1,1,11,0,0.004614,"\int \cot (a+b x) \, dx","Int[Cot[a + b*x],x]","\frac{\log (\sin (a+b x))}{b}","\frac{\log (\sin (a+b x))}{b}",1,"Log[Sin[a + b*x]]/b","A",1,1,6,0.1667,1,"{3475}"
2,1,15,0,0.0087821,"\int \cot ^2(a+b x) \, dx","Int[Cot[a + b*x]^2,x]","-\frac{\cot (a+b x)}{b}-x","-\frac{\cot (a+b x)}{b}-x",1,"-x - Cot[a + b*x]/b","A",2,2,8,0.2500,1,"{3473, 8}"
3,1,28,0,0.0126411,"\int \cot ^3(a+b x) \, dx","Int[Cot[a + b*x]^3,x]","-\frac{\cot ^2(a+b x)}{2 b}-\frac{\log (\sin (a+b x))}{b}","-\frac{\cot ^2(a+b x)}{2 b}-\frac{\log (\sin (a+b x))}{b}",1,"-Cot[a + b*x]^2/(2*b) - Log[Sin[a + b*x]]/b","A",2,2,8,0.2500,1,"{3473, 3475}"
4,1,27,0,0.0173004,"\int \cot ^4(a+b x) \, dx","Int[Cot[a + b*x]^4,x]","-\frac{\cot ^3(a+b x)}{3 b}+\frac{\cot (a+b x)}{b}+x","-\frac{\cot ^3(a+b x)}{3 b}+\frac{\cot (a+b x)}{b}+x",1,"x + Cot[a + b*x]/b - Cot[a + b*x]^3/(3*b)","A",3,2,8,0.2500,1,"{3473, 8}"
5,1,42,0,0.027822,"\int \cot ^5(a+b x) \, dx","Int[Cot[a + b*x]^5,x]","-\frac{\cot ^4(a+b x)}{4 b}+\frac{\cot ^2(a+b x)}{2 b}+\frac{\log (\sin (a+b x))}{b}","-\frac{\cot ^4(a+b x)}{4 b}+\frac{\cot ^2(a+b x)}{2 b}+\frac{\log (\sin (a+b x))}{b}",1,"Cot[a + b*x]^2/(2*b) - Cot[a + b*x]^4/(4*b) + Log[Sin[a + b*x]]/b","A",3,2,8,0.2500,1,"{3473, 3475}"
6,1,45,0,0.0244749,"\int \cot ^6(a+b x) \, dx","Int[Cot[a + b*x]^6,x]","-\frac{\cot ^5(a+b x)}{5 b}+\frac{\cot ^3(a+b x)}{3 b}-\frac{\cot (a+b x)}{b}-x","-\frac{\cot ^5(a+b x)}{5 b}+\frac{\cot ^3(a+b x)}{3 b}-\frac{\cot (a+b x)}{b}-x",1,"-x - Cot[a + b*x]/b + Cot[a + b*x]^3/(3*b) - Cot[a + b*x]^5/(5*b)","A",4,2,8,0.2500,1,"{3473, 8}"
7,1,58,0,0.0297959,"\int \cot ^7(a+b x) \, dx","Int[Cot[a + b*x]^7,x]","-\frac{\cot ^6(a+b x)}{6 b}+\frac{\cot ^4(a+b x)}{4 b}-\frac{\cot ^2(a+b x)}{2 b}-\frac{\log (\sin (a+b x))}{b}","-\frac{\cot ^6(a+b x)}{6 b}+\frac{\cot ^4(a+b x)}{4 b}-\frac{\cot ^2(a+b x)}{2 b}-\frac{\log (\sin (a+b x))}{b}",1,"-Cot[a + b*x]^2/(2*b) + Cot[a + b*x]^4/(4*b) - Cot[a + b*x]^6/(6*b) - Log[Sin[a + b*x]]/b","A",4,2,8,0.2500,1,"{3473, 3475}"
8,1,57,0,0.0335139,"\int \cot ^8(a+b x) \, dx","Int[Cot[a + b*x]^8,x]","-\frac{\cot ^7(a+b x)}{7 b}+\frac{\cot ^5(a+b x)}{5 b}-\frac{\cot ^3(a+b x)}{3 b}+\frac{\cot (a+b x)}{b}+x","-\frac{\cot ^7(a+b x)}{7 b}+\frac{\cot ^5(a+b x)}{5 b}-\frac{\cot ^3(a+b x)}{3 b}+\frac{\cot (a+b x)}{b}+x",1,"x + Cot[a + b*x]/b - Cot[a + b*x]^3/(3*b) + Cot[a + b*x]^5/(5*b) - Cot[a + b*x]^7/(7*b)","A",5,2,8,0.2500,1,"{3473, 8}"
9,1,232,0,0.1917424,"\int (c \cot (a+b x))^{7/2} \, dx","Int[(c*Cot[a + b*x])^(7/2),x]","\frac{2 c^3 \sqrt{c \cot (a+b x)}}{b}+\frac{c^{7/2} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{7/2} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{c^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}-\frac{c^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}-\frac{2 c (c \cot (a+b x))^{5/2}}{5 b}","\frac{2 c^3 \sqrt{c \cot (a+b x)}}{b}+\frac{c^{7/2} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{7/2} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{c^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}-\frac{c^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}-\frac{2 c (c \cot (a+b x))^{5/2}}{5 b}",1,"(c^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b) - (c^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b) + (2*c^3*Sqrt[c*Cot[a + b*x]])/b - (2*c*(c*Cot[a + b*x])^(5/2))/(5*b) + (c^(7/2)*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b) - (c^(7/2)*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b)","A",13,9,12,0.7500,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
10,1,212,0,0.1428433,"\int (c \cot (a+b x))^{5/2} \, dx","Int[(c*Cot[a + b*x])^(5/2),x]","\frac{c^{5/2} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{5/2} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}+\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}-\frac{2 c (c \cot (a+b x))^{3/2}}{3 b}","\frac{c^{5/2} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{5/2} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}+\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}-\frac{2 c (c \cot (a+b x))^{3/2}}{3 b}",1,"-((c^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b)) + (c^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b) - (2*c*(c*Cot[a + b*x])^(3/2))/(3*b) + (c^(5/2)*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b) - (c^(5/2)*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b)","A",12,9,12,0.7500,1,"{3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
