1,1,344,126,0.089000," ","int(sin(x)^5/(a+b*cos(x)+c*cos(x)^2),x)","-\frac{\cos^{3}\left(x \right)}{3 c}+\frac{b \left(\cos^{2}\left(x \right)\right)}{2 c^{2}}+\frac{\cos \left(x \right) a}{c^{2}}-\frac{\cos \left(x \right) b^{2}}{c^{3}}+\frac{2 \cos \left(x \right)}{c}-\frac{\ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right) a b}{c^{3}}+\frac{\ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right) b^{3}}{2 c^{4}}-\frac{b \ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right)}{c^{2}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a^{2}}{c^{2} \sqrt{4 c a -b^{2}}}+\frac{4 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2} a}{c^{3} \sqrt{4 c a -b^{2}}}-\frac{4 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a}{c \sqrt{4 c a -b^{2}}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right)}{\sqrt{4 c a -b^{2}}}-\frac{\arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{4}}{c^{4} \sqrt{4 c a -b^{2}}}+\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2}}{c^{2} \sqrt{4 c a -b^{2}}}"," ",0,"-1/3*cos(x)^3/c+1/2*b*cos(x)^2/c^2+1/c^2*cos(x)*a-1/c^3*cos(x)*b^2+2*cos(x)/c-1/c^3*ln(a+b*cos(x)+c*cos(x)^2)*a*b+1/2/c^4*ln(a+b*cos(x)+c*cos(x)^2)*b^3-b*ln(a+b*cos(x)+c*cos(x)^2)/c^2-2/c^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*a^2+4/c^3/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^2*a-4/c/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*a-2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))-1/c^4/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^4+2/c^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^2","B"
2,1,141,70,0.078000," ","int(sin(x)^3/(a+b*cos(x)+c*cos(x)^2),x)","\frac{\cos \left(x \right)}{c}-\frac{b \ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right)}{2 c^{2}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a}{c \sqrt{4 c a -b^{2}}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right)}{\sqrt{4 c a -b^{2}}}+\frac{\arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2}}{c^{2} \sqrt{4 c a -b^{2}}}"," ",0,"cos(x)/c-1/2*b*ln(a+b*cos(x)+c*cos(x)^2)/c^2-2/c/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*a-2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))+1/c^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^2","A"
3,1,36,31,0.063000," ","int(sin(x)/(a+b*cos(x)+c*cos(x)^2),x)","-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right)}{\sqrt{4 c a -b^{2}}}"," ",0,"-2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))","A"
4,1,223,119,0.115000," ","int(csc(x)/(a+b*cos(x)+c*cos(x)^2),x)","\frac{b \ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right)}{2 \left(a -b +c \right) \left(a +b +c \right)}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) c a}{\left(a -b +c \right) \left(a +b +c \right) \sqrt{4 c a -b^{2}}}+\frac{\arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2}}{\left(a -b +c \right) \left(a +b +c \right) \sqrt{4 c a -b^{2}}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \sqrt{4 c a -b^{2}}}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{2 a +2 b +2 c}-\frac{\ln \left(\cos \left(x \right)+1\right)}{2 a -2 b +2 c}"," ",0,"1/2*b*ln(a+b*cos(x)+c*cos(x)^2)/(a-b+c)/(a+b+c)-2/(a-b+c)/(a+b+c)/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*c*a+1/(a-b+c)/(a+b+c)/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^2-2/(a-b+c)/(a+b+c)/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*c^2+1/(2*a+2*b+2*c)*ln(-1+cos(x))-1/(2*a-2*b+2*c)*ln(cos(x)+1)","A"
5,1,546,193,0.139000," ","int(csc(x)^3/(a+b*cos(x)+c*cos(x)^2),x)","\frac{c \ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right) a b}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2}}-\frac{\ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right) b^{3}}{2 \left(a -b +c \right)^{2} \left(a +b +c \right)^{2}}+\frac{c^{2} \ln \left(a +b \cos \left(x \right)+c \left(\cos^{2}\left(x \right)\right)\right) b}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a^{2} c^{2}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}+\frac{4 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a \,b^{2} c}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}-\frac{4 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a \,c^{3}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}-\frac{\arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{4}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}+\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2} c^{2}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}-\frac{2 \arctan \left(\frac{b +2 c \cos \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) c^{4}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}+\frac{1}{\left(4 a +4 b +4 c \right) \left(-1+\cos \left(x \right)\right)}+\frac{\ln \left(-1+\cos \left(x \right)\right) a}{4 \left(a +b +c \right)^{2}}+\frac{\ln \left(-1+\cos \left(x \right)\right) b}{2 \left(a +b +c \right)^{2}}+\frac{3 \ln \left(-1+\cos \left(x \right)\right) c}{4 \left(a +b +c \right)^{2}}+\frac{1}{\left(4 a -4 b +4 c \right) \left(\cos \left(x \right)+1\right)}-\frac{\ln \left(\cos \left(x \right)+1\right) a}{4 \left(a -b +c \right)^{2}}+\frac{\ln \left(\cos \left(x \right)+1\right) b}{2 \left(a -b +c \right)^{2}}-\frac{3 \ln \left(\cos \left(x \right)+1\right) c}{4 \left(a -b +c \right)^{2}}"," ",0,"1/(a-b+c)^2/(a+b+c)^2*c*ln(a+b*cos(x)+c*cos(x)^2)*a*b-1/2/(a-b+c)^2/(a+b+c)^2*ln(a+b*cos(x)+c*cos(x)^2)*b^3+1/(a-b+c)^2/(a+b+c)^2*c^2*ln(a+b*cos(x)+c*cos(x)^2)*b-2/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*a^2*c^2+4/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*a*b^2*c-4/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*a*c^3-1/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^4+2/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*b^2*c^2-2/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*cos(x))/(4*a*c-b^2)^(1/2))*c^4+1/(4*a+4*b+4*c)/(-1+cos(x))+1/4/(a+b+c)^2*ln(-1+cos(x))*a+1/2/(a+b+c)^2*ln(-1+cos(x))*b+3/4/(a+b+c)^2*ln(-1+cos(x))*c+1/(4*a-4*b+4*c)/(cos(x)+1)-1/4/(a-b+c)^2*ln(cos(x)+1)*a+1/2/(a-b+c)^2*ln(cos(x)+1)*b-3/4/(a-b+c)^2*ln(cos(x)+1)*c","B"
