1,1,172,36,0.253000," ","int(cos(x)^4/(a+a*csc(x)),x)","-\frac{\tan^{7}\left(\frac{x}{2}\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{2 \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{7 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{2 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{7 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\tan \left(\frac{x}{2}\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{2}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\arctan \left(\tan \left(\frac{x}{2}\right)\right)}{4 a}"," ",0,"-1/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^7-2/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^6+7/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^5-2/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^4-7/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^3-2/3/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^2+1/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)-2/3/a/(tan(1/2*x)^2+1)^4-1/4/a*arctan(tan(1/2*x))","B"
2,1,18,19,0.233000," ","int(cos(x)^3/(a+a*csc(x)),x)","\frac{-\frac{\left(\sin^{3}\left(x \right)\right)}{3}+\frac{\left(\sin^{2}\left(x \right)\right)}{2}}{a}"," ",0,"1/a*(-1/3*sin(x)^3+1/2*sin(x)^2)","A"
3,1,87,23,0.295000," ","int(cos(x)^2/(a+a*csc(x)),x)","-\frac{\tan^{3}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3-2/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2+1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)-2/a/(tan(1/2*x)^2+1)^2-1/a*arctan(tan(1/2*x))","B"
4,1,27,17,0.265000," ","int(cos(x)/(a+a*csc(x)),x)","\frac{1}{a \csc \left(x \right)}+\frac{\ln \left(\csc \left(x \right)\right)}{a}-\frac{\ln \left(1+\csc \left(x \right)\right)}{a}"," ",0,"1/a/csc(x)+1/a*ln(csc(x))-1/a*ln(1+csc(x))","A"
5,1,33,27,0.367000," ","int(sec(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{\ln \left(1+\sin \left(x \right)\right)}{4 a}"," ",0,"-1/4/a*ln(-1+sin(x))+1/2/a/(1+sin(x))+1/4*ln(1+sin(x))/a","A"
6,1,47,19,0.427000," ","int(sec(x)^2/(a+a*csc(x)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{2}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{1}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{4}{8 \tan \left(\frac{x}{2}\right)+8}}{a}"," ",0,"4/a*(-1/8/(tan(1/2*x)-1)+1/6/(tan(1/2*x)+1)^3-1/4/(tan(1/2*x)+1)^2+1/8/(tan(1/2*x)+1))","B"
7,1,44,38,0.515000," ","int(sec(x)^3/(a+a*csc(x)),x)","-\frac{1}{8 a \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right)}{16 a}+\frac{1}{8 a \left(1+\sin \left(x \right)\right)^{2}}+\frac{\ln \left(1+\sin \left(x \right)\right)}{16 a}"," ",0,"-1/8/a/(-1+sin(x))-1/16/a*ln(-1+sin(x))+1/8/a/(1+sin(x))^2+1/16*ln(1+sin(x))/a","A"
8,1,87,28,0.533000," ","int(sec(x)^4/(a+a*csc(x)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{3}{8 \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{1}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2}{5 \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{1}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{3}{8 \left(\tan \left(\frac{x}{2}\right)+1\right)}}{a}"," ",0,"4/a*(-1/24/(tan(1/2*x)-1)^3-1/16/(tan(1/2*x)-1)^2-3/32/(tan(1/2*x)-1)-1/4/(tan(1/2*x)+1)^4+1/10/(tan(1/2*x)+1)^5+1/3/(tan(1/2*x)+1)^3-1/4/(tan(1/2*x)+1)^2+3/32/(tan(1/2*x)+1))","B"
9,1,514,118,0.325000," ","int(cos(x)^4/(a+b*csc(x)),x)","-\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{4 b^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{3} \sqrt{-a^{2}+b^{2}}}-\frac{2 b^{5} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{5} \sqrt{-a^{2}+b^{2}}}-\frac{5 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\left(\tan^{7}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{4 \left(\tan^{6}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2 b^{3} \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{3 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{8 \left(\tan^{4}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{6 \left(\tan^{4}\left(\frac{x}{2}\right)\right) b^{3}}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{3 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{20 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b}{3 a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{6 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b^{3}}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{5 \tan \left(\frac{x}{2}\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\tan \left(\frac{x}{2}\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{8 b}{3 a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2 b^{3}}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{4 