11,1,210,0,0.1395616,"\int (c \cot (a+b x))^{3/2} \, dx","Int[(c*Cot[a + b*x])^(3/2),x]","-\frac{c^{3/2} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{c^{3/2} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}+\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}-\frac{2 c \sqrt{c \cot (a+b x)}}{b}","-\frac{c^{3/2} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{c^{3/2} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}-\frac{c^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}+\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}-\frac{2 c \sqrt{c \cot (a+b x)}}{b}",1,"-((c^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b)) + (c^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b) - (2*c*Sqrt[c*Cot[a + b*x]])/b - (c^(3/2)*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b) + (c^(3/2)*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b)","A",12,9,12,0.7500,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
12,1,192,0,0.1151497,"\int \sqrt{c \cot (a+b x)} \, dx","Int[Sqrt[c*Cot[a + b*x]],x]","-\frac{\sqrt{c} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{\sqrt{c} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{\sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}","-\frac{\sqrt{c} \log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{\sqrt{c} \log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b}+\frac{\sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b}",1,"(Sqrt[c]*ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b) - (Sqrt[c]*ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]])/(Sqrt[2]*b) - (Sqrt[c]*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b) + (Sqrt[c]*Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]])/(2*Sqrt[2]*b)","A",11,8,12,0.6667,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
13,1,192,0,0.1122788,"\int \frac{1}{\sqrt{c \cot (a+b x)}} \, dx","Int[1/Sqrt[c*Cot[a + b*x]],x]","\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{c}}-\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{c}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b \sqrt{c}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b \sqrt{c}}","\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{c}}-\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{c}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b \sqrt{c}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b \sqrt{c}}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*Sqrt[c]) - ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*Sqrt[c]) + Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*Sqrt[c]) - Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*Sqrt[c])","A",11,8,12,0.6667,1,"{3476, 329, 211, 1165, 628, 1162, 617, 204}"
14,1,212,0,0.1401328,"\int \frac{1}{(c \cot (a+b x))^{3/2}} \, dx","Int[(c*Cot[a + b*x])^(-3/2),x]","\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{3/2}}-\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{3/2}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b c^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b c^{3/2}}+\frac{2}{b c \sqrt{c \cot (a+b x)}}","\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{3/2}}-\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{3/2}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b c^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b c^{3/2}}+\frac{2}{b c \sqrt{c \cot (a+b x)}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*c^(3/2))) + ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*c^(3/2)) + 2/(b*c*Sqrt[c*Cot[a + b*x]]) + Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*c^(3/2)) - Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*c^(3/2))","A",12,9,12,0.7500,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
15,1,214,0,0.1434805,"\int \frac{1}{(c \cot (a+b x))^{5/2}} \, dx","Int[(c*Cot[a + b*x])^(-5/2),x]","-\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{5/2}}+\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{5/2}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b c^{5/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b c^{5/2}}+\frac{2}{3 b c (c \cot (a+b x))^{3/2}}","-\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{5/2}}+\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{5/2}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b c^{5/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b c^{5/2}}+\frac{2}{3 b c (c \cot (a+b x))^{3/2}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*c^(5/2))) + ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*c^(5/2)) + 2/(3*b*c*(c*Cot[a + b*x])^(3/2)) - Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*c^(5/2)) + Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*c^(5/2))","A",12,9,12,0.7500,1,"{3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
