1,1,66,57,0.319000," ","int(sin(x)^4/(I+cot(x)),x)","\frac{3 i}{16 \left(i+\tan \left(x \right)\right)}+\frac{1}{32 \left(i+\tan \left(x \right)\right)^{2}}+\frac{5 \ln \left(i+\tan \left(x \right)\right)}{32}+\frac{i}{2 \tan \left(x \right)-2 i}-\frac{i}{24 \left(\tan \left(x \right)-i\right)^{3}}-\frac{7}{32 \left(\tan \left(x \right)-i\right)^{2}}-\frac{5 \ln \left(\tan \left(x \right)-i\right)}{32}"," ",0,"3/16*I/(I+tan(x))+1/32/(I+tan(x))^2+5/32*ln(I+tan(x))+1/2*I/(tan(x)-I)-1/24*I/(tan(x)-I)^3-7/32/(tan(x)-I)^2-5/32*ln(tan(x)-I)","A"
2,1,93,27,0.320000," ","int(sin(x)^3/(I+cot(x)),x)","-\frac{i}{4 \left(\tan \left(\frac{x}{2}\right)+i\right)^{2}}-\frac{1}{6 \left(\tan \left(\frac{x}{2}\right)+i\right)^{3}}-\frac{3}{8 \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{i}{\left(\tan \left(\frac{x}{2}\right)-i\right)^{4}}-\frac{i}{2 \left(\tan \left(\frac{x}{2}\right)-i\right)^{2}}+\frac{2}{5 \left(\tan \left(\frac{x}{2}\right)-i\right)^{5}}-\frac{1}{3 \left(\tan \left(\frac{x}{2}\right)-i\right)^{3}}+\frac{3}{8 \left(\tan \left(\frac{x}{2}\right)-i\right)}"," ",0,"-1/4*I/(tan(1/2*x)+I)^2-1/6/(tan(1/2*x)+I)^3-3/8/(tan(1/2*x)+I)-I/(tan(1/2*x)-I)^4-1/2*I/(tan(1/2*x)-I)^2+2/5/(tan(1/2*x)-I)^5-1/3/(tan(1/2*x)-I)^3+3/8/(tan(1/2*x)-I)","B"
3,1,47,36,0.321000," ","int(sin(x)^2/(I+cot(x)),x)","\frac{i}{8 i+8 \tan \left(x \right)}+\frac{3 \ln \left(i+\tan \left(x \right)\right)}{16}+\frac{i}{2 \tan \left(x \right)-2 i}-\frac{1}{8 \left(\tan \left(x \right)-i\right)^{2}}-\frac{3 \ln \left(\tan \left(x \right)-i\right)}{16}"," ",0,"1/8*I/(I+tan(x))+3/16*ln(I+tan(x))+1/2*I/(tan(x)-I)-1/8/(tan(x)-I)^2-3/16*ln(tan(x)-I)","A"
4,1,47,18,0.306000," ","int(sin(x)/(I+cot(x)),x)","-\frac{1}{2 \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{i}{\left(\tan \left(\frac{x}{2}\right)-i\right)^{2}}+\frac{2}{3 \left(\tan \left(\frac{x}{2}\right)-i\right)^{3}}+\frac{1}{2 \tan \left(\frac{x}{2}\right)-2 i}"," ",0,"-1/2/(tan(1/2*x)+I)-I/(tan(1/2*x)-I)^2+2/3/(tan(1/2*x)-I)^3+1/2/(tan(1/2*x)-I)","B"
5,1,12,12,0.139000," ","int(csc(x)/(I+cot(x)),x)","\frac{2}{\tan \left(\frac{x}{2}\right)-i}"," ",0,"2/(tan(1/2*x)-I)","A"
6,1,9,8,0.291000," ","int(csc(x)^2/(I+cot(x)),x)","-\ln \left(i+\cot \left(x \right)\right)"," ",0,"-ln(I+cot(x))","A"
7,1,24,11,0.249000," ","int(csc(x)^3/(I+cot(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{2}-i \ln \left(\tan \left(\frac{x}{2}\right)\right)-\frac{1}{2 \tan \left(\frac{x}{2}\right)}"," ",0,"-1/2*tan(1/2*x)-I*ln(tan(1/2*x))-1/2/tan(1/2*x)","B"
8,1,15,12,0.298000," ","int(csc(x)^4/(I+cot(x)),x)","-\frac{1}{2 \tan \left(x \right)^{2}}+\frac{i}{\tan \left(x \right)}"," ",0,"-1/2/tan(x)^2+I/tan(x)","A"
9,1,58,20,0.297000," ","int(csc(x)^5/(I+cot(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{8}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{24}-\frac{i \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{i}{8 \tan \left(\frac{x}{2}\right)^{2}}-\frac{1}{24 \tan \left(\frac{x}{2}\right)^{3}}-\frac{i \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2}-\frac{1}{8 \tan \left(\frac{x}{2}\right)}"," ",0,"-1/8*tan(1/2*x)-1/24*tan(1/2*x)^3-1/8*I*tan(1/2*x)^2+1/8*I/tan(1/2*x)^2-1/24/tan(1/2*x)^3-1/2*I*ln(tan(1/2*x))-1/8/tan(1/2*x)","B"
