1,1,56,57,0.262000," ","int(cos(x)^4/(I+cot(x)),x)","-\frac{i}{16 \left(i+\tan \left(x \right)\right)}+\frac{1}{32 \left(i+\tan \left(x \right)\right)^{2}}+\frac{\ln \left(i+\tan \left(x \right)\right)}{32}-\frac{i}{24 \left(\tan \left(x \right)-i\right)^{3}}+\frac{1}{32 \left(\tan \left(x \right)-i\right)^{2}}-\frac{\ln \left(\tan \left(x \right)-i\right)}{32}"," ",0,"-1/16*I/(I+tan(x))+1/32/(I+tan(x))^2+1/32*ln(I+tan(x))-1/24*I/(tan(x)-I)^3+1/32/(tan(x)-I)^2-1/32*ln(tan(x)-I)","A"
2,1,93,21,0.252000," ","int(cos(x)^3/(I+cot(x)),x)","\frac{i}{6 \left(\tan \left(\frac{x}{2}\right)+i\right)^{3}}-\frac{3 i}{8 \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{1}{4 \left(\tan \left(\frac{x}{2}\right)+i\right)^{2}}-\frac{4 i}{3 \left(\tan \left(\frac{x}{2}\right)-i\right)^{3}}+\frac{3 i}{8 \left(\tan \left(\frac{x}{2}\right)-i\right)}+\frac{2 i}{5 \left(\tan \left(\frac{x}{2}\right)-i\right)^{5}}+\frac{1}{\left(\tan \left(\frac{x}{2}\right)-i\right)^{4}}-\frac{1}{\left(\tan \left(\frac{x}{2}\right)-i\right)^{2}}"," ",0,"1/6*I/(tan(1/2*x)+I)^3-3/8*I/(tan(1/2*x)+I)-1/4/(tan(1/2*x)+I)^2-4/3*I/(tan(1/2*x)-I)^3+3/8*I/(tan(1/2*x)-I)+2/5*I/(tan(1/2*x)-I)^5+1/(tan(1/2*x)-I)^4-1/(tan(1/2*x)-I)^2","B"
3,1,37,36,0.256000," ","int(cos(x)^2/(I+cot(x)),x)","-\frac{i}{8 \left(i+\tan \left(x \right)\right)}+\frac{\ln \left(i+\tan \left(x \right)\right)}{16}+\frac{1}{8 \left(\tan \left(x \right)-i\right)^{2}}-\frac{\ln \left(\tan \left(x \right)-i\right)}{16}"," ",0,"-1/8*I/(I+tan(x))+1/16*ln(I+tan(x))+1/8/(tan(x)-I)^2-1/16*ln(tan(x)-I)","A"
4,1,49,14,0.245000," ","int(cos(x)/(I+cot(x)),x)","-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)+i\right)}+\frac{i}{2 \tan \left(\frac{x}{2}\right)-2 i}-\frac{2 i}{3 \left(\tan \left(\frac{x}{2}\right)-i\right)^{3}}-\frac{1}{\left(\tan \left(\frac{x}{2}\right)-i\right)^{2}}"," ",0,"-1/2*I/(tan(1/2*x)+I)+1/2*I/(tan(1/2*x)-I)-2/3*I/(tan(1/2*x)-I)^3-1/(tan(1/2*x)-I)^2","B"
5,1,34,16,0.295000," ","int(sec(x)/(I+cot(x)),x)","\frac{2 i}{\tan \left(\frac{x}{2}\right)-i}+i \ln \left(\tan \left(\frac{x}{2}\right)-1\right)-i \ln \left(\tan \left(\frac{x}{2}\right)+1\right)"," ",0,"2*I/(tan(1/2*x)-I)+I*ln(tan(1/2*x)-1)-I*ln(tan(1/2*x)+1)","B"
6,1,13,18,0.328000," ","int(sec(x)^2/(I+cot(x)),x)","-i \tan \left(x \right)+\ln \left(\tan \left(x \right)-i\right)"," ",0,"-I*tan(x)+ln(tan(x)-I)","A"
7,1,84,16,0.388000," ","int(sec(x)^3/(I+cot(x)),x)","-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{2}-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{1}{\tan \left(\frac{x}{2}\right)-1}-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{2}+\frac{1}{\tan \left(\frac{x}{2}\right)+1}-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-1/2*I*ln(tan(1/2*x)-1)-1/2*I/(tan(1/2*x)-1)^2-1/(tan(1/2*x)-1)-1/2*I/(tan(1/2*x)-1)+1/2*I/(tan(1/2*x)+1)^2+1/2*I*ln(tan(1/2*x)+1)+1/(tan(1/2*x)+1)-1/2*I/(tan(1/2*x)+1)","B"
8,1,15,14,0.355000," ","int(sec(x)^4/(I+cot(x)),x)","\frac{\left(\tan^{2}\left(x \right)\right)}{2}-\frac{i \left(\tan^{3}\left(x \right)\right)}{3}"," ",0,"1/2*tan(x)^2-1/3*I*tan(x)^3","A"
9,1,170,29,0.351000," ","int(sec(x)^5/(I+cot(x)),x)","\frac{i}{4 \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{1}{3 \left(\tan \left(\frac{x}{2}\right)-1\right)^{3}}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{8}-\frac{1}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{1}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{i}{8 \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{i}{8 \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{i}{4 \left(\tan \left(\frac{x}{2}\right)-1\right)^{4}}+\frac{1}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{3 i}{8 \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{1}{2 \tan \left(\frac{x}{2}\right)+2}+\frac{3 i}{8 \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{1}{2 \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{8}"," ",0,"1/4*I/(tan(1/2*x)+1)^4-1/2*I/(tan(1/2*x)-1)^3-1/3/(tan(1/2*x)-1)^3+1/8*I*ln(tan(1/2*x)+1)-1/2/(tan(1/2*x)-1)^2-1/2*I/(tan(1/2*x)+1)^3-1/2/(tan(1/2*x)-1)-1/8*I/(tan(1/2*x)-1)-1/8*I/(tan(1/2*x)+1)-1/4*I/(tan(1/2*x)-1)^4+1/3/(tan(1/2*x)+1)^3-3/8*I/(tan(1/2*x)-1)^2+1/2/(tan(1/2*x)+1)+3/8*I/(tan(1/2*x)+1)^2-1/2/(tan(1/2*x)+1)^2-1/8*I*ln(tan(1/2*x)-1)","B"