16,1,234,0,0.1709807,"\int \frac{1}{(c \cot (a+b x))^{7/2}} \, dx","Int[(c*Cot[a + b*x])^(-7/2),x]","-\frac{2}{b c^3 \sqrt{c \cot (a+b x)}}-\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{7/2}}+\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{7/2}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b c^{7/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b c^{7/2}}+\frac{2}{5 b c (c \cot (a+b x))^{5/2}}","-\frac{2}{b c^3 \sqrt{c \cot (a+b x)}}-\frac{\log \left(\sqrt{c} \cot (a+b x)-\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{7/2}}+\frac{\log \left(\sqrt{c} \cot (a+b x)+\sqrt{2} \sqrt{c \cot (a+b x)}+\sqrt{c}\right)}{2 \sqrt{2} b c^{7/2}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}\right)}{\sqrt{2} b c^{7/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c \cot (a+b x)}}{\sqrt{c}}+1\right)}{\sqrt{2} b c^{7/2}}+\frac{2}{5 b c (c \cot (a+b x))^{5/2}}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*c^(7/2)) - ArcTan[1 + (Sqrt[2]*Sqrt[c*Cot[a + b*x]])/Sqrt[c]]/(Sqrt[2]*b*c^(7/2)) + 2/(5*b*c*(c*Cot[a + b*x])^(5/2)) - 2/(b*c^3*Sqrt[c*Cot[a + b*x]]) - Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] - Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*c^(7/2)) + Log[Sqrt[c] + Sqrt[c]*Cot[a + b*x] + Sqrt[2]*Sqrt[c*Cot[a + b*x]]]/(2*Sqrt[2]*b*c^(7/2))","A",13,9,12,0.7500,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
17,1,242,0,0.4695613,"\int (c \cot (a+b x))^{4/3} \, dx","Int[(c*Cot[a + b*x])^(4/3),x]","-\frac{\sqrt{3} c^{4/3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}+\frac{\sqrt{3} c^{4/3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}+\frac{c^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b}-\frac{c^{4/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b}+\frac{c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b}-\frac{3 c \sqrt[3]{c \cot (a+b x)}}{b}","-\frac{\sqrt{3} c^{4/3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}+\frac{\sqrt{3} c^{4/3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}+\frac{c^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b}-\frac{c^{4/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b}+\frac{c^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b}-\frac{3 c \sqrt[3]{c \cot (a+b x)}}{b}",1,"(c^(4/3)*ArcTan[(c*Cot[a + b*x])^(1/3)/c^(1/3)])/b - (c^(4/3)*ArcTan[Sqrt[3] - (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)])/(2*b) + (c^(4/3)*ArcTan[Sqrt[3] + (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)])/(2*b) - (3*c*(c*Cot[a + b*x])^(1/3))/b - (Sqrt[3]*c^(4/3)*Log[c^(2/3) - Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b) + (Sqrt[3]*c^(4/3)*Log[c^(2/3) + Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b)","A",13,9,12,0.7500,1,"{3473, 3476, 329, 209, 634, 618, 204, 628, 203}"
18,1,225,0,0.3804648,"\int (c \cot (a+b x))^{2/3} \, dx","Int[(c*Cot[a + b*x])^(2/3),x]","-\frac{\sqrt{3} c^{2/3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}+\frac{\sqrt{3} c^{2/3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}-\frac{c^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b}+\frac{c^{2/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b}-\frac{c^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b}","-\frac{\sqrt{3} c^{2/3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}+\frac{\sqrt{3} c^{2/3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b}-\frac{c^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b}+\frac{c^{2/3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b}-\frac{c^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b}",1,"-((c^(2/3)*ArcTan[(c*Cot[a + b*x])^(1/3)/c^(1/3)])/b) + (c^(2/3)*ArcTan[Sqrt[3] - (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)])/(2*b) - (c^(2/3)*ArcTan[Sqrt[3] + (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)])/(2*b) - (Sqrt[3]*c^(2/3)*Log[c^(2/3) - Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b) + (Sqrt[3]*c^(2/3)*Log[c^(2/3) + Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b)","A",12,8,12,0.6667,1,"{3476, 329, 295, 634, 618, 204, 628, 203}"
