1,1,17,11,0.024000," ","int(cot(b*x+a),x)","-\frac{\ln \left(\cot^{2}\left(b x +a \right)+1\right)}{2 b}"," ",0,"-1/2/b*ln(cot(b*x+a)^2+1)","A"
2,1,26,15,0.025000," ","int(cot(b*x+a)^2,x)","\frac{-\cot \left(b x +a \right)+\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b*(-cot(b*x+a)+1/2*Pi-arccot(cot(b*x+a)))","A"
3,1,31,26,0.031000," ","int(cot(b*x+a)^3,x)","-\frac{\cot^{2}\left(b x +a \right)}{2 b}+\frac{\ln \left(\cot^{2}\left(b x +a \right)+1\right)}{2 b}"," ",0,"-1/2*cot(b*x+a)^2/b+1/2/b*ln(cot(b*x+a)^2+1)","A"
4,1,32,25,0.033000," ","int(cot(b*x+a)^4,x)","\frac{-\frac{\left(\cot^{3}\left(b x +a \right)\right)}{3}+\cot \left(b x +a \right)-\frac{\pi}{2}+\mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b*(-1/3*cot(b*x+a)^3+cot(b*x+a)-1/2*Pi+arccot(cot(b*x+a)))","A"
5,1,44,38,0.027000," ","int(cot(b*x+a)^5,x)","-\frac{\cot^{4}\left(b x +a \right)}{4 b}+\frac{\cot^{2}\left(b x +a \right)}{2 b}-\frac{\ln \left(\cot^{2}\left(b x +a \right)+1\right)}{2 b}"," ",0,"-1/4*cot(b*x+a)^4/b+1/2*cot(b*x+a)^2/b-1/2/b*ln(cot(b*x+a)^2+1)","A"
6,1,46,41,0.024000," ","int(cot(b*x+a)^6,x)","\frac{-\frac{\left(\cot^{5}\left(b x +a \right)\right)}{5}+\frac{\left(\cot^{3}\left(b x +a \right)\right)}{3}-\cot \left(b x +a \right)+\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b*(-1/5*cot(b*x+a)^5+1/3*cot(b*x+a)^3-cot(b*x+a)+1/2*Pi-arccot(cot(b*x+a)))","A"
7,1,57,52,0.026000," ","int(cot(b*x+a)^7,x)","-\frac{\cot^{6}\left(b x +a \right)}{6 b}+\frac{\cot^{4}\left(b x +a \right)}{4 b}-\frac{\cot^{2}\left(b x +a \right)}{2 b}+\frac{\ln \left(\cot^{2}\left(b x +a \right)+1\right)}{2 b}"," ",0,"-1/6*cot(b*x+a)^6/b+1/4*cot(b*x+a)^4/b-1/2*cot(b*x+a)^2/b+1/2/b*ln(cot(b*x+a)^2+1)","A"
8,1,52,51,0.025000," ","int(cot(b*x+a)^8,x)","\frac{-\frac{\left(\cot^{7}\left(b x +a \right)\right)}{7}+\frac{\left(\cot^{5}\left(b x +a \right)\right)}{5}-\frac{\left(\cot^{3}\left(b x +a \right)\right)}{3}+\cot \left(b x +a \right)-\frac{\pi}{2}+\mathrm{arccot}\left(\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b*(-1/7*cot(b*x+a)^7+1/5*cot(b*x+a)^5-1/3*cot(b*x+a)^3+cot(b*x+a)-1/2*Pi+arccot(cot(b*x+a)))","A"
9,1,200,179,0.434000," ","int((c*cot(b*x+a))^(7/2),x)","-\frac{2 c \left(c \cot \left(b x +a \right)\right)^{\frac{5}{2}}}{5 b}+\frac{2 c^{3} \sqrt{c \cot \left(b x +a \right)}}{b}-\frac{c^{3} \left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b}-\frac{c^{3} \left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b}+\frac{c^{3} \left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b}"," ",0,"-2/5*c*(c*cot(b*x+a))^(5/2)/b+2*c^3*(c*cot(b*x+a))^(1/2)/b-1/4/b*c^3*(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))-1/2/b*c^3*(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+1/2/b*c^3*(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)","A"
10,1,182,161,0.384000," ","int((c*cot(b*x+a))^(5/2),x)","-\frac{2 c \left(c \cot \left(b x +a \right)\right)^{\frac{3}{2}}}{3 b}+\frac{c^{3} \sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b \left(c^{2}\right)^{\frac{1}{4}}}+\frac{c^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \left(c^{2}\right)^{\frac{1}{4}}}-\frac{c^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \left(c^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*c*(c*cot(b*x+a))^(3/2)/b+1/4/b*c^3/(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))+1/2/b*c^3/(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)-1/2/b*c^3/(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)","A"