10,1,28,27,0.350000," ","int(sec(x)^6/(I+cot(x)),x)","\frac{\left(\tan^{2}\left(x \right)\right)}{2}-\frac{i \left(\tan^{3}\left(x \right)\right)}{3}+\frac{\left(\tan^{4}\left(x \right)\right)}{4}-\frac{i \left(\tan^{5}\left(x \right)\right)}{5}"," ",0,"1/2*tan(x)^2-1/3*I*tan(x)^3+1/4*tan(x)^4-1/5*I*tan(x)^5","A"
11,1,385,120,0.245000," ","int(cos(x)^4/(a+b*cot(x)),x)","-\frac{a^{4} b \ln \left(a \tan \left(x \right)+b \right)}{\left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(\tan^{3}\left(x \right)\right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}+\frac{\left(\tan^{3}\left(x \right)\right) b^{2} a^{3}}{4 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{\left(\tan^{3}\left(x \right)\right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{\left(\tan^{2}\left(x \right)\right) b \,a^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{\left(\tan^{2}\left(x \right)\right) a^{2} b^{3}}{2 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}+\frac{5 \tan \left(x \right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}+\frac{3 \tan \left(x \right) b^{2} a^{3}}{4 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}+\frac{\tan \left(x \right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{3 b \,a^{4}}{4 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{a^{2} b^{3}}{\left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{b^{5}}{4 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(x \right)\right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(x \right)\right) b^{2} a^{3}}{4 \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(x \right)\right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(x \right)\right) a^{4} b}{2 \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-a^4*b/(a^2+b^2)^3*ln(a*tan(x)+b)+3/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^3*a^5+1/4/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^3*b^2*a^3-1/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^3*a*b^4-1/2/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^2*b*a^4-1/2/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^2*a^2*b^3+5/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)*a^5+3/4/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)*b^2*a^3+1/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)*a*b^4-3/4/(a^2+b^2)^3/(1+tan(x)^2)^2*b*a^4-1/(a^2+b^2)^3/(1+tan(x)^2)^2*a^2*b^3-1/4/(a^2+b^2)^3/(1+tan(x)^2)^2*b^5+3/8/(a^2+b^2)^3*arctan(tan(x))*a^5-3/4/(a^2+b^2)^3*arctan(tan(x))*b^2*a^3-1/8/(a^2+b^2)^3*arctan(tan(x))*a*b^4+1/2/(a^2+b^2)^3*ln(1+tan(x)^2)*a^4*b","B"
12,1,170,115,0.258000," ","int(cos(x)^3/(a+b*cot(x)),x)","-\frac{4 a^{3} b \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(2 a^{4}+4 a^{2} b^{2}+2 b^{4}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-a^{3} \left(\tan^{5}\left(\frac{x}{2}\right)\right)+\left(2 a^{2} b +b^{3}\right) \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\left(-\frac{2}{3} a^{3}+\frac{4}{3} b^{2} a \right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+2 a^{2} b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a^{3} \tan \left(\frac{x}{2}\right)+\frac{4 a^{2} b}{3}+\frac{b^{3}}{3}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"-4*a^3*b/(2*a^4+4*a^2*b^2+2*b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)*(-a^3*tan(1/2*x)^5+(2*a^2*b+b^3)*tan(1/2*x)^4+(-2/3*a^3+4/3*b^2*a)*tan(1/2*x)^3+2*a^2*b*tan(1/2*x)^2-a^3*tan(1/2*x)+4/3*a^2*b+1/3*b^3)/(tan(1/2*x)^2+1)^3","A"