19,1,131,0,0.1016227,"\int \sqrt[3]{c \cot (a+b x)} \, dx","Int[(c*Cot[a + b*x])^(1/3),x]","\frac{\sqrt[3]{c} \log \left((c \cot (a+b x))^{2/3}+c^{2/3}\right)}{2 b}-\frac{\sqrt[3]{c} \log \left(-c^{2/3} (c \cot (a+b x))^{2/3}+(c \cot (a+b x))^{4/3}+c^{4/3}\right)}{4 b}+\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{c^{2/3}-2 (c \cot (a+b x))^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 b}","\frac{\sqrt[3]{c} \log \left((c \cot (a+b x))^{2/3}+c^{2/3}\right)}{2 b}-\frac{\sqrt[3]{c} \log \left(-c^{2/3} (c \cot (a+b x))^{2/3}+(c \cot (a+b x))^{4/3}+c^{4/3}\right)}{4 b}+\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{c^{2/3}-2 (c \cot (a+b x))^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 b}",1,"(Sqrt[3]*c^(1/3)*ArcTan[(c^(2/3) - 2*(c*Cot[a + b*x])^(2/3))/(Sqrt[3]*c^(2/3))])/(2*b) + (c^(1/3)*Log[c^(2/3) + (c*Cot[a + b*x])^(2/3)])/(2*b) - (c^(1/3)*Log[c^(4/3) - c^(2/3)*(c*Cot[a + b*x])^(2/3) + (c*Cot[a + b*x])^(4/3)])/(4*b)","A",9,9,12,0.7500,1,"{3476, 329, 275, 292, 31, 634, 617, 204, 628}"
20,1,131,0,0.0963444,"\int \frac{1}{\sqrt[3]{c \cot (a+b x)}} \, dx","Int[(c*Cot[a + b*x])^(-1/3),x]","-\frac{\log \left((c \cot (a+b x))^{2/3}+c^{2/3}\right)}{2 b \sqrt[3]{c}}+\frac{\log \left(-c^{2/3} (c \cot (a+b x))^{2/3}+(c \cot (a+b x))^{4/3}+c^{4/3}\right)}{4 b \sqrt[3]{c}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{c^{2/3}-2 (c \cot (a+b x))^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 b \sqrt[3]{c}}","-\frac{\log \left((c \cot (a+b x))^{2/3}+c^{2/3}\right)}{2 b \sqrt[3]{c}}+\frac{\log \left(-c^{2/3} (c \cot (a+b x))^{2/3}+(c \cot (a+b x))^{4/3}+c^{4/3}\right)}{4 b \sqrt[3]{c}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{c^{2/3}-2 (c \cot (a+b x))^{2/3}}{\sqrt{3} c^{2/3}}\right)}{2 b \sqrt[3]{c}}",1,"(Sqrt[3]*ArcTan[(c^(2/3) - 2*(c*Cot[a + b*x])^(2/3))/(Sqrt[3]*c^(2/3))])/(2*b*c^(1/3)) - Log[c^(2/3) + (c*Cot[a + b*x])^(2/3)]/(2*b*c^(1/3)) + Log[c^(4/3) - c^(2/3)*(c*Cot[a + b*x])^(2/3) + (c*Cot[a + b*x])^(4/3)]/(4*b*c^(1/3))","A",9,9,12,0.7500,1,"{3476, 329, 275, 200, 31, 634, 617, 204, 628}"
21,1,225,0,0.3095498,"\int \frac{1}{(c \cot (a+b x))^{2/3}} \, dx","Int[(c*Cot[a + b*x])^(-2/3),x]","\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{2/3}}-\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b c^{2/3}}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b c^{2/3}}","\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{2/3}}-\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b c^{2/3}}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b c^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b c^{2/3}}",1,"-(ArcTan[(c*Cot[a + b*x])^(1/3)/c^(1/3)]/(b*c^(2/3))) + ArcTan[Sqrt[3] - (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)]/(2*b*c^(2/3)) - ArcTan[Sqrt[3] + (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)]/(2*b*c^(2/3)) + (Sqrt[3]*Log[c^(2/3) - Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b*c^(2/3)) - (Sqrt[3]*Log[c^(2/3) + Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b*c^(2/3))","A",12,8,12,0.6667,1,"{3476, 329, 209, 634, 618, 204, 628, 203}"
22,1,244,0,0.4245632,"\int \frac{1}{(c \cot (a+b x))^{4/3}} \, dx","Int[(c*Cot[a + b*x])^(-4/3),x]","\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{4/3}}-\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b c^{4/3}}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b c^{4/3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b c^{4/3}}+\frac{3}{b c \sqrt[3]{c \cot (a+b x)}}","\frac{\sqrt{3} \log \left(-\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{4/3}}-\frac{\sqrt{3} \log \left(\sqrt{3} \sqrt[3]{c} \sqrt[3]{c \cot (a+b x)}+(c \cot (a+b x))^{2/3}+c^{2/3}\right)}{4 b c^{4/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{b c^{4/3}}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}\right)}{2 b c^{4/3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{c \cot (a+b x)}}{\sqrt[3]{c}}+\sqrt{3}\right)}{2 b c^{4/3}}+\frac{3}{b c \sqrt[3]{c \cot (a+b x)}}",1,"ArcTan[(c*Cot[a + b*x])^(1/3)/c^(1/3)]/(b*c^(4/3)) - ArcTan[Sqrt[3] - (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)]/(2*b*c^(4/3)) + ArcTan[Sqrt[3] + (2*(c*Cot[a + b*x])^(1/3))/c^(1/3)]/(2*b*c^(4/3)) + 3/(b*c*(c*Cot[a + b*x])^(1/3)) + (Sqrt[3]*Log[c^(2/3) - Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b*c^(4/3)) - (Sqrt[3]*Log[c^(2/3) + Sqrt[3]*c^(1/3)*(c*Cot[a + b*x])^(1/3) + (c*Cot[a + b*x])^(2/3)])/(4*b*c^(4/3))","A",13,9,12,0.7500,1,"{3474, 3476, 329, 295, 634, 618, 204, 628, 203}"