11,1,176,161,0.382000," ","int((c*cot(b*x+a))^(3/2),x)","-\frac{2 c \sqrt{c \cot \left(b x +a \right)}}{b}+\frac{c \left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{c \left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b}+\frac{c \left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b}"," ",0,"-2*c*(c*cot(b*x+a))^(1/2)/b+1/2/b*c*(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)-1/2/b*c*(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+1/4/b*c*(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))","A"
12,1,160,145,0.417000," ","int((c*cot(b*x+a))^(1/2),x)","-\frac{c \sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b \left(c^{2}\right)^{\frac{1}{4}}}-\frac{c \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \left(c^{2}\right)^{\frac{1}{4}}}+\frac{c \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \left(c^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4/b*c/(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))-1/2/b*c/(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+1/2/b*c/(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)","A"
13,1,166,145,0.346000," ","int(1/(c*cot(b*x+a))^(1/2),x)","-\frac{\left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b c}-\frac{\left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b c}+\frac{\left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b c}"," ",0,"-1/4/b/c*(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))-1/2/b/c*(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+1/2/b/c*(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)","A"
14,1,184,163,0.311000," ","int(1/(c*cot(b*x+a))^(3/2),x)","\frac{\sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b c \left(c^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b c \left(c^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b c \left(c^{2}\right)^{\frac{1}{4}}}+\frac{2}{b c \sqrt{c \cot \left(b x +a \right)}}"," ",0,"1/4/b/c/(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))+1/2/b/c/(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)-1/2/b/c/(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+2/b/c/(c*cot(b*x+a))^(1/2)","A"
15,1,184,163,0.280000," ","int(1/(c*cot(b*x+a))^(5/2),x)","\frac{2}{3 b c \left(c \cot \left(b x +a \right)\right)^{\frac{3}{2}}}+\frac{\left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b \,c^{3}}+\frac{\left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \,c^{3}}-\frac{\left(c^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \,c^{3}}"," ",0,"2/3/b/c/(c*cot(b*x+a))^(3/2)+1/4/b/c^3*(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))+1/2/b/c^3*(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)-1/2/b/c^3*(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)","A"
16,1,202,181,0.446000," ","int(1/(c*cot(b*x+a))^(7/2),x)","-\frac{\sqrt{2}\, \ln \left(\frac{c \cot \left(b x +a \right)-\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}{c \cot \left(b x +a \right)+\left(c^{2}\right)^{\frac{1}{4}} \sqrt{c \cot \left(b x +a \right)}\, \sqrt{2}+\sqrt{c^{2}}}\right)}{4 b \,c^{3} \left(c^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \,c^{3} \left(c^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{c \cot \left(b x +a \right)}}{\left(c^{2}\right)^{\frac{1}{4}}}+1\right)}{2 b \,c^{3} \left(c^{2}\right)^{\frac{1}{4}}}+\frac{2}{5 b c \left(c \cot \left(b x +a \right)\right)^{\frac{5}{2}}}-\frac{2}{b \,c^{3} \sqrt{c \cot \left(b x +a \right)}}"," ",0,"-1/4/b/c^3/(c^2)^(1/4)*2^(1/2)*ln((c*cot(b*x+a)-(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2))/(c*cot(b*x+a)+(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)*2^(1/2)+(c^2)^(1/2)))-1/2/b/c^3/(c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+1/2/b/c^3/(c^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(c^2)^(1/4)*(c*cot(b*x+a))^(1/2)+1)+2/5/b/c/(c*cot(b*x+a))^(5/2)-2/b/c^3/(c*cot(b*x+a))^(1/2)","A"
