1,1,102,49,0.485000," ","int(tan(x)^4/(a+a*csc(x)),x)","-\frac{1}{6 a \left(\tan \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{1}{4 a \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{5}{8 a \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{2}{5 a \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{1}{a \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{1}{a \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{11}{8 a \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-1/6/a/(tan(1/2*x)-1)^3-1/4/a/(tan(1/2*x)-1)^2+5/8/a/(tan(1/2*x)-1)+2/5/a/(tan(1/2*x)+1)^5-1/a/(tan(1/2*x)+1)^4+1/a/(tan(1/2*x)+1)^2+11/8/a/(tan(1/2*x)+1)+2/a*arctan(tan(1/2*x))","B"
2,1,55,58,0.451000," ","int(tan(x)^3/(a+a*csc(x)),x)","-\frac{1}{8 a \left(-1+\sin \left(x \right)\right)}+\frac{5 \ln \left(-1+\sin \left(x \right)\right)}{16 a}-\frac{1}{8 a \left(1+\sin \left(x \right)\right)^{2}}+\frac{3}{4 a \left(1+\sin \left(x \right)\right)}+\frac{11 \ln \left(1+\sin \left(x \right)\right)}{16 a}"," ",0,"-1/8/a/(-1+sin(x))+5/16/a*ln(-1+sin(x))-1/8/a/(1+sin(x))^2+3/4/a/(1+sin(x))+11/16*ln(1+sin(x))/a","A"
3,1,64,35,0.448000," ","int(tan(x)^2/(a+a*csc(x)),x)","-\frac{1}{2 a \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{2}{3 a \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{1}{a \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{3}{2 a \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-1/2/a/(tan(1/2*x)-1)+2/3/a/(tan(1/2*x)+1)^3-1/a/(tan(1/2*x)+1)^2-3/2/a/(tan(1/2*x)+1)-2/a*arctan(tan(1/2*x))","A"
4,1,33,34,0.411000," ","int(tan(x)/(a+a*csc(x)),x)","-\frac{\ln \left(-1+\sin \left(x \right)\right)}{4 a}-\frac{1}{2 a \left(1+\sin \left(x \right)\right)}-\frac{3 \ln \left(1+\sin \left(x \right)\right)}{4 a}"," ",0,"-1/4/a*ln(-1+sin(x))-1/2/a/(1+sin(x))-3/4*ln(1+sin(x))/a","A"
5,1,19,9,0.324000," ","int(cot(x)/(a+a*csc(x)),x)","-\frac{\ln \left(\csc \left(x \right)\right)}{a}+\frac{\ln \left(1+\csc \left(x \right)\right)}{a}"," ",0,"-1/a*ln(csc(x))+1/a*ln(1+csc(x))","A"
6,1,21,15,0.377000," ","int(cot(x)^2/(a+a*csc(x)),x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"1/a*ln(tan(1/2*x))-2/a*arctan(tan(1/2*x))","A"
7,1,16,16,0.313000," ","int(cot(x)^3/(a+a*csc(x)),x)","-\frac{\csc \left(x \right)}{a}+\frac{\ln \left(\csc \left(x \right)\right)}{a}"," ",0,"-csc(x)/a+1/a*ln(csc(x))","A"
8,1,64,27,0.398000," ","int(cot(x)^4/(a+a*csc(x)),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}-\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}+\frac{1}{2 a \tan \left(\frac{x}{2}\right)}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"1/8/a*tan(1/2*x)^2-1/2/a*tan(1/2*x)-1/8/a/tan(1/2*x)^2+1/2/a/tan(1/2*x)-1/2/a*ln(tan(1/2*x))+2/a*arctan(tan(1/2*x))","B"