23,1,46,0,0.0279433,"\int \cot ^n(a+b x) \, dx","Int[Cot[a + b*x]^n,x]","-\frac{\cot ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(a+b x)\right)}{b (n+1)}","-\frac{\cot ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(a+b x)\right)}{b (n+1)}",1,"-((Cot[a + b*x]^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Cot[a + b*x]^2])/(b*(1 + n)))","A",2,2,8,0.2500,1,"{3476, 364}"
24,1,51,0,0.0318807,"\int (b \cot (c+d x))^n \, dx","Int[(b*Cot[c + d*x])^n,x]","-\frac{(b \cot (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(c+d x)\right)}{b d (n+1)}","-\frac{(b \cot (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(c+d x)\right)}{b d (n+1)}",1,"-(((b*Cot[c + d*x])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Cot[c + d*x]^2])/(b*d*(1 + n)))","A",2,2,10,0.2000,1,"{3476, 364}"
25,1,36,0,0.0182863,"\int \left(a \cot ^2(x)\right)^{3/2} \, dx","Int[(a*Cot[x]^2)^(3/2),x]","-\frac{1}{2} a \cot (x) \sqrt{a \cot ^2(x)}-a \tan (x) \sqrt{a \cot ^2(x)} \log (\sin (x))","-\frac{1}{2} a \cot (x) \sqrt{a \cot ^2(x)}-a \tan (x) \sqrt{a \cot ^2(x)} \log (\sin (x))",1,"-(a*Cot[x]*Sqrt[a*Cot[x]^2])/2 - a*Sqrt[a*Cot[x]^2]*Log[Sin[x]]*Tan[x]","A",3,3,10,0.3000,1,"{3658, 3473, 3475}"
26,1,16,0,0.0205653,"\int \sqrt{a \cot ^2(x)} \, dx","Int[Sqrt[a*Cot[x]^2],x]","\tan (x) \sqrt{a \cot ^2(x)} \log (\sin (x))","\tan (x) \sqrt{a \cot ^2(x)} \log (\sin (x))",1,"Sqrt[a*Cot[x]^2]*Log[Sin[x]]*Tan[x]","A",2,2,10,0.2000,1,"{3658, 3475}"
27,1,17,0,0.0117983,"\int \frac{1}{\sqrt{a \cot ^2(x)}} \, dx","Int[1/Sqrt[a*Cot[x]^2],x]","-\frac{\cot (x) \log (\cos (x))}{\sqrt{a \cot ^2(x)}}","-\frac{\cot (x) \log (\cos (x))}{\sqrt{a \cot ^2(x)}}",1,"-((Cot[x]*Log[Cos[x]])/Sqrt[a*Cot[x]^2])","A",2,2,10,0.2000,1,"{3658, 3475}"
28,1,39,0,0.0181165,"\int \frac{1}{\left(a \cot ^2(x)\right)^{3/2}} \, dx","Int[(a*Cot[x]^2)^(-3/2),x]","\frac{\tan (x)}{2 a \sqrt{a \cot ^2(x)}}+\frac{\cot (x) \log (\cos (x))}{a \sqrt{a \cot ^2(x)}}","\frac{\tan (x)}{2 a \sqrt{a \cot ^2(x)}}+\frac{\cot (x) \log (\cos (x))}{a \sqrt{a \cot ^2(x)}}",1,"(Cot[x]*Log[Cos[x]])/(a*Sqrt[a*Cot[x]^2]) + Tan[x]/(2*a*Sqrt[a*Cot[x]^2])","A",3,3,10,0.3000,1,"{3658, 3473, 3475}"
29,1,200,0,0.097225,"\int \left(a \cot ^3(x)\right)^{3/2} \, dx","Int[(a*Cot[x]^3)^(3/2),x]","-\frac{2}{7} a \cot ^2(x) \sqrt{a \cot ^3(x)}+\frac{2}{3} a \sqrt{a \cot ^3(x)}-\frac{a \sqrt{a \cot ^3(x)} \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{a \sqrt{a \cot ^3(x)} \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{a \sqrt{a \cot ^3(x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}-\frac{a \sqrt{a \cot ^3(x)} \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}","-\frac{2}{7} a \cot ^2(x) \sqrt{a \cot ^3(x)}+\frac{2}{3} a \sqrt{a \cot ^3(x)}-\frac{a \sqrt{a \cot ^3(x)} \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{a \sqrt{a \cot ^3(x)} \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{a \sqrt{a \cot ^3(x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}-\frac{a \sqrt{a \cot ^3(x)} \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}",1,"(2*a*Sqrt[a*Cot[x]^3])/3 + (a*ArcTan[1 - Sqrt[2]*Sqrt[Cot[x]]]*Sqrt[a*Cot[x]^3])/(Sqrt[2]*Cot[x]^(3/2)) - (a*ArcTan[1 + Sqrt[2]*Sqrt[Cot[x]]]*Sqrt[a*Cot[x]^3])/(Sqrt[2]*Cot[x]^(3/2)) - (2*a*Cot[x]^2*Sqrt[a*Cot[x]^3])/7 - (a*Sqrt[a*Cot[x]^3]*Log[1 - Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*Cot[x]^(3/2)) + (a*Sqrt[a*Cot[x]^3]*Log[1 + Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*Cot[x]^(3/2))","A",14,10,10,1.000,1,"{3658, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
30,1,176,0,0.0872821,"\int \sqrt{a \cot ^3(x)} \, dx","Int[Sqrt[a*Cot[x]^3],x]","-\frac{\sqrt{a \cot ^3(x)} \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{\sqrt{a \cot ^3(x)} \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}-\frac{\sqrt{a \cot ^3(x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{\sqrt{a \cot ^3(x)} \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}-2 \tan (x) \sqrt{a \cot ^3(x)}","-\frac{\sqrt{a \cot ^3(x)} \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{\sqrt{a \cot ^3(x)} \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \cot ^{\frac{3}{2}}(x)}-\frac{\sqrt{a \cot ^3(x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}+\frac{\sqrt{a \cot ^3(x)} \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} \cot ^{\frac{3}{2}}(x)}-2 \tan (x) \sqrt{a \cot ^3(x)}",1,"-((ArcTan[1 - Sqrt[2]*Sqrt[Cot[x]]]*Sqrt[a*Cot[x]^3])/(Sqrt[2]*Cot[x]^(3/2))) + (ArcTan[1 + Sqrt[2]*Sqrt[Cot[x]]]*Sqrt[a*Cot[x]^3])/(Sqrt[2]*Cot[x]^(3/2)) - (Sqrt[a*Cot[x]^3]*Log[1 - Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*Cot[x]^(3/2)) + (Sqrt[a*Cot[x]^3]*Log[1 + Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*Cot[x]^(3/2)) - 2*Sqrt[a*Cot[x]^3]*Tan[x]","A",13,10,10,1.000,1,"{3658, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
