x\right) - 2}{18 \, {\left(\cos\left(x\right)^{2} - 4 \, \cos\left(x\right) + 13\right)}} - \frac{1}{54} \, \arctan\left(\frac{1}{3} \, \cos\left(x\right) - \frac{2}{3}\right)"," ",0,"-1/18*(cos(x) - 2)/(cos(x)^2 - 4*cos(x) + 13) - 1/54*arctan(1/3*cos(x) - 2/3)","A",0
13,0,0,0,0.000000," ","integrate(cos(x)^4/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\frac{-8 \, c^{3} \int \frac{2 \, {\left(b^{4} - 2 \, a b^{2} c\right)} \cos\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a^{2} b^{2} - a^{2} c^{2} - {\left(2 \, a^{3} - a b^{2}\right)} c\right)} \cos\left(2 \, x\right)^{2} + 2 \, {\left(b^{4} - 2 \, a b^{2} c\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{4} - 2 \, a b^{2} c\right)} \sin\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a^{2} b^{2} - a^{2} c^{2} - {\left(2 \, a^{3} - a b^{2}\right)} c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a b^{3} - 2 \, a b c^{2} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(b^{4} - 2 \, a b^{2} c\right)} \sin\left(x\right)^{2} + {\left({\left(b^{3} c - 2 \, a b c^{2}\right)} \cos\left(3 \, x\right) + 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} \cos\left(2 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2}\right)} \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2} + 2 \, {\left(4 \, a b^{3} - 2 \, a b c^{2} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(2 \, x\right) + 4 \, {\left(b^{4} - 2 \, a b^{2} c\right)} \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(a b^{2} c - a^{2} c^{2} + {\left(4 \, a b^{3} - 2 \, a b c^{2} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2}\right)} \cos\left(x\right) + {\left({\left(b^{3} c - 2 \, a b c^{2}\right)} \sin\left(3 \, x\right) + 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} \sin\left(2 \, x\right) + {\left(b^{3} c - 2 \, a b c^{2}\right)} \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left({\left(4 \, a b^{3} - 2 \, a b c^{2} - {\left(6 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right) + 2 \, {\left(b^{4} - 2 \, a b^{2} c\right)} \sin\left(x\right)\right)} \sin\left(3 \, x\right)}{c^{5} \cos\left(4 \, x\right)^{2} + 4 \, b^{2} c^{3} \cos\left(3 \, x\right)^{2} + 4 \, b^{2} c^{3} \cos\left(x\right)^{2} + c^{5} \sin\left(4 \, x\right)^{2} + 4 \, b^{2} c^{3} \sin\left(3 \, x\right)^{2} + 4 \, b^{2} c^{3} \sin\left(x\right)^{2} + 4 \, b c^{4} \cos\left(x\right) + c^{5} + 4 \, {\left(4 \, a^{2} c^{3} + 4 \, a c^{4} + c^{5}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{2} c^{3} + 4 \, a c^{4} + c^{5}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a b c^{3} + b c^{4}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, b c^{4} \cos\left(3 \, x\right) + 2 \, b c^{4} \cos\left(x\right) + c^{5} + 2 \, {\left(2 \, a c^{4} + c^{5}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, b^{2} c^{3} \cos\left(x\right) + b c^{4} + 2 \, {\left(2 \, a b c^{3} + b c^{4}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a c^{4} + c^{5} + 2 \, {\left(2 \, a b c^{3} + b c^{4}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(b c^{4} \sin\left(3 \, x\right) + b c^{4} \sin\left(x\right) + {\left(2 \, a c^{4} + c^{5}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(b^{2} c^{3} \sin\left(x\right) + {\left(2 \, a b c^{3} + b c^{4}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} + c^{2} \sin\left(2 \, x\right) - 4 \, b c \sin\left(x\right) + 2 \, {\left(2 \, b^{2} - 2 \, a c + c^{2}\right)} x}{4 \, c^{3}}"," ",0,"1/4*(4*c^3*integrate(-2*(2*(b^4 - 2*a*b^2*c)*cos(3*x)^2 + 4*(2*a^2*b^2 - a^2*c^2 - (2*a^3 - a*b^2)*c)*cos(2*x)^2 + 2*(b^4 - 2*a*b^2*c)*cos(x)^2 + 2*(b^4 - 2*a*b^2*c)*sin(3*x)^2 + 4*(2*a^2*b^2 - a^2*c^2 - (2*a^3 - a*b^2)*c)*sin(2*x)^2 + 2*(4*a*b^3 - 2*a*b*c^2 - (6*a^2*b - b^3)*c)*sin(2*x)*sin(x) + 2*(b^4 - 2*a*b^2*c)*sin(x)^2 + ((b^3*c - 2*a*b*c^2)*cos(3*x) + 2*(a*b^2*c - a^2*c^2)*cos(2*x) + (b^3*c - 2*a*b*c^2)*cos(x))*cos(4*x) + (b^3*c - 2*a*b*c^2 + 2*(4*a*b^3 - 2*a*b*c^2 - (6*a^2*b - b^3)*c)*cos(2*x) + 4*(b^4 - 2*a*b^2*c)*cos(x))*cos(3*x) + 2*(a*b^2*c - a^2*c^2 + (4*a*b^3 - 2*a*b*c^2 - (6*a^2*b - b^3)*c)*cos(x))*cos(2*x) + (b^3*c - 2*a*b*c^2)*cos(x) + ((b^3*c - 2*a*b*c^2)*sin(3*x) + 2*(a*b^2*c - a^2*c^2)*sin(2*x) + (b^3*c - 2*a*b*c^2)*sin(x))*sin(4*x) + 2*((4*a*b^3 - 2*a*b*c^2 - (6*a^2*b - b^3)*c)*sin(2*x) + 2*(b^4 - 2*a*b^2*c)*sin(x))*sin(3*x))/(c^5*cos(4*x)^2 + 4*b^2*c^3*cos(3*x)^2 + 4*b^2*c^3*cos(x)^2 + c^5*sin(4*x)^2 + 4*b^2*c^3*sin(3*x)^2 + 4*b^2*c^3*sin(x)^2 + 4*b*c^4*cos(x) + c^5 + 4*(4*a^2*c^3 + 4*a*c^4 + c^5)*cos(2*x)^2 + 4*(4*a^2*c^3 + 4*a*c^4 + c^5)*sin(2*x)^2 + 8*(2*a*b*c^3 + b*c^4)*sin(2*x)*sin(x) + 2*(2*b*c^4*cos(3*x) + 2*b*c^4*cos(x) + c^5 + 2*(2*a*c^4 + c^5)*cos(2*x))*cos(4*x) + 4*(2*b^2*c^3*cos(x) + b*c^4 + 2*(2*a*b*c^3 + b*c^4)*cos(2*x))*cos(3*x) + 4*(2*a*c^4 + c^5 + 2*(2*a*b*c^3 + b*c^4)*cos(x))*cos(2*x) + 4*(b*c^4*sin(3*x) + b*c^4*sin(x) + (2*a*c^4 + c^5)*sin(2*x))*sin(4*x) + 8*(b^2*c^3*sin(x) + (2*a*b*c^3 + b*c^4)*sin(2*x))*sin(3*x)), x) + c^2*sin(2*x) - 4*b*c*sin(x) + 2*(2*b^2 - 2*a*c + c^2)*x)/c^3","F",0
14,0,0,0,0.000000," ","integrate(cos(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","-\frac{-2 \, c^{2} \int \frac{2 \, {\left(b^{3} - a b c\right)} \cos\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a^{2} b + a b c\right)} \cos\left(2 \, x\right)^{2} + 2 \, {\left(b^{3} - a b c\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{3} - a b c\right)} \sin\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a^{2} b + a b c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a b^{2} - a c^{2} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(b^{3} - a b c\right)} \sin\left(x\right)^{2} + {\left(2 \, a b c \cos\left(2 \, x\right) + {\left(b^{2} c - a c^{2}\right)} \cos\left(3 \, x\right) + {\left(b^{2} c - a c^{2}\right)} \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(b^{2} c - a c^{2} + 2 \, {\left(4 \, a b^{2} - a c^{2} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \cos\left(2 \, x\right) + 4 \, {\left(b^{3} - a b c\right)} \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(a b c + {\left(4 \, a b^{2} - a c^{2} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b^{2} c - a c^{2}\right)} \cos\left(x\right) + {\left(2 \, a b c \sin\left(2 \, x\right) + {\left(b^{2} c - a c^{2}\right)} \sin\left(3 \, x\right) + {\left(b^{2} c - a c^{2}\right)} \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left({\left(4 \, a b^{2} - a c^{2} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \sin\left(2 \, x\right) + 2 \, {\left(b^{3} - a b c\right)} \sin\left(x\right)\right)} \sin\left(3 \, x\right)}{c^{4} \cos\left(4 \, x\right)^{2} + 4 \, b^{2} c^{2} \cos\left(3 \, x\right)^{2} + 4 \, b^{2} c^{2} \cos\left(x\right)^{2} + c^{4} \sin\left(4 \, x\right)^{2} + 4 \, b^{2} c^{2} \sin\left(3 \, x\right)^{2} + 4 \, b^{2} c^{2} \sin\left(x\right)^{2} + 4 \, b c^{3} \cos\left(x\right) + c^{4} + 4 \, {\left(4 \, a^{2} c^{2} + 4 \, a c^{3} + c^{4}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{2} c^{2} + 4 \, a c^{3} + c^{4}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a b c^{2} + b c^{3}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, b c^{3} \cos\left(3 \, x\right) + 2 \, b c^{3} \cos\left(x\right) + c^{4} + 2 \, {\left(2 \, a c^{3} + c^{4}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, b^{2} c^{2} \cos\left(x\right) + b c^{3} + 2 \, {\left(2 \, a b c^{2} + b c^{3}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a