9,1,35,32,0.385000," ","int(cot(x)^5/(a+a*csc(x)),x)","\frac{1}{2 a \sin \left(x \right)^{2}}-\frac{1}{3 a \sin \left(x \right)^{3}}+\frac{\ln \left(\sin \left(x \right)\right)}{a}+\frac{1}{a \sin \left(x \right)}"," ",0,"1/2/a/sin(x)^2-1/3/a/sin(x)^3+ln(sin(x))/a+1/a/sin(x)","A"
10,1,108,43,0.378000," ","int(cot(x)^6/(a+a*csc(x)),x)","\frac{\tan^{4}\left(\frac{x}{2}\right)}{64 a}-\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 a}-\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}+\frac{5 \tan \left(\frac{x}{2}\right)}{8 a}-\frac{1}{64 a \tan \left(\frac{x}{2}\right)^{4}}+\frac{1}{24 a \tan \left(\frac{x}{2}\right)^{3}}+\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}-\frac{5}{8 a \tan \left(\frac{x}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{8 a}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"1/64/a*tan(1/2*x)^4-1/24/a*tan(1/2*x)^3-1/8/a*tan(1/2*x)^2+5/8/a*tan(1/2*x)-1/64/a/tan(1/2*x)^4+1/24/a/tan(1/2*x)^3+1/8/a/tan(1/2*x)^2-5/8/a/tan(1/2*x)+3/8/a*ln(tan(1/2*x))-2/a*arctan(tan(1/2*x))","B"
11,1,55,52,0.379000," ","int(cot(x)^7/(a+a*csc(x)),x)","-\frac{1}{a \sin \left(x \right)^{2}}+\frac{2}{3 a \sin \left(x \right)^{3}}+\frac{1}{4 a \sin \left(x \right)^{4}}-\frac{\ln \left(\sin \left(x \right)\right)}{a}-\frac{1}{5 a \sin \left(x \right)^{5}}-\frac{1}{a \sin \left(x \right)}"," ",0,"-1/a/sin(x)^2+2/3/a/sin(x)^3+1/4/a/sin(x)^4-ln(sin(x))/a-1/5/a/sin(x)^5-1/a/sin(x)","A"
12,1,216,166,0.426000," ","int(tan(x)^5/(a+b*csc(x)),x)","\frac{b^{6} \ln \left(b +a \sin \left(x \right)\right)}{\left(a +b \right)^{3} \left(a -b \right)^{3} a}+\frac{1}{2 \left(8 a +8 b \right) \left(-1+\sin \left(x \right)\right)^{2}}+\frac{7 a}{16 \left(a +b \right)^{2} \left(-1+\sin \left(x \right)\right)}+\frac{9 b}{16 \left(a +b \right)^{2} \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right) a^{2}}{2 \left(a +b \right)^{3}}-\frac{21 \ln \left(-1+\sin \left(x \right)\right) a b}{16 \left(a +b \right)^{3}}-\frac{15 \ln \left(-1+\sin \left(x \right)\right) b^{2}}{16 \left(a +b \right)^{3}}+\frac{1}{2 \left(8 a -8 b \right) \left(1+\sin \left(x \right)\right)^{2}}-\frac{7 a}{16 \left(a -b \right)^{2} \left(1+\sin \left(x \right)\right)}+\frac{9 b}{16 \left(a -b \right)^{2} \left(1+\sin \left(x \right)\right)}-\frac{\ln \left(1+\sin \left(x \right)\right) a^{2}}{2 \left(a -b \right)^{3}}+\frac{21 \ln \left(1+\sin \left(x \right)\right) a b}{16 \left(a -b \right)^{3}}-\frac{15 \ln \left(1+\sin \left(x \right)\right) b^{2}}{16 \left(a -b \right)^{3}}"," ",0,"b^6/(a+b)^3/(a-b)^3/a*ln(b+a*sin(x))+1/2/(8*a+8*b)/(-1+sin(x))^2+7/16/(a+b)^2/(-1+sin(x))*a+9/16/(a+b)^2/(-1+sin(x))*b-1/2/(a+b)^3*ln(-1+sin(x))*a^2-21/16/(a+b)^3*ln(-1+sin(x))*a*b-15/16/(a+b)^3*ln(-1+sin(x))*b^2+1/2/(8*a-8*b)/(1+sin(x))^2-7/16/(a-b)^2/(1+sin(x))*a+9/16/(a-b)^2/(1+sin(x))*b-1/2/(a-b)^3*ln(1+sin(x))*a^2+21/16/(a-b)^3*ln(1+sin(x))*a*b-15/16/(a-b)^3*ln(1+sin(x))*b^2","A"
