1,1,24,11,0.787483,"\text{Not used}","int(cot(a + b*x),x)","-x\,1{}\mathrm{i}+\frac{\ln\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}-1\right)}{b}","Not used",1,"log(exp(a*2i)*exp(b*x*2i) - 1)/b - x*1i","B"
2,1,15,15,0.095605,"\text{Not used}","int(cot(a + b*x)^2,x)","-x-\frac{\mathrm{cot}\left(a+b\,x\right)}{b}","Not used",1,"- x - cot(a + b*x)/b","B"
3,1,78,28,3.028110,"\text{Not used}","int(cot(a + b*x)^3,x)","x\,1{}\mathrm{i}-\frac{\ln\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}-1\right)}{b}+\frac{2}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)}+\frac{2}{b\,\left(1+{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}-2\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\right)}","Not used",1,"x*1i - log(exp(a*2i)*exp(b*x*2i) - 1)/b + 2/(b*(exp(a*2i + b*x*2i) - 1)) + 2/(b*(exp(a*4i + b*x*4i) - 2*exp(a*2i + b*x*2i) + 1))","B"
4,1,23,27,0.124822,"\text{Not used}","int(cot(a + b*x)^4,x)","x+\frac{\mathrm{cot}\left(a+b\,x\right)-\frac{{\mathrm{cot}\left(a+b\,x\right)}^3}{3}}{b}","Not used",1,"x + (cot(a + b*x) - cot(a + b*x)^3/3)/b","B"
5,1,182,42,4.807590,"\text{Not used}","int(cot(a + b*x)^5,x)","-x\,1{}\mathrm{i}+\frac{\ln\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}-1\right)}{b}-\frac{4}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)}-\frac{8}{b\,\left(1+{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}-2\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\right)}-\frac{8}{b\,\left(3\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-3\,{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}-1\right)}-\frac{4}{b\,\left(1+6\,{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}-4\,{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}+{\mathrm{e}}^{a\,8{}\mathrm{i}+b\,x\,8{}\mathrm{i}}-4\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\right)}","Not used",1,"log(exp(a*2i)*exp(b*x*2i) - 1)/b - x*1i - 4/(b*(exp(a*2i + b*x*2i) - 1)) - 8/(b*(exp(a*4i + b*x*4i) - 2*exp(a*2i + b*x*2i) + 1)) - 8/(b*(3*exp(a*2i + b*x*2i) - 3*exp(a*4i + b*x*4i) + exp(a*6i + b*x*6i) - 1)) - 4/(b*(6*exp(a*4i + b*x*4i) - 4*exp(a*2i + b*x*2i) - 4*exp(a*6i + b*x*6i) + exp(a*8i + b*x*8i) + 1))","B"
6,1,36,45,0.085722,"\text{Not used}","int(cot(a + b*x)^6,x)","-x-\frac{\frac{{\mathrm{cot}\left(a+b\,x\right)}^5}{5}-\frac{{\mathrm{cot}\left(a+b\,x\right)}^3}{3}+\mathrm{cot}\left(a+b\,x\right)}{b}","Not used",1,"- x - (cot(a + b*x) - cot(a + b*x)^3/3 + cot(a + b*x)^5/5)/b","B"
7,1,340,58,7.462743,"\text{Not used}","int(cot(a + b*x)^7,x)","x\,1{}\mathrm{i}-\frac{\ln\left({\mathrm{e}}^{a\,2{}\mathrm{i}}\,{\mathrm{e}}^{b\,x\,2{}\mathrm{i}}-1\right)}{b}+\frac{32}{b\,\left(5\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-10\,{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+10\,{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}-5\,{\mathrm{e}}^{a\,8{}\mathrm{i}+b\,x\,8{}\mathrm{i}}+{\mathrm{e}}^{a\,10{}\mathrm{i}+b\,x\,10{}\mathrm{i}}-1\right)}+\frac{32}{3\,b\,\left(1+15\,{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}-20\,{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}+15\,{\mathrm{e}}^{a\,8{}\mathrm{i}+b\,x\,8{}\mathrm{i}}-6\,{\mathrm{e}}^{a\,10{}\mathrm{i}+b\,x\,10{}\mathrm{i}}+{\mathrm{e}}^{a\,12{}\mathrm{i}+b\,x\,12{}\mathrm{i}}-6\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\right)}+\frac{6}{b\,\left({\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