c^{3} + c^{4} + 2 \, {\left(2 \, a b c^{2} + b c^{3}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(b c^{3} \sin\left(3 \, x\right) + b c^{3} \sin\left(x\right) + {\left(2 \, a c^{3} + c^{4}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(b^{2} c^{2} \sin\left(x\right) + {\left(2 \, a b c^{2} + b c^{3}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} + b x - c \sin\left(x\right)}{c^{2}}"," ",0,"-(c^2*integrate(-2*(2*(b^3 - a*b*c)*cos(3*x)^2 + 4*(2*a^2*b + a*b*c)*cos(2*x)^2 + 2*(b^3 - a*b*c)*cos(x)^2 + 2*(b^3 - a*b*c)*sin(3*x)^2 + 4*(2*a^2*b + a*b*c)*sin(2*x)^2 + 2*(4*a*b^2 - a*c^2 - (2*a^2 - b^2)*c)*sin(2*x)*sin(x) + 2*(b^3 - a*b*c)*sin(x)^2 + (2*a*b*c*cos(2*x) + (b^2*c - a*c^2)*cos(3*x) + (b^2*c - a*c^2)*cos(x))*cos(4*x) + (b^2*c - a*c^2 + 2*(4*a*b^2 - a*c^2 - (2*a^2 - b^2)*c)*cos(2*x) + 4*(b^3 - a*b*c)*cos(x))*cos(3*x) + 2*(a*b*c + (4*a*b^2 - a*c^2 - (2*a^2 - b^2)*c)*cos(x))*cos(2*x) + (b^2*c - a*c^2)*cos(x) + (2*a*b*c*sin(2*x) + (b^2*c - a*c^2)*sin(3*x) + (b^2*c - a*c^2)*sin(x))*sin(4*x) + 2*((4*a*b^2 - a*c^2 - (2*a^2 - b^2)*c)*sin(2*x) + 2*(b^3 - a*b*c)*sin(x))*sin(3*x))/(c^4*cos(4*x)^2 + 4*b^2*c^2*cos(3*x)^2 + 4*b^2*c^2*cos(x)^2 + c^4*sin(4*x)^2 + 4*b^2*c^2*sin(3*x)^2 + 4*b^2*c^2*sin(x)^2 + 4*b*c^3*cos(x) + c^4 + 4*(4*a^2*c^2 + 4*a*c^3 + c^4)*cos(2*x)^2 + 4*(4*a^2*c^2 + 4*a*c^3 + c^4)*sin(2*x)^2 + 8*(2*a*b*c^2 + b*c^3)*sin(2*x)*sin(x) + 2*(2*b*c^3*cos(3*x) + 2*b*c^3*cos(x) + c^4 + 2*(2*a*c^3 + c^4)*cos(2*x))*cos(4*x) + 4*(2*b^2*c^2*cos(x) + b*c^3 + 2*(2*a*b*c^2 + b*c^3)*cos(2*x))*cos(3*x) + 4*(2*a*c^3 + c^4 + 2*(2*a*b*c^2 + b*c^3)*cos(x))*cos(2*x) + 4*(b*c^3*sin(3*x) + b*c^3*sin(x) + (2*a*c^3 + c^4)*sin(2*x))*sin(4*x) + 8*(b^2*c^2*sin(x) + (2*a*b*c^2 + b*c^3)*sin(2*x))*sin(3*x)), x) + b*x - c*sin(x))/c^2","F",0
15,0,0,0,0.000000," ","integrate(cos(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","-\frac{2 \, c \int \frac{2 \, b^{2} \cos\left(3 \, x\right)^{2} + 2 \, b^{2} \cos\left(x\right)^{2} + 2 \, b^{2} \sin\left(3 \, x\right)^{2} + 2 \, b^{2} \sin\left(x\right)^{2} + 4 \, {\left(2 \, a^{2} + a c\right)} \cos\left(2 \, x\right)^{2} + b c \cos\left(x\right) + 4 \, {\left(2 \, a^{2} + a c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a b + b c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + {\left(b c \cos\left(3 \, x\right) + 2 \, a c \cos\left(2 \, x\right) + b c \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(4 \, b^{2} \cos\left(x\right) + b c + 2 \, {\left(4 \, a b + b c\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(a c + {\left(4 \, a b + b c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b c \sin\left(3 \, x\right) + 2 \, a c \sin\left(2 \, x\right) + b c \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(2 \, b^{2} \sin\left(x\right) + {\left(4 \, a b + b c\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}{c^{3} \cos\left(4 \, x\right)^{2} + 4 \, b^{2} c \cos\left(3 \, x\right)^{2} + 4 \, b^{2} c \cos\left(x\right)^{2} + c^{3} \sin\left(4 \, x\right)^{2} + 4 \, b^{2} c \sin\left(3 \, x\right)^{2} + 4 \, b^{2} c \sin\left(x\right)^{2} + 4 \, b c^{2} \cos\left(x\right) + c^{3} + 4 \, {\left(4 \, a^{2} c + 4 \, a c^{2} + c^{3}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{2} c + 4 \, a c^{2} + c^{3}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a b c + b c^{2}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, b c^{2} \cos\left(3 \, x\right) + 2 \, b c^{2} \cos\left(x\right) + c^{3} + 2 \, {\left(2 \, a c^{2} + c^{3}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, b^{2} c \cos\left(x\right) + b c^{2} + 2 \, {\left(2 \, a b c + b c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a c^{2} + c^{3} + 2 \, {\left(2 \, a b c + b c^{2}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(b c^{2} \sin\left(3 \, x\right) + b c^{2} \sin\left(x\right) + {\left(2 \, a c^{2} + c^{3}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(b^{2} c \sin\left(x\right) + {\left(2 \, a b c + b c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} - x}{c}"," ",0,"-(c*integrate(2*(2*b^2*cos(3*x)^2 + 2*b^2*cos(x)^2 + 2*b^2*sin(3*x)^2 + 2*b^2*sin(x)^2 + 4*(2*a^2 + a*c)*cos(2*x)^2 + b*c*cos(x) + 4*(2*a^2 + a*c)*sin(2*x)^2 + 2*(4*a*b + b*c)*sin(2*x)*sin(x) + (b*c*cos(3*x) + 2*a*c*cos(2*x) + b*c*cos(x))*cos(4*x) + (4*b^2*cos(x) + b*c + 2*(4*a*b + b*c)*cos(2*x))*cos(3*x) + 2*(a*c + (4*a*b + b*c)*cos(x))*cos(2*x) + (b*c*sin(3*x) + 2*a*c*sin(2*x) + b*c*sin(x))*sin(4*x) + 2*(2*b^2*sin(x) + (4*a*b + b*c)*sin(2*x))*sin(3*x))/(c^3*cos(4*x)^2 + 4*b^2*c*cos(3*x)^2 + 4*b^2*c*cos(x)^2 + c^3*sin(4*x)^2 + 4*b^2*c*sin(3*x)^2 + 4*b^2*c*sin(x)^2 + 4*b*c^2*cos(x) + c^3 + 4*(4*a^2*c + 4*a*c^2 + c^3)*cos(2*x)^2 + 4*(4*a^2*c + 4*a*c^2 + c^3)*sin(2*x)^2 + 8*(2*a*b*c + b*c^2)*sin(2*x)*sin(x) + 2*(2*b*c^2*cos(3*x) + 2*b*c^2*cos(x) + c^3 + 2*(2*a*c^2 + c^3)*cos(2*x))*cos(4*x) + 4*(2*b^2*c*cos(x) + b*c^2 + 2*(2*a*b*c + b*c^2)*cos(2*x))*cos(3*x) + 4*(2*a*c^2 + c^3 + 2*(2*a*b*c + b*c^2)*cos(x))*cos(2*x) + 4*(b*c^2*sin(3*x) + b*c^2*sin(x) + (2*a*c^2 + c^3)*sin(2*x))*sin(4*x) + 8*(b^2*c*sin(x) + (2*a*b*c + b*c^2)*sin(2*x))*sin(3*x)), x) - x)/c","F",0
16,0,0,0,0.000000," ","integrate(cos(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right)}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\,{d x}"," ",0,"integrate(cos(x)/(c*cos(x)^2 + b*cos(x) + a), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\int \frac{1}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\,{d x}"," ",0,"integrate(1/(c*cos(x)^2 + b*cos(x) + a), x)","F",0
18,0,0,0,0.000000," ","integrate(sec(x)/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","-\frac{4 \, a \int \frac{2 \, b c \cos\left(3 \, x\right)^{2} + 2 \, b c \cos\left(x\right)^{2} + 2 \, b c \sin\left(3 \, x\right)^{2} + 2 \, b c \sin\left(x\right)^{2} + 4 \, {\left(2 \, a b + b c\right)} \cos\left(2 \, x\right)^{2} + c^{2} \cos\left(x\right) + 4 \, {\left(2 \, a b + b c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(2 \, b^{2} + 2 \, a c + c^{2}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + {\left(c^{2} \cos\left(3 \, x\right) + 2 \, b c \cos\left(2 \, x\right) + c^{2} \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(4 \, b c \cos\left(x\right) + c^{2} + 2 \, {\left(2 \, b^{2} + 2 \, a c + c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(b c + {\left(2 \, b^{2} + 2 \, a c + c^{2}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(c^{2} \sin\left(3 \, x\right) + 2 \, b c \sin\left(2 \, x\right) + c^{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(2 \, b c \sin\left(x\right) + {\left(2 \, b^{2} + 2 \, a c + c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}{a c^{2} \cos\left(4 \, x\right)^{2} + 4 \, a b^{2} \cos\left(3 \, x\right)^{2} + 4 \, a b^{2} \cos\left(x\right)^{2} + a c^{2} \sin\left(4 \, x\right)^{2} + 4 \, a b^{2} \sin\left(3 \, x\right)^{2} + 4 \, a b^{2} \sin\left(x\right)^{2} + 4 \, a b c \cos\left(x\right) + a c^{2} + 4 \, {\left(4 \, a^{3} + 4 \, a^{2} c + a c^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{3} + 4 \, a^{2} c + a c^{2}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a^{2} b + a b c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, a b c \cos\left(3 \, x\right) + 2 \, a b c \cos\left(x\right) + a c^{2} + 2 \, {\left(2 \, a^{2} c + a c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, a b^{2} \cos\left(x\right) + a b c + 2 \, {\left(2 \, a^{2} b + a