13,1,117,105,0.506000," ","int(tan(x)^3/(a+b*csc(x)),x)","\frac{b^{4} \ln \left(b +a \sin \left(x \right)\right)}{\left(a +b \right)^{2} \left(a -b \right)^{2} a}-\frac{1}{\left(4 a +4 b \right) \left(-1+\sin \left(x \right)\right)}+\frac{a \ln \left(-1+\sin \left(x \right)\right)}{2 \left(a +b \right)^{2}}+\frac{3 \ln \left(-1+\sin \left(x \right)\right) b}{4 \left(a +b \right)^{2}}+\frac{1}{\left(4 a -4 b \right) \left(1+\sin \left(x \right)\right)}-\frac{3 \ln \left(1+\sin \left(x \right)\right) b}{4 \left(a -b \right)^{2}}+\frac{a \ln \left(1+\sin \left(x \right)\right)}{2 \left(a -b \right)^{2}}"," ",0,"b^4/(a+b)^2/(a-b)^2/a*ln(b+a*sin(x))-1/(4*a+4*b)/(-1+sin(x))+1/2*a/(a+b)^2*ln(-1+sin(x))+3/4/(a+b)^2*ln(-1+sin(x))*b+1/(4*a-4*b)/(1+sin(x))-3/4/(a-b)^2*ln(1+sin(x))*b+1/2*a*ln(1+sin(x))/(a-b)^2","A"
14,1,60,62,0.536000," ","int(tan(x)/(a+b*csc(x)),x)","\frac{b^{2} \ln \left(b +a \sin \left(x \right)\right)}{\left(a +b \right) \left(a -b \right) a}-\frac{\ln \left(-1+\sin \left(x \right)\right)}{2 a +2 b}-\frac{\ln \left(1+\sin \left(x \right)\right)}{2 a -2 b}"," ",0,"b^2/(a+b)/(a-b)/a*ln(b+a*sin(x))-1/(2*a+2*b)*ln(-1+sin(x))-1/(2*a-2*b)*ln(1+sin(x))","A"
15,1,21,19,0.325000," ","int(cot(x)/(a+b*csc(x)),x)","\frac{\ln \left(a +b \csc \left(x \right)\right)}{a}-\frac{\ln \left(\csc \left(x \right)\right)}{a}"," ",0,"ln(a+b*csc(x))/a-1/a*ln(csc(x))","A"
16,1,44,38,0.381000," ","int(cot(x)^3/(a+b*csc(x)),x)","\frac{a \ln \left(b +a \sin \left(x \right)\right)}{b^{2}}-\frac{\ln \left(b +a \sin \left(x \right)\right)}{a}-\frac{1}{b \sin \left(x \right)}-\frac{a \ln \left(\sin \left(x \right)\right)}{b^{2}}"," ",0,"1/b^2*a*ln(b+a*sin(x))-1/a*ln(b+a*sin(x))-1/b/sin(x)-a/b^2*ln(sin(x))","A"
17,1,100,68,0.320000," ","int(cot(x)^5/(a+b*csc(x)),x)","\frac{a^{3} \ln \left(b +a \sin \left(x \right)\right)}{b^{4}}-\frac{2 a \ln \left(b +a \sin \left(x \right)\right)}{b^{2}}+\frac{\ln \left(b +a \sin \left(x \right)\right)}{a}-\frac{1}{3 b \sin \left(x \right)^{3}}-\frac{a^{2}}{b^{3} \sin \left(x \right)}+\frac{2}{b \sin \left(x \right)}+\frac{a}{2 b^{2} \sin \left(x \right)^{2}}-\frac{a^{3} \ln \left(\sin \left(x \right)\right)}{b^{4}}+\frac{2 a \ln \left(\sin \left(x \right)\right)}{b^{2}}"," ",0,"1/b^4*a^3*ln(b+a*sin(x))-2/b^2*a*ln(b+a*sin(x))+1/a*ln(b+a*sin(x))-1/3/b/sin(x)^3-1/b^3/sin(x)*a^2+2/b/sin(x)+1/2*a/b^2/sin(x)^2-1/b^4*a^3*ln(sin(x))+2*a/b^2*ln(sin(x))","A"
18,1,181,114,0.332000," ","int(cot(x)^7/(a+b*csc(x)),x)","\frac{a^{5} \ln \left(b +a \sin \left(x \right)\right)}{b^{6}}-\frac{3 a^{3} \ln \left(b +a \sin \left(x \right)\right)}{b^{4}}+\frac{3 a \ln \left(b +a \sin \left(x \right)\right)}{b^{2}}-\frac{\ln \left(b +a \sin \left(x \right)\right)}{a}-\frac{1}{5 b \sin \left(x \right)^{5}}-\frac{a^{2}}{3 b^{3} \sin \left(x \right)^{3}}+\frac{1}{b \sin \left(x \right)^{3}}-\frac{a^{4}}{b^{5} \sin \left(x \right)}+\frac{3 a^{2}}{b^{3} \sin \left(x \right)}-\frac{3}{b \sin \left(x \right)}+\frac{a}{4 b^{2} \sin \left(x \right)^{4}}+\frac{a^{3}}{2 b^{4} \sin \left(x \right)^{2}}-\frac{3 a}{2 b^{2} \sin \left(x \right)^{2}}-\frac{a^{5} \ln \left(\sin \left(x \right)\right)}{b^{6}}+\frac{3 a^{3} \ln \left(\sin \left(x \right)\right)}{b^{4}}-\frac{3 a \ln \left(\sin \left(x \right)\right)}{b^{2}}"," ",0,"1/b^6*a^5*ln(b+a*sin(x))-3/b^4*a^3*ln(b+a*sin(x))+3/b^2*a*ln(b+a*sin(x))-1/a*ln(b+a*sin(x))-1/5/b/sin(x)^5-1/3/b^3/sin(x)^3*a^2+1/b/sin(x)^3-1/b^5/sin(x)*a^4+3/b^3/sin(x)*a^2-3/b/sin(x)+1/4*a/b^2/sin(x)^4+1/2/b^4*a^3/sin(x)^2-3/2*a/b^2/sin(x)^2-1/b^6*a^5*ln(sin(x))+3/b^4*a^3*ln(sin(x))-3*a/b^2*ln(sin(x))","A"
19,1,210,149,0.421000," ","int(tan(x)^4/(a+b*csc(x)),x)","-\frac{2 b^{5} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{64}{3 \left(\tan \left(\frac{x}{2}\right)-1\right)^{3} \left(64 a +64 b \right)}-\frac{32}{\left(64 a +64 b \right) \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{a}{\left(a +b \right)^{2} \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{3 b}{2 \left(a +b \right)^{2} \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{64}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3} \left(64 a -64 b \right)}+\frac{32}{\left(64 a -64 b \right) \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{3 b}{2 \left(a -b \right)^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{a}{\left(a -b \right)^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-2/(a-b)^2/(a+b)^2*b^5/a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-64/3/(tan(1/2*x)-1)^3/(64*a+64*b)-32/(64*a+64*b)/(tan(1/2*x)-1)^2+1/(a+b)^2/(tan(1/2*x)-1)*a+3/2/(a+b)^2/(tan(1/2*x)-1)*b-64/3/(tan(1/2*x)+1)^3/(64*a-64*b)+32/(64*a-64*b)/(tan(1/2*x)+1)^2-3/2/(a-b)^2/(tan(1/2*x)+1)*b+1/(a-b)^2/(tan(1/2*x)+1)*a+2/a*arctan(tan(1/2*x))","A"
20,1,106,78,0.515000," ","int(tan(x)^2/(a+b*csc(x)),x)","-\frac{16}{\left(16 a -16 b \right) \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{2 b^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\left(a -b \right) \left(a +b \right) a \sqrt{-a^{2}+b^{2}}}-\frac{16}{\left(16 a +16 b \right) \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-16/(16*a-16*b)/(tan(1/2*x)+1)-2/(a-b)/(a+b)*b^3/a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-16/(16*a+16*b)/(tan(1/2*x)-1)-2/a*arctan(tan(1/2*x))","A"
21,1,105,55,0.352000," ","int(cot(x)^2/(a+b*csc(x)),x)","-\frac{2 a \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \sqrt{-a^{2}+b^{2}}}+\frac{2 b \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a \sqrt{-a^{2}+b^{2}}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{b}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-2/b*a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+2*b/a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+1/b*ln(tan(1/2*x))-2/a*arctan(tan(1/2*x))","A"