17,1,214,184,0.534000," ","int((c*cot(b*x+a))^(4/3),x)","-\frac{3 c \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{b}-\frac{c \sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b}+\frac{c \left(c^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 b}+\frac{c \left(c^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{\left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}\right)}{b}+\frac{c \sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b}+\frac{c \left(c^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 b}"," ",0,"-3*c*(c*cot(b*x+a))^(1/3)/b-1/4/b*c*3^(1/2)*(c^2)^(1/6)*ln((c*cot(b*x+a))^(2/3)-3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))+1/2/b*c*(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)-3^(1/2))+1/b*c*(c^2)^(1/6)*arctan((c*cot(b*x+a))^(1/3)/(c^2)^(1/6))+1/4/b*c*3^(1/2)*(c^2)^(1/6)*ln((c*cot(b*x+a))^(2/3)+3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))+1/2/b*c*(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)+3^(1/2))","A"
18,1,203,169,0.447000," ","int((c*cot(b*x+a))^(2/3),x)","-\frac{\sqrt{3}\, \left(c^{2}\right)^{\frac{5}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b c}-\frac{c \arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 b \left(c^{2}\right)^{\frac{1}{6}}}-\frac{c \arctan \left(\frac{\left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}\right)}{b \left(c^{2}\right)^{\frac{1}{6}}}+\frac{\sqrt{3}\, \left(c^{2}\right)^{\frac{5}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b c}-\frac{c \arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 b \left(c^{2}\right)^{\frac{1}{6}}}"," ",0,"-1/4/b/c*3^(1/2)*(c^2)^(5/6)*ln((c*cot(b*x+a))^(2/3)-3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))-1/2/b*c/(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)-3^(1/2))-1/b*c/(c^2)^(1/6)*arctan((c*cot(b*x+a))^(1/3)/(c^2)^(1/6))+1/4/b/c*3^(1/2)*(c^2)^(5/6)*ln((c*cot(b*x+a))^(2/3)+3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))-1/2/b*c/(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)+3^(1/2))","A"
19,1,114,98,0.361000," ","int((c*cot(b*x+a))^(1/3),x)","\frac{c \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{2 b \left(c^{2}\right)^{\frac{1}{3}}}-\frac{c \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{4}{3}}-\left(c^{2}\right)^{\frac{1}{3}} \left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\left(c^{2}\right)^{\frac{2}{3}}\right)}{4 b \left(c^{2}\right)^{\frac{1}{3}}}-\frac{c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}}{\left(c^{2}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 b \left(c^{2}\right)^{\frac{1}{3}}}"," ",0,"1/2/b*c/(c^2)^(1/3)*ln((c*cot(b*x+a))^(2/3)+(c^2)^(1/3))-1/4/b*c/(c^2)^(1/3)*ln((c*cot(b*x+a))^(4/3)-(c^2)^(1/3)*(c*cot(b*x+a))^(2/3)+(c^2)^(2/3))-1/2/b*c*3^(1/2)/(c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/(c^2)^(1/3)*(c*cot(b*x+a))^(2/3)-1))","A"
20,1,114,98,0.271000," ","int(1/(c*cot(b*x+a))^(1/3),x)","-\frac{c \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{2 b \left(c^{2}\right)^{\frac{2}{3}}}+\frac{c \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{4}{3}}-\left(c^{2}\right)^{\frac{1}{3}} \left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\left(c^{2}\right)^{\frac{2}{3}}\right)}{4 b \left(c^{2}\right)^{\frac{2}{3}}}-\frac{c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}}{\left(c^{2}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 b \left(c^{2}\right)^{\frac{2}{3}}}"," ",0,"-1/2/b*c/(c^2)^(2/3)*ln((c*cot(b*x+a))^(2/3)+(c^2)^(1/3))+1/4/b*c/(c^2)^(2/3)*ln((c*cot(b*x+a))^(4/3)-(c^2)^(1/3)*(c*cot(b*x+a))^(2/3)+(c^2)^(2/3))-1/2/b*c/(c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c^2)^(1/3)*(c*cot(b*x+a))^(2/3)-1))","A"