b c\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a^{2} c + a c^{2} + 2 \, {\left(2 \, a^{2} b + a b c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(a b c \sin\left(3 \, x\right) + a b c \sin\left(x\right) + {\left(2 \, a^{2} c + a c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(a b^{2} \sin\left(x\right) + {\left(2 \, a^{2} b + a b c\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} - \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)}{2 \, a}"," ",0,"-1/2*(2*a*integrate(2*(2*b*c*cos(3*x)^2 + 2*b*c*cos(x)^2 + 2*b*c*sin(3*x)^2 + 2*b*c*sin(x)^2 + 4*(2*a*b + b*c)*cos(2*x)^2 + c^2*cos(x) + 4*(2*a*b + b*c)*sin(2*x)^2 + 2*(2*b^2 + 2*a*c + c^2)*sin(2*x)*sin(x) + (c^2*cos(3*x) + 2*b*c*cos(2*x) + c^2*cos(x))*cos(4*x) + (4*b*c*cos(x) + c^2 + 2*(2*b^2 + 2*a*c + c^2)*cos(2*x))*cos(3*x) + 2*(b*c + (2*b^2 + 2*a*c + c^2)*cos(x))*cos(2*x) + (c^2*sin(3*x) + 2*b*c*sin(2*x) + c^2*sin(x))*sin(4*x) + 2*(2*b*c*sin(x) + (2*b^2 + 2*a*c + c^2)*sin(2*x))*sin(3*x))/(a*c^2*cos(4*x)^2 + 4*a*b^2*cos(3*x)^2 + 4*a*b^2*cos(x)^2 + a*c^2*sin(4*x)^2 + 4*a*b^2*sin(3*x)^2 + 4*a*b^2*sin(x)^2 + 4*a*b*c*cos(x) + a*c^2 + 4*(4*a^3 + 4*a^2*c + a*c^2)*cos(2*x)^2 + 4*(4*a^3 + 4*a^2*c + a*c^2)*sin(2*x)^2 + 8*(2*a^2*b + a*b*c)*sin(2*x)*sin(x) + 2*(2*a*b*c*cos(3*x) + 2*a*b*c*cos(x) + a*c^2 + 2*(2*a^2*c + a*c^2)*cos(2*x))*cos(4*x) + 4*(2*a*b^2*cos(x) + a*b*c + 2*(2*a^2*b + a*b*c)*cos(2*x))*cos(3*x) + 4*(2*a^2*c + a*c^2 + 2*(2*a^2*b + a*b*c)*cos(x))*cos(2*x) + 4*(a*b*c*sin(3*x) + a*b*c*sin(x) + (2*a^2*c + a*c^2)*sin(2*x))*sin(4*x) + 8*(a*b^2*sin(x) + (2*a^2*b + a*b*c)*sin(2*x))*sin(3*x)), x) - log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1))/a","F",0
19,0,0,0,0.000000," ","integrate(sec(x)^2/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(2 \, x\right)^{2} + 2 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \int \frac{2 \, b^{2} c \cos\left(3 \, x\right)^{2} + 2 \, b^{2} c \cos\left(x\right)^{2} + 2 \, b^{2} c \sin\left(3 \, x\right)^{2} + 2 \, b^{2} c \sin\left(x\right)^{2} + b c^{2} \cos\left(x\right) + 4 \, {\left(2 \, a b^{2} - a c^{2} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, a b^{2} - a c^{2} - {\left(2 \, a^{2} - b^{2}\right)} c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(2 \, b^{3} + b c^{2}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + {\left(b c^{2} \cos\left(3 \, x\right) + b c^{2} \cos\left(x\right) + 2 \, {\left(b^{2} c - a c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + {\left(4 \, b^{2} c \cos\left(x\right) + b c^{2} + 2 \, {\left(2 \, b^{3} + b c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(b^{2} c - a c^{2} + {\left(2 \, b^{3} + b c^{2}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b c^{2} \sin\left(3 \, x\right) + b c^{2} \sin\left(x\right) + 2 \, {\left(b^{2} c - a c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(2 \, b^{2} c \sin\left(x\right) + {\left(2 \, b^{3} + b c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}{a^{2} c^{2} \cos\left(4 \, x\right)^{2} + 4 \, a^{2} b^{2} \cos\left(3 \, x\right)^{2} + 4 \, a^{2} b^{2} \cos\left(x\right)^{2} + a^{2} c^{2} \sin\left(4 \, x\right)^{2} + 4 \, a^{2} b^{2} \sin\left(3 \, x\right)^{2} + 4 \, a^{2} b^{2} \sin\left(x\right)^{2} + 4 \, a^{2} b c \cos\left(x\right) + a^{2} c^{2} + 4 \, {\left(4 \, a^{4} + 4 \, a^{3} c + a^{2} c^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{4} + 4 \, a^{3} c + a^{2} c^{2}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a^{3} b + a^{2} b c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, a^{2} b c \cos\left(3 \, x\right) + 2 \, a^{2} b c \cos\left(x\right) + a^{2} c^{2} + 2 \, {\left(2 \, a^{3} c + a^{2} c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, a^{2} b^{2} \cos\left(x\right) + a^{2} b