10,1,28,25,0.298000," ","int(csc(x)^6/(I+cot(x)),x)","-\frac{1}{2 \tan \left(x \right)^{2}}+\frac{i}{3 \tan \left(x \right)^{3}}-\frac{1}{4 \tan \left(x \right)^{4}}+\frac{i}{\tan \left(x \right)}"," ",0,"-1/2/tan(x)^2+1/3*I/tan(x)^3-1/4/tan(x)^4+I/tan(x)","A"
11,1,92,29,0.327000," ","int(csc(x)^7/(I+cot(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{16}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right)}{160}-\frac{i \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{64}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{32}-\frac{i \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{i}{8 \tan \left(\frac{x}{2}\right)^{2}}-\frac{1}{32 \tan \left(\frac{x}{2}\right)^{3}}+\frac{i}{64 \tan \left(\frac{x}{2}\right)^{4}}-\frac{3 i \ln \left(\tan \left(\frac{x}{2}\right)\right)}{8}-\frac{1}{160 \tan \left(\frac{x}{2}\right)^{5}}-\frac{1}{16 \tan \left(\frac{x}{2}\right)}"," ",0,"-1/16*tan(1/2*x)-1/160*tan(1/2*x)^5-1/64*I*tan(1/2*x)^4-1/32*tan(1/2*x)^3-1/8*I*tan(1/2*x)^2+1/8*I/tan(1/2*x)^2-1/32/tan(1/2*x)^3+1/64*I/tan(1/2*x)^4-3/8*I*ln(tan(1/2*x))-1/160/tan(1/2*x)^5-1/16/tan(1/2*x)","B"
12,1,133,75,0.287000," ","int(csc(x)^6/(a+b*cot(x)),x)","-\frac{\ln \left(a \tan \left(x \right)+b \right) a^{4}}{b^{5}}-\frac{2 \ln \left(a \tan \left(x \right)+b \right) a^{2}}{b^{3}}-\frac{\ln \left(a \tan \left(x \right)+b \right)}{b}-\frac{1}{4 b \tan \left(x \right)^{4}}-\frac{a^{2}}{2 b^{3} \tan \left(x \right)^{2}}-\frac{1}{b \tan \left(x \right)^{2}}+\frac{\ln \left(\tan \left(x \right)\right) a^{4}}{b^{5}}+\frac{2 \ln \left(\tan \left(x \right)\right) a^{2}}{b^{3}}+\frac{\ln \left(\tan \left(x \right)\right)}{b}+\frac{a}{3 b^{2} \tan \left(x \right)^{3}}+\frac{a^{3}}{b^{4} \tan \left(x \right)}+\frac{2 a}{b^{2} \tan \left(x \right)}"," ",0,"-1/b^5*ln(a*tan(x)+b)*a^4-2/b^3*ln(a*tan(x)+b)*a^2-1/b*ln(a*tan(x)+b)-1/4/b/tan(x)^4-1/2/b^3/tan(x)^2*a^2-1/b/tan(x)^2+1/b^5*ln(tan(x))*a^4+2/b^3*ln(tan(x))*a^2+1/b*ln(tan(x))+1/3*a/b^2/tan(x)^3+1/b^4*a^3/tan(x)+2/b^2*a/tan(x)","A"
13,1,64,36,0.253000," ","int(csc(x)^4/(a+b*cot(x)),x)","-\frac{\ln \left(a \tan \left(x \right)+b \right) a^{2}}{b^{3}}-\frac{\ln \left(a \tan \left(x \right)+b \right)}{b}-\frac{1}{2 b \tan \left(x \right)^{2}}+\frac{\ln \left(\tan \left(x \right)\right) a^{2}}{b^{3}}+\frac{\ln \left(\tan \left(x \right)\right)}{b}+\frac{a}{b^{2} \tan \left(x \right)}"," ",0,"-1/b^3*ln(a*tan(x)+b)*a^2-1/b*ln(a*tan(x)+b)-1/2/b/tan(x)^2+1/b^3*ln(tan(x))*a^2+1/b*ln(tan(x))+1/b^2*a/tan(x)","A"
14,1,13,12,0.190000," ","int(csc(x)^2/(a+b*cot(x)),x)","-\frac{\ln \left(a +b \cot \left(x \right)\right)}{b}"," ",0,"-ln(a+b*cot(x))/b","A"