21,1,209,169,0.358000," ","int(1/(c*cot(b*x+a))^(2/3),x)","\frac{\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}-\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b c}-\frac{\left(c^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 b c}-\frac{\left(c^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{\left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}\right)}{b c}-\frac{\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b c}-\frac{\left(c^{2}\right)^{\frac{1}{6}} \arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 b c}"," ",0,"1/4/b/c*3^(1/2)*(c^2)^(1/6)*ln((c*cot(b*x+a))^(2/3)-3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))-1/2/b/c*(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)-3^(1/2))-1/b/c*(c^2)^(1/6)*arctan((c*cot(b*x+a))^(1/3)/(c^2)^(1/6))-1/4/b/c*3^(1/2)*(c^2)^(1/6)*ln((c*cot(b*x+a))^(2/3)+3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))-1/2/b/c*(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)+3^(1/2))","A"
22,1,229,186,0.408000," ","int(1/(c*cot(b*x+a))^(4/3),x)","\frac{\sqrt{3}\, \left(c^{2}\right)^{\frac{5}{6}} \ln \left(\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}-\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}-\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b \,c^{3}}+\frac{\arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{2 b c \left(c^{2}\right)^{\frac{1}{6}}}+\frac{\arctan \left(\frac{\left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}\right)}{b c \left(c^{2}\right)^{\frac{1}{6}}}-\frac{\sqrt{3}\, \left(c^{2}\right)^{\frac{5}{6}} \ln \left(\left(c \cot \left(b x +a \right)\right)^{\frac{2}{3}}+\sqrt{3}\, \left(c^{2}\right)^{\frac{1}{6}} \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}+\left(c^{2}\right)^{\frac{1}{3}}\right)}{4 b \,c^{3}}+\frac{\arctan \left(\frac{2 \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}{\left(c^{2}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{2 b c \left(c^{2}\right)^{\frac{1}{6}}}+\frac{3}{b c \left(c \cot \left(b x +a \right)\right)^{\frac{1}{3}}}"," ",0,"1/4/b/c^3*3^(1/2)*(c^2)^(5/6)*ln(3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)-(c*cot(b*x+a))^(2/3)-(c^2)^(1/3))+1/2/b/c/(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)-3^(1/2))+1/b/c/(c^2)^(1/6)*arctan((c*cot(b*x+a))^(1/3)/(c^2)^(1/6))-1/4/b/c^3*3^(1/2)*(c^2)^(5/6)*ln((c*cot(b*x+a))^(2/3)+3^(1/2)*(c^2)^(1/6)*(c*cot(b*x+a))^(1/3)+(c^2)^(1/3))+1/2/b/c/(c^2)^(1/6)*arctan(2*(c*cot(b*x+a))^(1/3)/(c^2)^(1/6)+3^(1/2))+3/b/c/(c*cot(b*x+a))^(1/3)","A"
23,0,0,44,1.347000," ","int(cot(b*x+a)^n,x)","\int \cot^{n}\left(b x +a \right)\, dx"," ",0,"int(cot(b*x+a)^n,x)","F"
24,0,0,49,1.184000," ","int((b*cot(d*x+c))^n,x)","\int \left(b \cot \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((b*cot(d*x+c))^n,x)","F"
25,1,29,30,0.149000," ","int((a*cot(x)^2)^(3/2),x)","\frac{\left(a \left(\cot^{2}\left(x \right)\right)\right)^{\frac{3}{2}} \left(-\left(\cot^{2}\left(x \right)\right)+\ln \left(\cot^{2}\left(x \right)+1\right)\right)}{2 \cot \left(x \right)^{3}}"," ",0,"1/2*(a*cot(x)^2)^(3/2)*(-cot(x)^2+ln(cot(x)^2+1))/cot(x)^3","A"
26,1,22,14,0.170000," ","int((a*cot(x)^2)^(1/2),x)","-\frac{\sqrt{a \left(\cot^{2}\left(x \right)\right)}\, \ln \left(\cot^{2}\left(x \right)+1\right)}{2 \cot \left(x \right)}"," ",0,"-1/2*(a*cot(x)^2)^(1/2)/cot(x)*ln(cot(x)^2+1)","A"