a}-\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{4}}{a^{5}}"," ",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))+4/a^3*b^3/(-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^5/a^5/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-5/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^7+1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)^7*b^2-4/a^2/(tan(1/2*x)^2+1)^4*tan(1/2*x)^6*b+2/a^4/(tan(1/2*x)^2+1)^4*b^3*tan(1/2*x)^6+3/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^5+1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)^5*b^2-8/a^2/(tan(1/2*x)^2+1)^4*tan(1/2*x)^4*b+6/a^4/(tan(1/2*x)^2+1)^4*tan(1/2*x)^4*b^3-3/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^3-1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)^3*b^2-20/3/a^2/(tan(1/2*x)^2+1)^4*tan(1/2*x)^2*b+6/a^4/(tan(1/2*x)^2+1)^4*tan(1/2*x)^2*b^3+5/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)-1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)*b^2-8/3/a^2/(tan(1/2*x)^2+1)^4*b+2/a^4/(tan(1/2*x)^2+1)^4*b^3+3/4/a*arctan(tan(1/2*x))-3/a^3*arctan(tan(1/2*x))*b^2+2/a^5*arctan(tan(1/2*x))*b^4","B"
10,1,64,57,0.334000," ","int(cos(x)^3/(a+b*csc(x)),x)","-\frac{\sin^{3}\left(x \right)}{3 a}+\frac{b \left(\sin^{2}\left(x \right)\right)}{2 a^{2}}+\frac{\sin \left(x \right)}{a}-\frac{b^{2} \sin \left(x \right)}{a^{3}}-\frac{b \ln \left(b +a \sin \left(x \right)\right)}{a^{2}}+\frac{b^{3} \ln \left(b +a \sin \left(x \right)\right)}{a^{4}}"," ",0,"-1/3*sin(x)^3/a+1/2*b*sin(x)^2/a^2+sin(x)/a-1/a^3*b^2*sin(x)-b*ln(b+a*sin(x))/a^2+b^3/a^4*ln(b+a*sin(x))","A"
11,1,184,70,0.274000," ","int(cos(x)^2/(a+b*csc(x)),x)","-\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{2 b^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{3} \sqrt{-a^{2}+b^{2}}}-\frac{\tan^{3}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2 b}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}+\frac{x}{2 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/a^3*b^3/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3-2/a^2/(tan(1/2*x)^2+1)^2*b*tan(1/2*x)^2+1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)-2/a^2/(tan(1/2*x)^2+1)^2*b-2/a^3*arctan(tan(1/2*x))*b^2+1/2*x/a","B"
12,1,31,20,0.269000," ","int(cos(x)/(a+b*csc(x)),x)","-\frac{b \ln \left(a +b \csc \left(x \right)\right)}{a^{2}}+\frac{1}{a \csc \left(x \right)}+\frac{b \ln \left(\csc \left(x \right)\right)}{a^{2}}"," ",0,"-b/a^2*ln(a+b*csc(x))+1/a/csc(x)+b/a^2*ln(csc(x))","A"
13,1,55,50,0.336000," ","int(sec(x)/(a+b*csc(x)),x)","-\frac{b \ln \left(b +a \sin \left(x \right)\right)}{\left(a -b \right) \left(a +b \right)}-\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/(a-b)/(a+b)*ln(b+a*sin(x))-1/(2*a+2*b)*ln(-1+sin(x))+1/(2*a-2*b)*ln(1+sin(x))","A"
14,1,92,59,0.440000," ","int(sec(x)^2/(a+b*csc(x)),x)","-\frac{4}{\left(4 a -4 b \right) \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{2 a b \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) \sqrt{-a^{2}+b^{2}}}-\frac{4}{\left(4 a +4 b \right) \left(\tan \left(\frac{x}{2}\right)-1\right)}"," ",0,"-4/(4*a-4*b)/(tan(1/2*x)+1)-2*a*b/(a-b)/(a+b)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-4/(4*a+4*b)/(tan(1/2*x)-1)","A"
15,1,89,79,0.510000," ","int(sec(x)^3/(a+b*csc(x)),x)","-\frac{a^{2} b \ln \left(b +a \sin \left(x \right)\right)}{\left(a +b \right)^{2} \left(a -b \right)^{2}}-\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)}{4 \left(a +b \right)^{2}}-\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)}{4 \left(a -b \right)^{2}}"," ",0,"-a^2*b/(a+b)^2/(a-b)^2*ln(b+a*sin(x))-1/(4*a+4*b)/(-1+sin(x))-1/4*a/(a+b)^2*ln(-1+sin(x))-1/(4*a-4*b)/(1+sin(x))+1/4*a*ln(1+sin(x))/(a-b)^2","A"
16,1,200,99,0.545000," ","int(sec(x)^4/(a+b*csc(x)),x)","-\frac{2 a^{3} b \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} \sqrt{-a^{2}+b^{2}}}-\frac{4}{3 \left(\tan \left(\frac{x}{2}\right)-1\right)^{3} \left(4 a +4 b \right)}-\frac{2}{\left(4 a +4 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{b}{2 \left(a +b \right)^{2} \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{4}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3} \left(4 a -4 b \right)}+\frac{2}{\left(4 a -4 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{b}{2 \left(a -b \right)^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-2*a^3*b/(a-b)^2/(a+b)^2/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-4/3/(tan(1/2*x)-1)^3/(4*a+4*b)-2/(4*a+4*b)/(tan(1/2*x)-1)^2-1/(a+b)^2/(tan(1/2*x)-1)*a-1/2/(a+b)^2/(tan(1/2*x)-1)*b-4/3/(tan(1/2*x)+1)^3/(4*a-4*b)+2/(4*a-4*b)/(tan(1/2*x)+1)^2-1/(a-b)^2/(tan(1/2*x)+1)*a+1/2/(a-b)^2/(tan(1/2*x)+1)*b","B"