6,1,2608,324,0.152000," ","int(sin(x)^4/(a+b*cos(x)+c*cos(x)^2),x)","\text{Expression too large to display}"," ",0,"1/c^3*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3-2/c^2*a/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b+2/c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2+1/c^3/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/c^2/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2+2/c*a/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+1/c^2/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+2/c*a/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))-2/c*b/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-2/c*b/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+b/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+4*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-b/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-4*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))-2/c^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3*b-2/c^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)*b+2*c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-2*c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+1/c^3/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-1/c^3*a/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2+1/c^3/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4-1/c^3/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4-3/c^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b+4/c^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2-4/c^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-2/c*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b+3/c^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b+2/c*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-1/c^3*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-3/c*arctan(tan(1/2*x))+1/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+1/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+2/c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2-2/c^2*a/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b-2/c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2-1/c/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+1/c/(tan(1/2*x)^2+1)^2*tan(1/2*x)-2/c^2*arctan(tan(1/2*x))*a+2/c^3*arctan(tan(1/2*x))*b^2-2/c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-1/c^3*a/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2","B"
7,1,1157,221,0.108000," ","int(sin(x)^2/(a+b*cos(x)+c*cos(x)^2),x)","\frac{a \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{c \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{c \sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 a \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{a \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{c \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{a \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{c \sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 a \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{c \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{c \sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{b \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{c \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{c \sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{b \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\sqrt{-4 c a +b^{2}}\, \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{c}"," ",0,"1/c*a/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+1/c*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b+2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+1/c*a/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))-1/c*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b-2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))-1/c*b/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-1/c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-b/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-1/c*b/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+1/c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+b/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+1/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+2*c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+1/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))-2*c/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))-2/c*arctan(tan(1/2*x))","B"
8,1,2816,283,0.150000," ","int(csc(x)^2/(a+b*cos(x)+c*cos(x)^2),x)","\text{output too large to display}"," ",0,"6/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b-2/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2-6/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b+3/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b*c+2/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2-3/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b*c-1/2/(a+b+c)/tan(1/2*x)-3/(a+b+c)/(a-b+c)^2*b/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^3-2/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^3-4/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^3+3/(a+b+c)/(a-b+c)^2*b/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^3+1/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3+4/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^3-2/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*c^2+2/(a+b+c)/(a-b+c)^2*a/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2-2/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2+1/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^3+1/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^3-1/(a+b+c)/(a-b+c)^2*a/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+2/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*c^2+2/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^3+1/2/(a-b+c)*tan(1/2*x)+1/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3+1/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4+2/(a+b+c)/(a-b+c)^2*a/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2-1/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4-2/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2+2/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^4-2/(a+b+c)/(a-b+c)^2/(-4*a*c+b^2)^(1/2)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^4+1/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*a^2-1/(a+b+c)/(a-b+c)^2*a/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-1/(a+b+c)/(a-b+c)^2*a/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+1/(a+b+c)/(a-b+c)^2/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*a^2","B"
9,1,16,17,0.082000," ","int(sin(x)/(-2+cos(x)+cos(x)^2),x)","\frac{\ln \left(2+\cos \left(x \right)\right)}{3}-\frac{\ln \left(-1+\cos \left(x \right)\right)}{3}"," ",0,"1/3*ln(2+cos(x))-1/3*ln(-1+cos(x))","A"
10,1,16,19,0.083000," ","int(sin(x)/(4-5*cos(x)+cos(x)^2),x)","-\frac{\ln \left(\cos \left(x \right)-4\right)}{3}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{3}"," ",0,"-1/3*ln(cos(x)-4)+1/3*ln(-1+cos(x))","A"
11,1,18,17,0.070000," ","int(sin(x)/(3-2*cos(x)+cos(x)^2),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-2+2 \cos \left(x \right)\right) \sqrt{2}}{4}\right)}{2}"," ",0,"-1/2*2^(1/2)*arctan(1/4*(-2+2*cos(x))*2^(1/2))","A"
12,1,31,30,0.078000," ","int(sin(x)/(13-4*cos(x)+cos(x)^2)^2,x)","-\frac{2 \cos \left(x \right)-4}{36 \left(13-4 \cos \left(x \right)+\cos^{2}\left(x \right)\right)}-\frac{\arctan \left(-\frac{2}{3}+\frac{\cos \left(x \right)}{3}\right)}{54}"," ",0,"-1/36*(2*cos(x)-4)/(13-4*cos(x)+cos(x)^2)-1/54*arctan(-2/3+1/3*cos(x))","A"