27,1,28,15,0.188000," ","int(1/(a*cot(x)^2)^(1/2),x)","-\frac{\cot \left(x \right) \left(2 \ln \left(\cot \left(x \right)\right)-\ln \left(\cot^{2}\left(x \right)+1\right)\right)}{2 \sqrt{a \left(\cot^{2}\left(x \right)\right)}}"," ",0,"-1/2*cot(x)*(2*ln(cot(x))-ln(cot(x)^2+1))/(a*cot(x)^2)^(1/2)","A"
28,1,37,33,0.122000," ","int(1/(a*cot(x)^2)^(3/2),x)","\frac{\cot \left(x \right) \left(2 \ln \left(\cot \left(x \right)\right) \left(\cot^{2}\left(x \right)\right)-\ln \left(\cot^{2}\left(x \right)+1\right) \left(\cot^{2}\left(x \right)\right)+1\right)}{2 \left(a \left(\cot^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/2*cot(x)*(2*ln(cot(x))*cot(x)^2-ln(cot(x)^2+1)*cot(x)^2+1)/(a*cot(x)^2)^(3/2)","A"
29,1,189,148,0.165000," ","int((a*cot(x)^3)^(3/2),x)","-\frac{\left(a \left(\cot^{3}\left(x \right)\right)\right)^{\frac{3}{2}} \left(24 \left(a \cot \left(x \right)\right)^{\frac{7}{2}} \left(a^{2}\right)^{\frac{1}{4}}-56 \left(a \cot \left(x \right)\right)^{\frac{3}{2}} a^{2} \left(a^{2}\right)^{\frac{1}{4}}+21 a^{4} \sqrt{2}\, \ln \left(-\frac{\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}-a \cot \left(x \right)-\sqrt{a^{2}}}{a \cot \left(x \right)+\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}+\sqrt{a^{2}}}\right)+42 a^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}+\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)+42 a^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}-\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)\right)}{84 \cot \left(x \right)^{3} \left(a \cot \left(x \right)\right)^{\frac{3}{2}} a^{2} \left(a^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/84*(a*cot(x)^3)^(3/2)*(24*(a*cot(x))^(7/2)*(a^2)^(1/4)-56*(a*cot(x))^(3/2)*a^2*(a^2)^(1/4)+21*a^4*2^(1/2)*ln(-((a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)-a*cot(x)-(a^2)^(1/2))/(a*cot(x)+(a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)+(a^2)^(1/2)))+42*a^4*2^(1/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)+(a^2)^(1/4))/(a^2)^(1/4))+42*a^4*2^(1/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)-(a^2)^(1/4))/(a^2)^(1/4)))/cot(x)^3/(a*cot(x))^(3/2)/a^2/(a^2)^(1/4)","A"
30,1,165,130,0.173000," ","int((a*cot(x)^3)^(1/2),x)","\frac{\sqrt{a \left(\cot^{3}\left(x \right)\right)}\, \left(\left(a^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(-\frac{a \cot \left(x \right)+\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}+\sqrt{a^{2}}}{\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}-a \cot \left(x \right)-\sqrt{a^{2}}}\right)+2 \left(a^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}+\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)+2 \left(a^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}-\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)-8 \sqrt{a \cot \left(x \right)}\right)}{4 \cot \left(x \right) \sqrt{a \cot \left(x \right)}}"," ",0,"1/4*(a*cot(x)^3)^(1/2)*((a^2)^(1/4)*2^(1/2)*ln(-(a*cot(x)+(a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)+(a^2)^(1/2))/((a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)-a*cot(x)-(a^2)^(1/2)))+2*(a^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)+(a^2)^(1/4))/(a^2)^(1/4))+2*(a^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)-(a^2)^(1/4))/(a^2)^(1/4))-8*(a*cot(x))^(1/2))/cot(x)/(a*cot(x))^(1/2)","A"