31,1,176,0,0.0902691,"\int \frac{1}{\sqrt{a \cot ^3(x)}} \, dx","Int[1/Sqrt[a*Cot[x]^3],x]","\frac{2 \cot (x)}{\sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} \sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} \sqrt{a \cot ^3(x)}}","\frac{2 \cot (x)}{\sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} \sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} \sqrt{a \cot ^3(x)}}",1,"(2*Cot[x])/Sqrt[a*Cot[x]^3] - (ArcTan[1 - Sqrt[2]*Sqrt[Cot[x]]]*Cot[x]^(3/2))/(Sqrt[2]*Sqrt[a*Cot[x]^3]) + (ArcTan[1 + Sqrt[2]*Sqrt[Cot[x]]]*Cot[x]^(3/2))/(Sqrt[2]*Sqrt[a*Cot[x]^3]) + (Cot[x]^(3/2)*Log[1 - Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*Sqrt[a*Cot[x]^3]) - (Cot[x]^(3/2)*Log[1 + Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*Sqrt[a*Cot[x]^3])","A",13,10,10,1.000,1,"{3658, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
32,1,212,0,0.096023,"\int \frac{1}{\left(a \cot ^3(x)\right)^{3/2}} \, dx","Int[(a*Cot[x]^3)^(-3/2),x]","-\frac{2}{3 a \sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} a \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} a \sqrt{a \cot ^3(x)}}+\frac{2 \tan ^2(x)}{7 a \sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} a \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} a \sqrt{a \cot ^3(x)}}","-\frac{2}{3 a \sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)-\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} a \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \log \left(\cot (x)+\sqrt{2} \sqrt{\cot (x)}+1\right)}{2 \sqrt{2} a \sqrt{a \cot ^3(x)}}+\frac{2 \tan ^2(x)}{7 a \sqrt{a \cot ^3(x)}}+\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (x)}\right)}{\sqrt{2} a \sqrt{a \cot ^3(x)}}-\frac{\cot ^{\frac{3}{2}}(x) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (x)}+1\right)}{\sqrt{2} a \sqrt{a \cot ^3(x)}}",1,"-2/(3*a*Sqrt[a*Cot[x]^3]) + (ArcTan[1 - Sqrt[2]*Sqrt[Cot[x]]]*Cot[x]^(3/2))/(Sqrt[2]*a*Sqrt[a*Cot[x]^3]) - (ArcTan[1 + Sqrt[2]*Sqrt[Cot[x]]]*Cot[x]^(3/2))/(Sqrt[2]*a*Sqrt[a*Cot[x]^3]) + (Cot[x]^(3/2)*Log[1 - Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*a*Sqrt[a*Cot[x]^3]) - (Cot[x]^(3/2)*Log[1 + Sqrt[2]*Sqrt[Cot[x]] + Cot[x]])/(2*Sqrt[2]*a*Sqrt[a*Cot[x]^3]) + (2*Tan[x]^2)/(7*a*Sqrt[a*Cot[x]^3])","A",14,10,10,1.000,1,"{3658, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
33,1,70,0,0.0271455,"\int \left(a \cot ^4(x)\right)^{3/2} \, dx","Int[(a*Cot[x]^4)^(3/2),x]","-\frac{1}{5} a \cot ^3(x) \sqrt{a \cot ^4(x)}+\frac{1}{3} a \cot (x) \sqrt{a \cot ^4(x)}-a x \tan ^2(x) \sqrt{a \cot ^4(x)}-a \tan (x) \sqrt{a \cot ^4(x)}","-\frac{1}{5} a \cot ^3(x) \sqrt{a \cot ^4(x)}+\frac{1}{3} a \cot (x) \sqrt{a \cot ^4(x)}-a x \tan ^2(x) \sqrt{a \cot ^4(x)}-a \tan (x) \sqrt{a \cot ^4(x)}",1,"(a*Cot[x]*Sqrt[a*Cot[x]^4])/3 - (a*Cot[x]^3*Sqrt[a*Cot[x]^4])/5 - a*Sqrt[a*Cot[x]^4]*Tan[x] - a*x*Sqrt[a*Cot[x]^4]*Tan[x]^2","A",5,3,10,0.3000,1,"{3658, 3473, 8}"
34,1,32,0,0.0154425,"\int \sqrt{a \cot ^4(x)} \, dx","Int[Sqrt[a*Cot[x]^4],x]","-x \tan ^2(x) \sqrt{a \cot ^4(x)}-\tan (x) \sqrt{a \cot ^4(x)}","-x \tan ^2(x) \sqrt{a \cot ^4(x)}-\tan (x) \sqrt{a \cot ^4(x)}",1,"-(Sqrt[a*Cot[x]^4]*Tan[x]) - x*Sqrt[a*Cot[x]^4]*Tan[x]^2","A",3,3,10,0.3000,1,"{3658, 3473, 8}"
35,1,31,0,0.0161043,"\int \frac{1}{\sqrt{a \cot ^4(x)}} \, dx","Int[1/Sqrt[a*Cot[x]^4],x]","\frac{\cot (x)}{\sqrt{a \cot ^4(x)}}-\frac{x \cot ^2(x)}{\sqrt{a \cot ^4(x)}}","\frac{\cot (x)}{\sqrt{a \cot ^4(x)}}-\frac{x \cot ^2(x)}{\sqrt{a \cot ^4(x)}}",1,"Cot[x]/Sqrt[a*Cot[x]^4] - (x*Cot[x]^2)/Sqrt[a*Cot[x]^4]","A",3,3,10,0.3000,1,"{3658, 3473, 8}"
36,1,77,0,0.0257301,"\int \frac{1}{\left(a \cot ^4(x)\right)^{3/2}} \, dx","Int[(a*Cot[x]^4)^(-3/2),x]","-\frac{x \cot ^2(x)}{a \sqrt{a \cot ^4(x)}}+\frac{\cot (x)}{a \sqrt{a \cot ^4(x)}}+\frac{\tan ^3(x)}{5 a \sqrt{a \cot ^4(x)}}-\frac{\tan (x)}{3 a \sqrt{a \cot ^4(x)}}","-\frac{x \cot ^2(x)}{a \sqrt{a \cot ^4(x)}}+\frac{\cot (x)}{a \sqrt{a \cot ^4(x)}}+\frac{\tan ^3(x)}{5 a \sqrt{a \cot ^4(x)}}-\frac{\tan (x)}{3 a \sqrt{a \cot ^4(x)}}",1,"Cot[x]/(a*Sqrt[a*Cot[x]^4]) - (x*Cot[x]^2)/(a*Sqrt[a*Cot[x]^4]) - Tan[x]/(3*a*Sqrt[a*Cot[x]^4]) + Tan[x]^3/(5*a*Sqrt[a*Cot[x]^4])","A",5,3,10,0.3000,1,"{3658, 3473, 8}"