13,1,3427,283,0.122000," ","int(cos(x)^4/(a+b*cos(x)+c*cos(x)^2),x)","\text{output too large to display}"," ",0,"-2/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b+1/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4-1/c^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2*a^2-2/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b+1/c^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^5-1/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4-1/c^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^5+1/2*x/c+1/c*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2+3/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^3-1/c*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2-3/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^3-3/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b-2/c^3*a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4-2/c^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3*b-2/c^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)*b+3/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^3*b-7/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b^2+2/c^3*a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4+2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^3-3/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b-2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^3+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^2+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^2+2/c^3*a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3+1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^3-1/c^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^3+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2-1/c^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4+4/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^2+1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+1/c^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b^3-4/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^2+7/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b^2-3/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^3*b-1/c^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b^3+2/c^3*a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3-1/c^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2*a^2-1/c/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+1/c/(tan(1/2*x)^2+1)^2*tan(1/2*x)-2/c^2*arctan(tan(1/2*x))*a+2/c^3*arctan(tan(1/2*x))*b^2","B"
14,1,2503,255,0.112000," ","int(cos(x)^3/(a+b*cos(x)+c*cos(x)^2),x)","\text{Expression too large to display}"," ",0,"1/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4-1/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4+5/c*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2-2/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^3-5/c*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+2/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^3+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b+1/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2*b^2+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a-2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^3+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b+2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^3-2/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^2-2/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^2-1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3+1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2+1/c^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2-1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2+2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^2+1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2-2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^2-1/c^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2*b^2+2/c*tan(1/2*x)/(tan(1/2*x)^2+1)-2/c^2*b*arctan(tan(1/2*x))+3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b-3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b-1/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3","B"
15,1,1948,216,0.105000," ","int(cos(x)^2/(a+b*cos(x)+c*cos(x)^2),x)","\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a b}{c \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a b}{c \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{b \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a^{2}}{c \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{3}}{c \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{c \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a^{2}}{c \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{c \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a \,b^{2}}{c \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a^{2}}{c \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{3}}{c \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a^{2}}{c \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a \,b^{2}}{c \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{c}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}"," ",0,"2/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b+2/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b-1/c*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2+1/c*b/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2+1/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2-1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2-1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2-1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b^2-1/c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+2/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b^2+2/c*arctan(tan(1/2*x))+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b-1/c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*a+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*a","B"
16,1,1264,190,0.099000," ","int(cos(x)/(a+b*cos(x)+c*cos(x)^2),x)","\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{3 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{3 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}"," ",0,"2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a^2-3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a^2+3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*a-c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*a+c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b-c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))","B"
17,1,1262,183,0.096000," ","int(1/(a+b*cos(x)+c*cos(x)^2),x)","\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) a b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) a}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{3 c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{3 c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}"," ",0,"1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*a-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*a*b+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a*b-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*a+1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*a-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-3*c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+3*c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b+c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2+c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))","B"