13,1,175,69,0.267000," ","int(cos(x)^2/(a+b*cot(x)),x)","-\frac{a^{2} b \ln \left(a \tan \left(x \right)+b \right)}{\left(a^{2}+b^{2}\right)^{2}}+\frac{\tan \left(x \right) a^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}+\frac{\tan \left(x \right) b^{2} a}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}-\frac{a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}-\frac{b^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}+\frac{\arctan \left(\tan \left(x \right)\right) a^{3}}{2 \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(x \right)\right) b^{2} a}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(1+\tan^{2}\left(x \right)\right) a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-a^2*b/(a^2+b^2)^2*ln(a*tan(x)+b)+1/2/(a^2+b^2)^2/(1+tan(x)^2)*tan(x)*a^3+1/2/(a^2+b^2)^2/(1+tan(x)^2)*tan(x)*b^2*a-1/2/(a^2+b^2)^2/(1+tan(x)^2)*a^2*b-1/2/(a^2+b^2)^2/(1+tan(x)^2)*b^3+1/2/(a^2+b^2)^2*arctan(tan(x))*a^3-1/2/(a^2+b^2)^2*arctan(tan(x))*b^2*a+1/2/(a^2+b^2)^2*ln(1+tan(x)^2)*a^2*b","B"
14,1,81,61,0.258000," ","int(cos(x)/(a+b*cot(x)),x)","-\frac{4 a b \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(2 a^{2}+2 b^{2}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-a \tan \left(\frac{x}{2}\right)+b \right)}{\left(a^{2}+b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"-4*a*b/(2*a^2+2*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))-2/(a^2+b^2)*(-a*tan(1/2*x)+b)/(tan(1/2*x)^2+1)","A"
15,1,63,43,0.278000," ","int(sec(x)/(a+b*cot(x)),x)","-\frac{2 b \arctanh \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)-1\right)}{a}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{a}"," ",0,"-2/a*b/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))-1/a*ln(tan(1/2*x)-1)+1/a*ln(tan(1/2*x)+1)","A"
16,1,21,29,0.301000," ","int(sec(x)^2/(a+b*cot(x)),x)","\frac{\tan \left(x \right)}{a}-\frac{b \ln \left(a \tan \left(x \right)+b \right)}{a^{2}}"," ",0,"tan(x)/a-b/a^2*ln(a*tan(x)+b)","A"
17,1,172,71,0.346000," ","int(sec(x)^3/(a+b*cot(x)),x)","-\frac{2 b \sqrt{a^{2}+b^{2}}\, \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{a^{3}}+\frac{1}{2 a \left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{1}{2 a \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{b}{a^{2} \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{2 a}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-1\right) b^{2}}{a^{3}}-\frac{1}{2 a \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{1}{2 a \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{b}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{2 a}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)+1\right) b^{2}}{a^{3}}"," ",0,"-2*b*(a^2+b^2)^(1/2)/a^3*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))+1/2/a/(tan(1/2*x)-1)^2+1/2/a/(tan(1/2*x)-1)+1/a^2/(tan(1/2*x)-1)*b-1/2/a*ln(tan(1/2*x)-1)-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)-1/a^2/(tan(1/2*x)+1)*b+1/2/a*ln(tan(1/2*x)+1)+1/a^3*ln(tan(1/2*x)+1)*b^2","B"
18,1,64,69,0.328000," ","int(sec(x)^4/(a+b*cot(x)),x)","\frac{\tan^{3}\left(x \right)}{3 a}-\frac{b \left(\tan^{2}\left(x \right)\right)}{2 a^{2}}+\frac{\tan \left(x \right)}{a}+\frac{b^{2} \tan \left(x \right)}{a^{3}}-\frac{b \ln \left(a \tan \left(x \right)+b \right)}{a^{2}}-\frac{b^{3} \ln \left(a \tan \left(x \right)+b \right)}{a^{4}}"," ",0,"1/3*tan(x)^3/a-1/2*b*tan(x)^2/a^2+tan(x)/a+1/a^3*b^2*tan(x)-b/a^2*ln(a*tan(x)+b)-b^3/a^4*ln(a*tan(x)+b)","A"
19,1,37,22,0.312000," ","int(sec(x)/(1+2*cot(x)),x)","-\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \tan \left(\frac{x}{2}\right)-1\right) \sqrt{5}}{5}\right)}{5}-\ln \left(\tan \left(\frac{x}{2}\right)-1\right)+\ln \left(\tan \left(\frac{x}{2}\right)+1\right)"," ",0,"-4/5*5^(1/2)*arctanh(1/5*(2*tan(1/2*x)-1)*5^(1/2))-ln(tan(1/2*x)-1)+ln(tan(1/2*x)+1)","A"