c + 2 \, {\left(2 \, a^{3} b + a^{2} b c\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a^{3} c + a^{2} c^{2} + 2 \, {\left(2 \, a^{3} b + a^{2} b c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(a^{2} b c \sin\left(3 \, x\right) + a^{2} b c \sin\left(x\right) + {\left(2 \, a^{3} c + a^{2} c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(a^{2} b^{2} \sin\left(x\right) + {\left(2 \, a^{3} b + a^{2} b c\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} - {\left(b \cos\left(2 \, x\right)^{2} + b \sin\left(2 \, x\right)^{2} + 2 \, b \cos\left(2 \, x\right) + b\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left(b \cos\left(2 \, x\right)^{2} + b \sin\left(2 \, x\right)^{2} + 2 \, b \cos\left(2 \, x\right) + b\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, a \sin\left(2 \, x\right)}{2 \, {\left(a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(2 \, x\right)^{2} + 2 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)}}"," ",0,"1/2*(2*(a^2*cos(2*x)^2 + a^2*sin(2*x)^2 + 2*a^2*cos(2*x) + a^2)*integrate(2*(2*b^2*c*cos(3*x)^2 + 2*b^2*c*cos(x)^2 + 2*b^2*c*sin(3*x)^2 + 2*b^2*c*sin(x)^2 + b*c^2*cos(x) + 4*(2*a*b^2 - a*c^2 - (2*a^2 - b^2)*c)*cos(2*x)^2 + 4*(2*a*b^2 - a*c^2 - (2*a^2 - b^2)*c)*sin(2*x)^2 + 2*(2*b^3 + b*c^2)*sin(2*x)*sin(x) + (b*c^2*cos(3*x) + b*c^2*cos(x) + 2*(b^2*c - a*c^2)*cos(2*x))*cos(4*x) + (4*b^2*c*cos(x) + b*c^2 + 2*(2*b^3 + b*c^2)*cos(2*x))*cos(3*x) + 2*(b^2*c - a*c^2 + (2*b^3 + b*c^2)*cos(x))*cos(2*x) + (b*c^2*sin(3*x) + b*c^2*sin(x) + 2*(b^2*c - a*c^2)*sin(2*x))*sin(4*x) + 2*(2*b^2*c*sin(x) + (2*b^3 + b*c^2)*sin(2*x))*sin(3*x))/(a^2*c^2*cos(4*x)^2 + 4*a^2*b^2*cos(3*x)^2 + 4*a^2*b^2*cos(x)^2 + a^2*c^2*sin(4*x)^2 + 4*a^2*b^2*sin(3*x)^2 + 4*a^2*b^2*sin(x)^2 + 4*a^2*b*c*cos(x) + a^2*c^2 + 4*(4*a^4 + 4*a^3*c + a^2*c^2)*cos(2*x)^2 + 4*(4*a^4 + 4*a^3*c + a^2*c^2)*sin(2*x)^2 + 8*(2*a^3*b + a^2*b*c)*sin(2*x)*sin(x) + 2*(2*a^2*b*c*cos(3*x) + 2*a^2*b*c*cos(x) + a^2*c^2 + 2*(2*a^3*c + a^2*c^2)*cos(2*x))*cos(4*x) + 4*(2*a^2*b^2*cos(x) + a^2*b*c + 2*(2*a^3*b + a^2*b*c)*cos(2*x))*cos(3*x) + 4*(2*a^3*c + a^2*c^2 + 2*(2*a^3*b + a^2*b*c)*cos(x))*cos(2*x) + 4*(a^2*b*c*sin(3*x) + a^2*b*c*sin(x) + (2*a^3*c + a^2*c^2)*sin(2*x))*sin(4*x) + 8*(a^2*b^2*sin(x) + (2*a^3*b + a^2*b*c)*sin(2*x))*sin(3*x)), x) - (b*cos(2*x)^2 + b*sin(2*x)^2 + 2*b*cos(2*x) + b)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + (b*cos(2*x)^2 + b*sin(2*x)^2 + 2*b*cos(2*x) + b)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*a*sin(2*x))/(a^2*cos(2*x)^2 + a^2*sin(2*x)^2 + 2*a^2*cos(2*x) + a^2)","F",0
20,0,0,0,0.000000," ","integrate(sec(x)^3/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","-\frac{8 \, a^{2} \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 8 \, a^{2} \cos\left(2 \, x\right) \sin\left(x\right) + 4 \, a^{2} \sin\left(x\right) - 4 \, {\left(a^{2} \sin\left(3 \, x\right) + 2 \, a b \sin\left(2 \, x\right) - a^{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 8 \, {\left(a^{3} \cos\left(4 \, x\right)^{2} + 4 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(4 \, x\right)^{2} + 4 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a^{3} \sin\left(2 \, x\right)^{2} + 4 \, a^{3} \cos\left(2 \, x\right) + a^{3} + 2 \, {\left(2 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(4 \, x\right)\right)} \int \frac{2 \, {\left(b^{3} c - a b c^{2}\right)} \cos\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a b^{3} - 2 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(2 \, x\right)^{2} + 2 \, {\left(b^{3} c - a b c^{2}\right)} \cos\left(x\right)^{2} + 2 \, {\left(b^{3} c - a b c^{2}\right)} \sin\left(3 \, x\right)^{2} + 4 \, {\left(2 \, a b^{3} - 2 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(2 \, b^{4} - 2 \, a b^{2} c - a c^{3} - {\left(2 \, a^{2} - b^{2}\right)} c^{2}\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(b^{3} c - a b c^{2}\right)} \sin\left(x\right)^{2} + {\left({\left(b^{2} c^{2} - a c^{3}\right)} \cos\left(3 \, x\right) + 2 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} \cos\left(2 \, x\right) + {\left(b^{2} c^{2} - a c^{3}\right)} \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(b^{2} c^{2} - a c^{3} + 2 \, {\left(2 \, b^{4} - 2 \, a b^{2} c - a c^{3} - {\left(2 \, a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(2 \, x\right) + 4 \, {\left(b^{3} c - a b c^{2}\right)} \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(b^{3} c - 2 \, a b c^{2} + {\left(2 \, b^{4} - 2 \, a b^{2} c - a c^{3} - {\left(2 \, a^{2} - b^{2}\right)} c^{2}\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(b^{2} c^{2} - a c^{3}\right)} \cos\left(x\right) + {\left({\left(b^{2} c^{2} - a c^{3}\right)} \sin\left(3 \, x\right) + 2 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} \sin\left(2 \, x\right) + {\left(b^{2} c^{2} - a c^{3}\right)} \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left({\left(2 \, b^{4} - 2 \, a b^{2} c - a c^{3} - {\left(2 \, a^{2} - b^{2}\right)} c^{2}\right)} \sin\left(2 \, x\right) + 2 \, {\left(b^{3} c - a b c^{2}\right)} \sin\left(x\right)\right)} \sin\left(3 \, x\right)}{a^{3} c^{2} \cos\left(4 \, x\right)^{2} + 4 \, a^{3} b^{2} \cos\left(3 \, x\right)^{2} + 4 \, a^{3} b^{2} \cos\left(x\right)^{2} + a^{3} c^{2} \sin\left(4 \, x\right)^{2} + 4 \, a^{3} b^{2} \sin\left(3 \, x\right)^{2} + 4 \, a^{3} b^{2} \sin\left(x\right)^{2} + 4 \, a^{3} b c \cos\left(x\right) + a^{3} c^{2} + 4 \, {\left(4 \, a^{5} + 4 \, a^{4} c + a^{3} c^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, {\left(4 \, a^{5} + 4 \, a^{4} c + a^{3} c^{2}\right)} \sin\left(2 \, x\right)^{2} + 8 \, {\left(2 \, a^{4} b + a^{3} b c\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(2 \, a^{3} b c \cos\left(3 \, x\right) + 2 \, a^{3} b c \cos\left(x\right) + a^{3} c^{2} + 2 \, {\left(2 \, a^{4} c + a^{3} c^{2}\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(2 \, a^{3} b^{2} \cos\left(x\right) + a^{3} b c + 2 \, {\left(2 \, a^{4} b + a^{3} b c\right)} \cos\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, a^{4} c + a^{3} c^{2} + 2 \, {\left(2 \, a^{4} b + a^{3} b c\right)} \cos\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, {\left(a^{3} b c \sin\left(3 \, x\right) + a^{3} b c \sin\left(x\right) + {\left(2 \, a^{4} c + a^{3} c^{2}\right)} \sin\left(2 \, x\right)\right)} \sin\left(4 \, x\right) + 8 \, {\left(a^{3} b^{2} \sin\left(x\right) + {\left(2 \, a^{4} b + a^{3} b c\right)} \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right)}\,{d x} - {\left({\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(4 \, x\right)^{2} + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(2 \, x\right)^{2} + {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \sin\left(4 \, x\right)^{2} + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \sin\left(2 \, x\right)^{2} + a^{2} + 2 \, b^{2} - 2 \, a c + 2 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c + 2 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left({\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(4 \, x\right)^{2} + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(2 \, x\right)^{2} + {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \sin\left(4 \, x\right)^{2} + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \sin\left(2 \, x\right)^{2} + a^{2} + 2 \, b^{2} - 2 \, a c + 2 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c + 2 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 4 \, {\left(a^{2} + 2 \, b^{2} - 2 \, a c\right)} \cos\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, {\left(a^{2} \cos\left(3 \, x\right) + 2 \, a b \cos\left(2 \, x\right) - a^{2} \cos\left(x\right) + 2 \, a b\right)} \sin\left(4 \, x\right) - 4 \, {\left(2 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \sin\left(3 \, x\right) - 8 \, {\left(a^{2} \cos\left(x\right) - a b\right)} \sin\left(2 \, x\right)}{4 \, {\left(a^{3} \cos\left(4 \, x\right)^{2} + 4 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(4 \, x\right)^{2} + 4 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a^{3} \sin\left(2 \, x\right)^{2} + 4 \, a^{3} \cos\left(2 \, x\right) + a^{3} + 2 \, {\left(2 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(4 \, x\right)\right)}}"," ",0,"-1/4*(8*a^2*cos(3*x)*sin(2*x) + 8*a^2*cos(2*x)*sin(x) + 4*a^2*sin(x) - 4*(a^2*sin(3*x) + 2*a*b*sin(2*x) - a^2*sin(x))*cos(4*x) - 4*(a^3*cos(4*x)^2 + 4*a^3*cos(2*x)^2 + a^3*sin(4*x)^2 + 4*a^3*sin(4*x)*sin(2*x) + 4*a^3*sin(2*x)^2 + 4*a^3*cos(2*x) + a^3 + 2*(2*a^3*cos(2*x) + a^3)*cos(4*x))*integrate(-2*(2*(b^3*c - a*b*c^2)*cos(3*x)^2 + 4*(2*a*b^3 - 2*a*b*c^2 - (4*a^2*b - b^3)*c)*cos(2*x)^2 + 2*(b^3*c - a*b*c^2)*cos(x)^2 + 2*(b^3*c - a*b*c^2)*sin(3*x)^2 + 4*(2*a*b^3 - 2*a*b*c^2 - (4*a^2*b - b^3)*c)*sin(2*x)^2 + 2*(2*b^4 - 2*a*b^2*c - a*c^3 - (2*a^2 - b^2)*c^2)*sin(2*x)*sin(x) + 2*(b^3*c - a*b*c^2)*sin(x)^2 + ((b^2*c^2 - a*c^3)*cos(3*x) + 2*(b^3*c - 2*a*b*c^2)*cos(2*x) + (b^2*c^2 - a*c^3)*cos(x))*cos(4*x) + (b^2*c^2 - a*c^3 + 2*(2*b^4 - 2*a*b^2*c - a*c^3 - (2*a^2 - b^2)*c^2)*cos(2*x) + 4*(b^3*c - a*b*c^2)*cos(x))*cos(3*x) + 2*(b^3*c - 2*a*b*c^2 + (2*b^4 - 2*a*b^2*c - a*c^3 - (2*a^2 - b^2)*c^2)*cos(x))*cos(2*x) + (b^2*c^2 - a*c^3)*cos(x) + ((b^2*c^2 - a*c^3)*sin(3*x) + 2*(b^3*c - 2*a*b*c^2)*sin(2*x) + (b^2*c^2 - a*c^3)*sin(x))*sin(4*x) + 2*((2*b^4 - 2*a*b^2*c - a*c^3 - (2*a^2 - b^2)*c^2)*sin(2*x) + 2*(b^3*c - a*b*c^2)*sin(x))*sin(3*x))/(a^3*c^2*cos(4*x)^2 + 4*a^3*b^2*cos(3*x)^2 + 4*a^3*b^2*cos(x)^2 + a^3*c^2*sin(4*x)^2 + 4*a^3*b^2*sin(3*x)^2 + 4*a^3*b^2*sin(x)^2 + 4*a^3*b*c*cos(x) + a^3*c^2 + 4*(4*a^5 + 4*a^4*c + a^3*c^2)*cos(2*x)^2 + 4*(4*a^5 + 4*a^4*c + a^3*c^2)*sin(2*x)^2 + 8*(2*a^4*b + a^3*b*c)*sin(2*x)*sin(x) + 2*(2*a^3*b*c*cos(3*x) + 2*a^3*b*c*cos(x) + a^3*c^2 + 2*(2*a^4*c + a^3*c^2)*cos(2*x))*cos(4*x) + 4*(2*a^3*b^2*cos(x) + a^3*b*c + 2*(2*a^4*b + a^3*b*c)*cos(2*x))*cos(3*x) + 4*(2*a^4*c + a^3*c^2 + 2*(2*a^4*b + a^3*b*c)*cos(x))*cos(2*x) + 4*(a^3*b*c*sin(3*x) + a^3*b*c*sin(x) + (2*a^4*c + a^3*c^2)*sin(2*x))*sin(4*x) + 8*(a^3*b^2*sin(x) + (2*a^4*b + a^3*b*c)*sin(2*x))*sin(3*x)), x) - ((a^2 + 2*b^2 - 2*a*c)*cos(4*x)^2 + 4*(a^2 + 2*b^2 - 2*a*c)*cos(2*x)^2 + (a^2 + 2*b^2 - 2*a*c)*sin(4*x)^2 + 4*(a^2 + 2*b^2 - 2*a*c)*sin(4*x)*sin(2*x) + 4*(a^2 + 2*b^2 - 2*a*c)*sin(2*x)^2 + a^2 + 2*b^2 - 2*a*c + 2*(a^2 + 2*b^2 - 2*a*c + 2*(a^2 + 2*b^2 - 2*a*c)*cos(2*x))*cos(4*x) + 4*(a^2 + 2*b^2 - 2*a*c)*cos(2*x))*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + ((a^2 + 2*b^2 - 2*a*c)*cos(4*x)^2 + 4*(a^2 + 2*b^2 - 2*a*c)*cos(2*x)^2 + (a^2 + 2*b^2 - 2*a*c)*sin(4*x)^2 + 4*(a^2 + 2*b^2 - 2*a*c)*sin(4*x)*sin(2*x) + 4*(a^2 + 2*b^2 - 2*a*c)*sin(2*x)^2 + a^2 + 2*b^2 - 2*a*c + 2*(a^2 + 2*b^2 - 2*a*c + 2*(a^2 + 2*b^2 - 2*a*c)*cos(2*x))*cos(4*x) + 4*(a^2 + 2*b^2 - 2*a*c)*cos(2*x))*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*(a^2*cos(3*x) + 2*a*b*cos(2*x) - a^2*cos(x) + 2*a*b)*sin(4*x) - 4*(2*a^2*cos(2*x) + a^2)*sin(3*x) - 8*(a^2*cos(x) - a*b)*sin(2*x))/(a^3*cos(4*x)^2 + 4*a^3*cos(2*x)^2 + a^3*sin(4*x)^2 + 4*a^3*sin(4*x)*sin(2*x) + 4*a^3*sin(2*x)^2 + 4*a^3*cos(2*x) + a^3 + 2*(2*a^3*cos(2*x) + a^3)*cos(4*x))","F",0