18,1,1957,205,0.136000," ","int(sec(x)/(a+b*cos(x)+c*cos(x)^2),x)","\frac{c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right)}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right)}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c^{2}}{a \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c^{2} b}{a \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c \,b^{2}}{a \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{a}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c^{2} b}{a \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c \,b^{2}}{a \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{2}}{a \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{\arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b^{3}}{a \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{3}}{a \sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c^{2}}{a \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{\arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b^{2}}{a \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}-\frac{2 b \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c}{a \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{2 b \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) c}{a \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}+\frac{2 \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) c a}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}-\frac{c \arctan \left(\frac{\left(a -b +c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}\right) b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}+a -c \right) \left(a -b +c \right)}}+\frac{c \arctanh \left(\frac{\left(-a +b -c \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}\right) b}{\sqrt{-4 c a +b^{2}}\, \left(a -b +c \right) \sqrt{\left(\sqrt{-4 c a +b^{2}}-a +c \right) \left(a -b +c \right)}}"," ",0,"c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))+c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2-1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b+1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b+2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2-2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2+1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-1/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b-1/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2-1/a*ln(tan(1/2*x)-1)+1/a*ln(tan(1/2*x)+1)+1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2+1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2+1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3-2/a*b/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c+1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-2/a*b/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*a+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*a+c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b","B"
19,1,2530,236,0.154000," ","int(sec(x)^2/(a+b*cos(x)+c*cos(x)^2),x)","\text{Expression too large to display}"," ",0,"-c/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))-c/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))+2/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2-1/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4+1/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4+2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^3-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b-2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^3-1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2+b/a^2*ln(tan(1/2*x)-1)-b/a^2*ln(tan(1/2*x)+1)+5/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b-5/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b-2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2+2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2-2/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^3+2/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^3+1/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b^2-1/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b^2-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^2-1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2-1/a/(tan(1/2*x)-1)-1/a/(tan(1/2*x)+1)+1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3+1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^2-1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3+3*c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b-3*c/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b+2/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b","B"
20,1,3476,286,0.158000," ","int(sec(x)^3/(a+b*cos(x)+c*cos(x)^2),x)","\text{output too large to display}"," ",0,"1/a^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b^2-2/a^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^3+1/a^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^5+1/a^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b^2-2/a^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^3-1/a^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^5+1/a^2/(tan(1/2*x)-1)*b+1/a^2*ln(tan(1/2*x)-1)*c-1/a^3*ln(tan(1/2*x)-1)*b^2+1/a^2/(tan(1/2*x)+1)*b-1/a^2*ln(tan(1/2*x)+1)*c+1/a^3*ln(tan(1/2*x)+1)*b^2+1/2/a/(tan(1/2*x)-1)^2-1/2/a/(tan(1/2*x)+1)^2-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2-1/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4+1/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4-2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^3+3/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b+2/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^3-1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2+1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b-1/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b-4/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2+4/a/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^2-2/a^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^4+3/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b*c^3-3/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b*c^3+2/a^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^4+1/a^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b^3-1/a^3/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b^3+3/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^3-3/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c*b^3-7/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2*b^2+7/a^2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b^2-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^3+2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2-2/(-4*a*c+b^2)^(1/2)/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^3-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^3-1/2/a*ln(tan(1/2*x)-1)+1/2/a*ln(tan(1/2*x)+1)+1/a^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*b^4+1/a^3/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*b^4-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^3-1/a/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c^2+1/2/a/(tan(1/2*x)-1)+1/2/a/(tan(1/2*x)+1)+2/a*b/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c+2/a*b/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c-1/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2)*arctanh((-a+b-c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)-a+c)*(a-b+c))^(1/2))*c*b^2+3/a^2/(a-b+c)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2)*arctan((a-b+c)*tan(1/2*x)/(((-4*a*c+b^2)^(1/2)+a-c)*(a-b+c))^(1/2))*c^2*b","B"