37,1,60,0,0.0397252,"\int \left(b \cot ^p(c+d x)\right)^n \, dx","Int[(b*Cot[c + d*x]^p)^n,x]","-\frac{\cot (c+d x) \left(b \cot ^p(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\cot ^2(c+d x)\right)}{d (n p+1)}","-\frac{\cot (c+d x) \left(b \cot ^p(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\cot ^2(c+d x)\right)}{d (n p+1)}",1,"-((Cot[c + d*x]*(b*Cot[c + d*x]^p)^n*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Cot[c + d*x]^2])/(d*(1 + n*p)))","A",3,3,12,0.2500,1,"{3659, 3476, 364}"
38,1,62,0,0.0449681,"\int \left(a (b \cot (c+d x))^p\right)^n \, dx","Int[(a*(b*Cot[c + d*x])^p)^n,x]","-\frac{\cot (c+d x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\cot ^2(c+d x)\right) \left(a (b \cot (c+d x))^p\right)^n}{d (n p+1)}","-\frac{\cot (c+d x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\cot ^2(c+d x)\right) \left(a (b \cot (c+d x))^p\right)^n}{d (n p+1)}",1,"-((Cot[c + d*x]*(a*(b*Cot[c + d*x])^p)^n*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Cot[c + d*x]^2])/(d*(1 + n*p)))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
39,1,87,0,0.0966597,"\int (b \cot (e+f x))^n (a \sin (e+f x))^m \, dx","Int[(b*Cot[e + f*x])^n*(a*Sin[e + f*x])^m,x]","-\frac{(a \sin (e+f x))^m (b \cot (e+f x))^{n+1} \sin ^2(e+f x)^{\frac{1}{2} (-m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{n+3}{2};\cos ^2(e+f x)\right)}{b f (n+1)}","-\frac{(a \sin (e+f x))^m (b \cot (e+f x))^{n+1} \sin ^2(e+f x)^{\frac{1}{2} (-m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{n+3}{2};\cos ^2(e+f x)\right)}{b f (n+1)}",1,"-(((b*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[(1 + n)/2, (1 - m + n)/2, (3 + n)/2, Cos[e + f*x]^2]*(a*Sin[e + f*x])^m*(Sin[e + f*x]^2)^((1 - m + n)/2))/(b*f*(1 + n)))","A",2,2,21,0.09524,1,"{2603, 2617}"
40,1,84,0,0.1013816,"\int (a \cos (e+f x))^m (b \cot (e+f x))^n \, dx","Int[(a*Cos[e + f*x])^m*(b*Cot[e + f*x])^n,x]","-\frac{\sin ^2(e+f x)^{\frac{n+1}{2}} (a \cos (e+f x))^m (b \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(e+f x)\right)}{b f (m+n+1)}","-\frac{\sin ^2(e+f x)^{\frac{n+1}{2}} (a \cos (e+f x))^m (b \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(e+f x)\right)}{b f (m+n+1)}",1,"-(((a*Cos[e + f*x])^m*(b*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[(1 + n)/2, (1 + m + n)/2, (3 + m + n)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((1 + n)/2))/(b*f*(1 + m + n)))","A",2,2,21,0.09524,1,"{2602, 2576}"
41,1,64,0,0.0373172,"\int (a \cot (e+f x))^m (b \cot (e+f x))^n \, dx","Int[(a*Cot[e + f*x])^m*(b*Cot[e + f*x])^n,x]","-\frac{(a \cot (e+f x))^{m+1} (b \cot (e+f x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);-\cot ^2(e+f x)\right)}{a f (m+n+1)}","-\frac{(a \cot (e+f x))^{m+1} (b \cot (e+f x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);-\cot ^2(e+f x)\right)}{a f (m+n+1)}",1,"-(((a*Cot[e + f*x])^(1 + m)*(b*Cot[e + f*x])^n*Hypergeometric2F1[1, (1 + m + n)/2, (3 + m + n)/2, -Cot[e + f*x]^2])/(a*f*(1 + m + n)))","A",3,3,21,0.1429,1,"{20, 3476, 364}"
42,1,90,0,0.1534488,"\int (b \cot (e+f x))^n (a \sec (e+f x))^m \, dx","Int[(b*Cot[e + f*x])^n*(a*Sec[e + f*x])^m,x]","-\frac{\sin ^2(e+f x)^{\frac{n+1}{2}} (a \sec (e+f x))^m (b \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);\cos ^2(e+f x)\right)}{b f (-m+n+1)}","-\frac{\sin ^2(e+f x)^{\frac{n+1}{2}} (a \sec (e+f x))^m (b \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (-m+n+1);\frac{1}{2} (-m+n+3);\cos ^2(e+f x)\right)}{b f (-m+n+1)}",1,"-(((b*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[(1 + n)/2, (1 - m + n)/2, (3 - m + n)/2, Cos[e + f*x]^2]*(a*Sec[e + f*x])^m*(Sin[e + f*x]^2)^((1 + n)/2))/(b*f*(1 - m + n)))","A",3,3,21,0.1429,1,"{2618, 2602, 2576}"
43,1,76,0,0.070749,"\int (d \cot (e+f x))^n \csc ^6(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Csc[e + f*x]^6,x]","-\frac{2 (d \cot (e+f x))^{n+3}}{d^3 f (n+3)}-\frac{(d \cot (e+f x))^{n+5}}{d^5 f (n+5)}-\frac{(d \cot (e+f x))^{n+1}}{d f (n+1)}","-\frac{2 (d \cot (e+f x))^{n+3}}{d^3 f (n+3)}-\frac{(d \cot (e+f x))^{n+5}}{d^5 f (n+5)}-\frac{(d \cot (e+f x))^{n+1}}{d f (n+1)}",1,"-((d*Cot[e + f*x])^(1 + n)/(d*f*(1 + n))) - (2*(d*Cot[e + f*x])^(3 + n))/(d^3*f*(3 + n)) - (d*Cot[e + f*x])^(5 + n)/(d^5*f*(5 + n))","A",3,2,19,0.1053,1,"{2607, 270}"