31,1,164,130,0.204000," ","int(1/(a*cot(x)^3)^(1/2),x)","\frac{\cot \left(x \right) \left(\sqrt{2}\, \sqrt{a \cot \left(x \right)}\, \ln \left(-\frac{\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}-a \cot \left(x \right)-\sqrt{a^{2}}}{a \cot \left(x \right)+\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}+\sqrt{a^{2}}}\right)+2 \sqrt{2}\, \sqrt{a \cot \left(x \right)}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}+\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)+2 \sqrt{2}\, \sqrt{a \cot \left(x \right)}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}-\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)+8 \left(a^{2}\right)^{\frac{1}{4}}\right)}{4 \sqrt{a \left(\cot^{3}\left(x \right)\right)}\, \left(a^{2}\right)^{\frac{1}{4}}}"," ",0,"1/4*cot(x)*(2^(1/2)*(a*cot(x))^(1/2)*ln(-((a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)-a*cot(x)-(a^2)^(1/2))/(a*cot(x)+(a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)+(a^2)^(1/2)))+2*2^(1/2)*(a*cot(x))^(1/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)+(a^2)^(1/4))/(a^2)^(1/4))+2*2^(1/2)*(a*cot(x))^(1/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)-(a^2)^(1/4))/(a^2)^(1/4))+8*(a^2)^(1/4))/(a*cot(x)^3)^(1/2)/(a^2)^(1/4)","A"
32,1,185,160,0.115000," ","int(1/(a*cot(x)^3)^(3/2),x)","-\frac{\cot \left(x \right) \left(21 \left(a^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(a \cot \left(x \right)\right)^{\frac{7}{2}} \ln \left(-\frac{a \cot \left(x \right)+\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}+\sqrt{a^{2}}}{\left(a^{2}\right)^{\frac{1}{4}} \sqrt{a \cot \left(x \right)}\, \sqrt{2}-a \cot \left(x \right)-\sqrt{a^{2}}}\right)+42 \left(a^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(a \cot \left(x \right)\right)^{\frac{7}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}+\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)+42 \left(a^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \left(a \cot \left(x \right)\right)^{\frac{7}{2}} \arctan \left(\frac{\sqrt{2}\, \sqrt{a \cot \left(x \right)}-\left(a^{2}\right)^{\frac{1}{4}}}{\left(a^{2}\right)^{\frac{1}{4}}}\right)+56 \left(\cot^{2}\left(x \right)\right) a^{4}-24 a^{4}\right)}{84 a^{4} \left(a \left(\cot^{3}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/84*cot(x)/a^4*(21*(a^2)^(1/4)*2^(1/2)*(a*cot(x))^(7/2)*ln(-(a*cot(x)+(a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)+(a^2)^(1/2))/((a^2)^(1/4)*(a*cot(x))^(1/2)*2^(1/2)-a*cot(x)-(a^2)^(1/2)))+42*(a^2)^(1/4)*2^(1/2)*(a*cot(x))^(7/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)+(a^2)^(1/4))/(a^2)^(1/4))+42*(a^2)^(1/4)*2^(1/2)*(a*cot(x))^(7/2)*arctan((2^(1/2)*(a*cot(x))^(1/2)-(a^2)^(1/4))/(a^2)^(1/4))+56*cot(x)^2*a^4-24*a^4)/(a*cot(x)^3)^(3/2)","A"
33,1,40,58,0.170000," ","int((a*cot(x)^4)^(3/2),x)","\frac{\left(a \left(\cot^{4}\left(x \right)\right)\right)^{\frac{3}{2}} \left(-3 \left(\cot^{5}\left(x \right)\right)+5 \left(\cot^{3}\left(x \right)\right)+\frac{15 \pi}{2}-15 \,\mathrm{arccot}\left(\cot \left(x \right)\right)-15 \cot \left(x \right)\right)}{15 \cot \left(x \right)^{6}}"," ",0,"1/15*(a*cot(x)^4)^(3/2)*(-3*cot(x)^5+5*cot(x)^3+15/2*Pi-15*arccot(cot(x))-15*cot(x))/cot(x)^6","A"
34,1,27,28,0.204000," ","int((a*cot(x)^4)^(1/2),x)","\frac{\sqrt{a \left(\cot^{4}\left(x \right)\right)}\, \left(-\cot \left(x \right)+\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(x \right)\right)\right)}{\cot \left(x \right)^{2}}"," ",0,"(a*cot(x)^4)^(1/2)/cot(x)^2*(-cot(x)+1/2*Pi-arccot(cot(x)))","A"
35,1,26,27,0.221000," ","int(1/(a*cot(x)^4)^(1/2),x)","\frac{\cot \left(x \right) \left(\left(\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(x \right)\right)\right) \cot \left(x \right)+1\right)}{\sqrt{a \left(\cot^{4}\left(x \right)\right)}}"," ",0,"cot(x)*((1/2*Pi-arccot(cot(x)))*cot(x)+1)/(a*cot(x)^4)^(1/2)","A"