-1\right)}+\frac{18}{b\,\left(1+{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}-2\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\right)}+\frac{104}{3\,b\,\left(3\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}-3\,{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}+{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}-1\right)}+\frac{44}{b\,\left(1+6\,{\mathrm{e}}^{a\,4{}\mathrm{i}+b\,x\,4{}\mathrm{i}}-4\,{\mathrm{e}}^{a\,6{}\mathrm{i}+b\,x\,6{}\mathrm{i}}+{\mathrm{e}}^{a\,8{}\mathrm{i}+b\,x\,8{}\mathrm{i}}-4\,{\mathrm{e}}^{a\,2{}\mathrm{i}+b\,x\,2{}\mathrm{i}}\right)}","Not used",1,"x*1i - log(exp(a*2i)*exp(b*x*2i) - 1)/b + 32/(b*(5*exp(a*2i + b*x*2i) - 10*exp(a*4i + b*x*4i) + 10*exp(a*6i + b*x*6i) - 5*exp(a*8i + b*x*8i) + exp(a*10i + b*x*10i) - 1)) + 32/(3*b*(15*exp(a*4i + b*x*4i) - 6*exp(a*2i + b*x*2i) - 20*exp(a*6i + b*x*6i) + 15*exp(a*8i + b*x*8i) - 6*exp(a*10i + b*x*10i) + exp(a*12i + b*x*12i) + 1)) + 6/(b*(exp(a*2i + b*x*2i) - 1)) + 18/(b*(exp(a*4i + b*x*4i) - 2*exp(a*2i + b*x*2i) + 1)) + 104/(3*b*(3*exp(a*2i + b*x*2i) - 3*exp(a*4i + b*x*4i) + exp(a*6i + b*x*6i) - 1)) + 44/(b*(6*exp(a*4i + b*x*4i) - 4*exp(a*2i + b*x*2i) - 4*exp(a*6i + b*x*6i) + exp(a*8i + b*x*8i) + 1))","B"
8,1,43,57,0.111550,"\text{Not used}","int(cot(a + b*x)^8,x)","x+\frac{-\frac{{\mathrm{cot}\left(a+b\,x\right)}^7}{7}+\frac{{\mathrm{cot}\left(a+b\,x\right)}^5}{5}-\frac{{\mathrm{cot}\left(a+b\,x\right)}^3}{3}+\mathrm{cot}\left(a+b\,x\right)}{b}","Not used",1,"x + (cot(a + b*x) - cot(a + b*x)^3/3 + cot(a + b*x)^5/5 - cot(a + b*x)^7/7)/b","B"
9,1,91,232,0.842449,"\text{Not used}","int((c*cot(a + b*x))^(7/2),x)","\frac{2\,c^3\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{b}-\frac{2\,c\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{5/2}}{5\,b}+\frac{{\left(-1\right)}^{1/4}\,c^{7/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b}+\frac{{\left(-1\right)}^{1/4}\,c^{7/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}\,1{}\mathrm{i}}{\sqrt{c}}\right)}{b}","Not used",1,"(2*c^3*(c*cot(a + b*x))^(1/2))/b - (2*c*(c*cot(a + b*x))^(5/2))/(5*b) + ((-1)^(1/4)*c^(7/2)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/b + ((-1)^(1/4)*c^(7/2)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2)*1i)/c^(1/2)))/b","B"
10,1,74,212,0.425254,"\text{Not used}","int((c*cot(a + b*x))^(5/2),x)","\frac{{\left(-1\right)}^{1/4}\,c^{5/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)}{b}-\frac{2\,c\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{3/2}}{3\,b}-\frac{{\left(-1\right)}^{1/4}\,c^{5/2}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)}{b}","Not used",1,"((-1)^(1/4)*c^(5/2)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)))/b - (2*c*(c*cot(a + b*x))^(3/2))/(3*b) - ((-1)^(1/4)*c^(5/2)*atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)))/b","B"
11,1,75,210,0.368597,"\text{Not used}","int((c*cot(a + b*x))^(3/2),x)","-\frac{2\,c\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{b}-\frac{{\left(-1\right)}^{1/4}\,c^{3/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b}-\frac{{\left(-1\right)}^{1/4}\,c^{3/2}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b}","Not used",1,"- (2*c*(c*cot(a + b*x))^(1/2))/b - ((-1)^(1/4)*c^(3/2)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/b - ((-1)^(1/4)*c^(3/2)*atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/b","B"