15,1,173,68,0.238000," ","int(sin(x)^2/(a+b*cot(x)),x)","-\frac{b^{3} \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{b^{3} \ln \left(1+\tan^{2}\left(x \right)\right)}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(x \right)\right) b^{2} a}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(x \right)\right) a^{3}}{2 \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-b^3/(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*b^3*ln(1+tan(x)^2)+3/2/(a^2+b^2)^2*arctan(tan(x))*b^2*a+1/2/(a^2+b^2)^2*arctan(tan(x))*a^3","B"
16,1,407,114,0.238000," ","int(sin(x)^4/(a+b*cot(x)),x)","-\frac{b^{5} \ln \left(a \tan \left(x \right)+b \right)}{\left(a^{2}+b^{2}\right)^{3}}-\frac{7 \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{9 \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{5 \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^{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{3 \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{\left(\tan^{2}\left(x \right)\right) b^{5}}{\left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{3 \tan \left(x \right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}-\frac{5 \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{7 \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{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{3 b^{5}}{4 \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(x \right)\right)^{2}}+\frac{b^{5} \ln \left(1+\tan^{2}\left(x \right)\right)}{2 \left(a^{2}+b^{2}\right)^{3}}+\frac{15 \arctan \left(\tan \left(x \right)\right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(x \right)\right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3}}+\frac{5 \arctan \left(\tan \left(x \right)\right) b^{2} a^{3}}{4 \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-b^5/(a^2+b^2)^3*ln(a*tan(x)+b)-7/4/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^3*b^2*a^3-9/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^3*a*b^4-5/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^3*a^5+1/2/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^2*b*a^4+3/2/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^2*a^2*b^3+1/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)^2*b^5-3/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)*a^5-5/4/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)*b^2*a^3-7/8/(a^2+b^2)^3/(1+tan(x)^2)^2*tan(x)*a*b^4+1/4/(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+3/4/(a^2+b^2)^3/(1+tan(x)^2)^2*b^5+1/2/(a^2+b^2)^3*b^5*ln(1+tan(x)^2)+15/8/(a^2+b^2)^3*arctan(tan(x))*a*b^4+3/8/(a^2+b^2)^3*arctan(tan(x))*a^5+5/4/(a^2+b^2)^3*arctan(tan(x))*b^2*a^3","B"
17,1,232,91,0.258000," ","int(csc(x)^5/(a+b*cot(x)),x)","-\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 b}-\frac{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8 b^{2}}-\frac{a^{2} \tan \left(\frac{x}{2}\right)}{2 b^{3}}-\frac{5 \tan \left(\frac{x}{2}\right)}{8 b}+\frac{2 \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right) a^{4}}{b^{4} \sqrt{a^{2}+b^{2}}}+\frac{4 \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{b^{2} \sqrt{a^{2}+b^{2}}}+\frac{2 \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}-\frac{1}{24 b \tan \left(\frac{x}{2}\right)^{3}}-\frac{a^{2}}{2 b^{3} \tan \left(\frac{x}{2}\right)}-\frac{5}{8 b \tan \left(\frac{x}{2}\right)}+\frac{a}{8 b^{2} \tan \left(\frac{x}{2}\right)^{2}}-\frac{a^{3} \ln \left(\tan \left(\frac{x}{2}\right)\right)}{b^{4}}-\frac{3 a \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 b^{2}}"," ",0,"-1/24/b*tan(1/2*x)^3-1/8/b^2*a*tan(1/2*x)^2-1/2/b^3*a^2*tan(1/2*x)-5/8/b*tan(1/2*x)+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))*a^4+4/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))*a^2+2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))-1/24/b/tan(1/2*x)^3-1/2/b^3/tan(1/2*x)*a^2-5/8/b/tan(1/2*x)+1/8*a/b^2/tan(1/2*x)^2-1/b^4*a^3*ln(tan(1/2*x))-3/2/b^2*a*ln(tan(1/2*x))","B"
18,1,107,49,0.267000," ","int(csc(x)^3/(a+b*cot(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{2 b}+\frac{2 \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{b^{2} \sqrt{a^{2}+b^{2}}}+\frac{2 \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}-\frac{1}{2 b \tan \left(\frac{x}{2}\right)}-\frac{a \ln \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}}"," ",0,"-1/2/b*tan(1/2*x)+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))*a^2+2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))-1/2/b/tan(1/2*x)-1/b^2*a*ln(tan(1/2*x))","B"
19,1,35,32,0.179000," ","int(csc(x)/(a+b*cot(x)),x)","\frac{2 \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}"," ",0,"2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*tan(1/2*x)*b-2*a)/(a^2+b^2)^(1/2))","A"
20,1,84,62,0.252000," ","int(sin(x)/(a+b*cot(x)),x)","\frac{8 b^{2} \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(4 a^{2}+4 b^{2}\right) \sqrt{a^{2}+b^{2}}}+\frac{-2 \tan \left(\frac{x}{2}\right) b -2 a}{\left(a^{2}+b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"8*b^2/(4*a^2+4*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)*(-tan(1/2*x)*b-a)/(tan(1/2*x)^2+1)","A"
21,1,163,113,0.262000," ","int(sin(x)^3/(a+b*cot(x)),x)","\frac{32 b^{4} \arctanh \left(\frac{2 \tan \left(\frac{x}{2}\right) b -2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(16 a^{4}+32 a^{2} b^{2}+16 b^{4}\right) \sqrt{a^{2}+b^{2}}}+\frac{-2 b^{3} \left(\tan^{5}\left(\frac{x}{2}\right)\right)-2 b^{2} a \left(\tan^{4}\left(\frac{x}{2}\right)\right)+2 \left(-\frac{4}{3} a^{2} b -\frac{10}{3} b^{3}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+2 \left(-2 a^{3}-4 b^{2} a \right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 b^{3} \tan \left(\frac{x}{2}\right)-\frac{4 a^{3}}{3}-\frac{10 b^{2} a}{3}}{\left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"32*b^4/(16*a^4+32*a^2*b^2+16*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^2+b^2)^2*(-b^3*tan(1/2*x)^5-b^2*a*tan(1/2*x)^4+(-4/3*a^2*b-10/3*b^3)*tan(1/2*x)^3+(-2*a^3-4*a*b^2)*tan(1/2*x)^2-b^3*tan(1/2*x)-2/3*a^3-5/3*b^2*a)/(tan(1/2*x)^2+1)^3","A"
22,1,13,12,0.202000," ","int(csc(x)^2/(a+b*cot(x))^2,x)","\frac{1}{b \left(a +b \cot \left(x \right)\right)}"," ",0,"1/b/(a+b*cot(x))","A"
23,1,21,20,0.325000," ","int((a+b*cot(x))^n*csc(x)^2,x)","-\frac{\left(a +b \cot \left(x \right)\right)^{1+n}}{b \left(1+n \right)}"," ",0,"-(a+b*cot(x))^(1+n)/b/(1+n)","A"