36,1,42,65,0.115000," ","int(1/(a*cot(x)^4)^(3/2),x)","\frac{\cot \left(x \right) \left(15 \left(\frac{\pi}{2}-\mathrm{arccot}\left(\cot \left(x \right)\right)\right) \left(\cot^{5}\left(x \right)\right)+15 \left(\cot^{4}\left(x \right)\right)-5 \left(\cot^{2}\left(x \right)\right)+3\right)}{15 \left(a \left(\cot^{4}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/15*cot(x)*(15*(1/2*Pi-arccot(cot(x)))*cot(x)^5+15*cot(x)^4-5*cot(x)^2+3)/(a*cot(x)^4)^(3/2)","A"
37,-1,0,56,180.000000," ","int((b*cot(d*x+c)^p)^n,x)","\int \left(b \left(\cot^{p}\left(d x +c \right)\right)\right)^{n}\, dx"," ",0,"int((b*cot(d*x+c)^p)^n,x)","F"
38,-1,0,58,180.000000," ","int((a*(b*cot(d*x+c))^p)^n,x)","\int \left(a \left(b \cot \left(d x +c \right)\right)^{p}\right)^{n}\, dx"," ",0,"int((a*(b*cot(d*x+c))^p)^n,x)","F"
39,0,0,81,2.955000," ","int((b*cot(f*x+e))^n*(a*sin(f*x+e))^m,x)","\int \left(b \cot \left(f x +e \right)\right)^{n} \left(a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((b*cot(f*x+e))^n*(a*sin(f*x+e))^m,x)","F"
40,0,0,82,2.637000," ","int((a*cos(f*x+e))^m*(b*cot(f*x+e))^n,x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \cot \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*cot(f*x+e))^n,x)","F"
41,0,0,66,1.619000," ","int((a*cot(f*x+e))^m*(b*cot(f*x+e))^n,x)","\int \left(a \cot \left(f x +e \right)\right)^{m} \left(b \cot \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cot(f*x+e))^m*(b*cot(f*x+e))^n,x)","F"
42,0,0,84,2.900000," ","int((b*cot(f*x+e))^n*(a*sec(f*x+e))^m,x)","\int \left(b \cot \left(f x +e \right)\right)^{n} \left(a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((b*cot(f*x+e))^n*(a*sec(f*x+e))^m,x)","F"
43,1,21900,76,4.521000," ","int((d*cot(f*x+e))^n*csc(f*x+e)^6,x)","\text{output too large to display}"," ",0,"result too large to display","C"
44,1,10907,51,1.915000," ","int((d*cot(f*x+e))^n*csc(f*x+e)^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
45,1,26,25,0.257000," ","int((d*cot(f*x+e))^n*csc(f*x+e)^2,x)","-\frac{\left(d \cot \left(f x +e \right)\right)^{1+n}}{d f \left(1+n \right)}"," ",0,"-(d*cot(f*x+e))^(1+n)/d/f/(1+n)","A"
46,0,0,49,4.186000," ","int((d*cot(f*x+e))^n*sin(f*x+e)^2,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(\sin^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((d*cot(f*x+e))^n*sin(f*x+e)^2,x)","F"
47,0,0,49,4.953000," ","int((d*cot(f*x+e))^n*sin(f*x+e)^4,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(\sin^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((d*cot(f*x+e))^n*sin(f*x+e)^4,x)","F"
48,0,0,73,1.635000," ","int((d*cot(f*x+e))^n*csc(f*x+e)^3,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(\csc^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((d*cot(f*x+e))^n*csc(f*x+e)^3,x)","F"
49,0,0,71,1.474000," ","int((d*cot(f*x+e))^n*csc(f*x+e),x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \csc \left(f x +e \right)\, dx"," ",0,"int((d*cot(f*x+e))^n*csc(f*x+e),x)","F"
50,0,0,67,2.256000," ","int((d*cot(f*x+e))^n*sin(f*x+e),x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \sin \left(f x +e \right)\, dx"," ",0,"int((d*cot(f*x+e))^n*sin(f*x+e),x)","F"
51,0,0,73,3.886000," ","int((d*cot(f*x+e))^n*sin(f*x+e)^3,x)","\int \left(d \cot \left(f x +e \right)\right)^{n} \left(\sin^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((d*cot(f*x+e))^n*sin(f*x+e)^3,x)","F"
52,0,0,81,2.952000," ","int((b*cot(f*x+e))^n*(a*csc(f*x+e))^m,x)","\int \left(b \cot \left(f x +e \right)\right)^{n} \left(a \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((b*cot(f*x+e))^n*(a*csc(f*x+e))^m,x)","F"