44,1,51,0,0.0527326,"\int (d \cot (e+f x))^n \csc ^4(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Csc[e + f*x]^4,x]","-\frac{(d \cot (e+f x))^{n+3}}{d^3 f (n+3)}-\frac{(d \cot (e+f x))^{n+1}}{d f (n+1)}","-\frac{(d \cot (e+f x))^{n+3}}{d^3 f (n+3)}-\frac{(d \cot (e+f x))^{n+1}}{d f (n+1)}",1,"-((d*Cot[e + f*x])^(1 + n)/(d*f*(1 + n))) - (d*Cot[e + f*x])^(3 + n)/(d^3*f*(3 + n))","A",3,2,19,0.1053,1,"{2607, 14}"
45,1,25,0,0.042452,"\int (d \cot (e+f x))^n \csc ^2(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Csc[e + f*x]^2,x]","-\frac{(d \cot (e+f x))^{n+1}}{d f (n+1)}","-\frac{(d \cot (e+f x))^{n+1}}{d f (n+1)}",1,"-((d*Cot[e + f*x])^(1 + n)/(d*f*(1 + n)))","A",2,2,19,0.1053,1,"{2607, 32}"
46,1,51,0,0.0491075,"\int (d \cot (e+f x))^n \sin ^2(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Sin[e + f*x]^2,x]","-\frac{(d \cot (e+f x))^{n+1} \, _2F_1\left(2,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(e+f x)\right)}{d f (n+1)}","-\frac{(d \cot (e+f x))^{n+1} \, _2F_1\left(2,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[2, (1 + n)/2, (3 + n)/2, -Cot[e + f*x]^2])/(d*f*(1 + n)))","A",2,2,19,0.1053,1,"{2607, 364}"
47,1,51,0,0.0479054,"\int (d \cot (e+f x))^n \sin ^4(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Sin[e + f*x]^4,x]","-\frac{(d \cot (e+f x))^{n+1} \, _2F_1\left(3,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(e+f x)\right)}{d f (n+1)}","-\frac{(d \cot (e+f x))^{n+1} \, _2F_1\left(3,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[3, (1 + n)/2, (3 + n)/2, -Cot[e + f*x]^2])/(d*f*(1 + n)))","A",2,2,19,0.1053,1,"{2607, 364}"
48,1,79,0,0.0405785,"\int (d \cot (e+f x))^n \csc ^3(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Csc[e + f*x]^3,x]","-\frac{\csc ^3(e+f x) \sin ^2(e+f x)^{\frac{n+4}{2}} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+4}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}","-\frac{\csc ^3(e+f x) \sin ^2(e+f x)^{\frac{n+4}{2}} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+4}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cot[e + f*x])^(1 + n)*Csc[e + f*x]^3*Hypergeometric2F1[(1 + n)/2, (4 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((4 + n)/2))/(d*f*(1 + n)))","A",1,1,19,0.05263,1,"{2617}"
49,1,77,0,0.029108,"\int (d \cot (e+f x))^n \csc (e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Csc[e + f*x],x]","-\frac{\csc (e+f x) \sin ^2(e+f x)^{\frac{n+2}{2}} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}","-\frac{\csc (e+f x) \sin ^2(e+f x)^{\frac{n+2}{2}} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n+1}{2},\frac{n+2}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cot[e + f*x])^(1 + n)*Csc[e + f*x]*Hypergeometric2F1[(1 + n)/2, (2 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((2 + n)/2))/(d*f*(1 + n)))","A",1,1,17,0.05882,1,"{2617}"
50,1,73,0,0.0411376,"\int (d \cot (e+f x))^n \sin (e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Sin[e + f*x],x]","-\frac{\sin (e+f x) \sin ^2(e+f x)^{n/2} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}","-\frac{\sin (e+f x) \sin ^2(e+f x)^{n/2} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[n/2, (1 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*Sin[e + f*x]*(Sin[e + f*x]^2)^(n/2))/(d*f*(1 + n)))","A",1,1,17,0.05882,1,"{2617}"
51,1,79,0,0.0424696,"\int (d \cot (e+f x))^n \sin ^3(e+f x) \, dx","Int[(d*Cot[e + f*x])^n*Sin[e + f*x]^3,x]","-\frac{\sin ^3(e+f x) \sin ^2(e+f x)^{\frac{n-2}{2}} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n-2}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}","-\frac{\sin ^3(e+f x) \sin ^2(e+f x)^{\frac{n-2}{2}} (d \cot (e+f x))^{n+1} \, _2F_1\left(\frac{n-2}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[(-2 + n)/2, (1 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*Sin[e + f*x]^3*(Sin[e + f*x]^2)^((-2 + n)/2))/(d*f*(1 + n)))","A",1,1,19,0.05263,1,"{2617}"
52,1,83,0,0.0457312,"\int (b \cot (e+f x))^n (a \csc (e+f x))^m \, dx","Int[(b*Cot[e + f*x])^n*(a*Csc[e + f*x])^m,x]","-\frac{(a \csc (e+f x))^m (b \cot (e+f x))^{n+1} \sin ^2(e+f x)^{\frac{1}{2} (m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{n+3}{2};\cos ^2(e+f x)\right)}{b f (n+1)}","-\frac{(a \csc (e+f x))^m (b \cot (e+f x))^{n+1} \sin ^2(e+f x)^{\frac{1}{2} (m+n+1)} \, _2F_1\left(\frac{n+1}{2},\frac{1}{2} (m+n+1);\frac{n+3}{2};\cos ^2(e+f x)\right)}{b f (n+1)}",1,"-(((b*Cot[e + f*x])^(1 + n)*(a*Csc[e + f*x])^m*Hypergeometric2F1[(1 + n)/2, (1 + m + n)/2, (3 + n)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^((1 + m + n)/2))/(b*f*(1 + n)))","A",1,1,21,0.04762,1,"{2617}"