22,1,206,81,0.329000," ","int(cot(x)^4/(a+b*csc(x)),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 b}-\frac{a \tan \left(\frac{x}{2}\right)}{2 b^{2}}-\frac{2 a^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} \sqrt{-a^{2}+b^{2}}}+\frac{4 a \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \sqrt{-a^{2}+b^{2}}}-\frac{2 b \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a \sqrt{-a^{2}+b^{2}}}-\frac{1}{8 b \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right) a^{2}}{b^{3}}-\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 b}+\frac{a}{2 b^{2} \tan \left(\frac{x}{2}\right)}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"1/8/b*tan(1/2*x)^2-1/2/b^2*a*tan(1/2*x)-2/b^3*a^3/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+4/b*a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-2*b/a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/8/b/tan(1/2*x)^2+1/b^3*ln(tan(1/2*x))*a^2-3/2/b*ln(tan(1/2*x))+1/2*a/b^2/tan(1/2*x)+2/a*arctan(tan(1/2*x))","B"
23,1,363,168,0.340000," ","int(cot(x)^6/(a+b*csc(x)),x)","\frac{\tan^{4}\left(\frac{x}{2}\right)}{64 b}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) a}{24 b^{2}}+\frac{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8 b^{3}}-\frac{\tan^{2}\left(\frac{x}{2}\right)}{4 b}-\frac{a^{3} \tan \left(\frac{x}{2}\right)}{2 b^{4}}+\frac{9 a \tan \left(\frac{x}{2}\right)}{8 b^{2}}-\frac{2 a^{5} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{5} \sqrt{-a^{2}+b^{2}}}+\frac{6 a^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} \sqrt{-a^{2}+b^{2}}}-\frac{6 a \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \sqrt{-a^{2}+b^{2}}}+\frac{2 b \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a \sqrt{-a^{2}+b^{2}}}-\frac{1}{64 b \tan \left(\frac{x}{2}\right)^{4}}-\frac{a^{2}}{8 b^{3} \tan \left(\frac{x}{2}\right)^{2}}+\frac{1}{4 b \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right) a^{4}}{b^{5}}-\frac{5 \ln \left(\tan \left(\frac{x}{2}\right)\right) a^{2}}{2 b^{3}}+\frac{15 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{8 b}+\frac{a}{24 b^{2} \tan \left(\frac{x}{2}\right)^{3}}+\frac{a^{3}}{2 b^{4} \tan \left(\frac{x}{2}\right)}-\frac{9 a}{8 b^{2} \tan \left(\frac{x}{2}\right)}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"1/64/b*tan(1/2*x)^4-1/24/b^2*tan(1/2*x)^3*a+1/8/b^3*a^2*tan(1/2*x)^2-1/4/b*tan(1/2*x)^2-1/2/b^4*a^3*tan(1/2*x)+9/8/b^2*a*tan(1/2*x)-2*a^5/b^5/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+6/b^3*a^3/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-6/b*a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+2*b/a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/64/b/tan(1/2*x)^4-1/8/b^3/tan(1/2*x)^2*a^2+1/4/b/tan(1/2*x)^2+1/b^5*ln(tan(1/2*x))*a^4-5/2/b^3*ln(tan(1/2*x))*a^2+15/8/b*ln(tan(1/2*x))+1/24*a/b^2/tan(1/2*x)^3+1/2*a^3/b^4/tan(1/2*x)-9/8*a/b^2/tan(1/2*x)-2/a*arctan(tan(1/2*x))","B"