12,1,50,192,0.245697,"\text{Not used}","int((c*cot(a + b*x))^(1/2),x)","-\frac{{\left(-1\right)}^{1/4}\,\sqrt{c}\,\left(\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)-\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\right)}{b}","Not used",1,"-((-1)^(1/4)*c^(1/2)*(atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)) - atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))))/b","B"
13,1,57,192,0.335217,"\text{Not used}","int(1/(c*cot(a + b*x))^(1/2),x)","\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b\,\sqrt{c}}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b\,\sqrt{c}}","Not used",1,"((-1)^(1/4)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/(b*c^(1/2)) + ((-1)^(1/4)*atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/(b*c^(1/2))","B"
14,1,76,212,0.363915,"\text{Not used}","int(1/(c*cot(a + b*x))^(3/2),x)","\frac{2}{b\,c\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)}{b\,c^{3/2}}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)}{b\,c^{3/2}}","Not used",1,"2/(b*c*(c*cot(a + b*x))^(1/2)) + ((-1)^(1/4)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)))/(b*c^(3/2)) - ((-1)^(1/4)*atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)))/(b*c^(3/2))","B"
15,1,77,214,0.622680,"\text{Not used}","int(1/(c*cot(a + b*x))^(5/2),x)","\frac{2}{3\,b\,c\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{3/2}}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b\,c^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{b\,c^{5/2}}","Not used",1,"2/(3*b*c*(c*cot(a + b*x))^(3/2)) - ((-1)^(1/4)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/(b*c^(5/2)) - ((-1)^(1/4)*atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2))*1i)/(b*c^(5/2))","B"
16,1,91,234,0.679860,"\text{Not used}","int(1/(c*cot(a + b*x))^(7/2),x)","\frac{\frac{2}{5\,c}-\frac{2\,{\mathrm{cot}\left(a+b\,x\right)}^2}{c}}{b\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)}{b\,c^{7/2}}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{c\,\mathrm{cot}\left(a+b\,x\right)}}{\sqrt{c}}\right)}{b\,c^{7/2}}","Not used",1,"(2/(5*c) - (2*cot(a + b*x)^2)/c)/(b*(c*cot(a + b*x))^(5/2)) - ((-1)^(1/4)*atan(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)))/(b*c^(7/2)) + ((-1)^(1/4)*atanh(((-1)^(1/4)*(c*cot(a + b*x))^(1/2))/c^(1/2)))/(b*c^(7/2))","B"
17,1,246,242,0.627590,"\text{Not used}","int((c*cot(a + b*x))^(4/3),x)","-\frac{3\,c\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{b}+\frac{{\left(-1\right)}^{1/6}\,c^{4/3}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{5/6}\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}\,1{}\mathrm{i}}{c^{1/3}}\right)\,1{}\mathrm{i}}{b}-\frac{{\left(-1\right)}^{1/6}\,c^{4/3}\,\ln\left({\left(-1\right)}^{1/6}\,c^{1/3}-2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}+{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b}-\frac{{\left(-1\right)}^{1/6}\,c^{4/3}\,\ln\left(2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}+{\left(-1\right)}^{1/6}\,c^{1/3}-{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b}+\frac{{\left(-1\right)}^{1/6}\,c^{4/3}\,\ln\left(2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}+{\left(-1\right)}^{1/6}\,c^{1/3}+{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b}+\frac{{\left(-1\right)}^{1/6}\,c^{4/3}\,\ln\left(2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}-{\left(-1\right)}^{1/6}\,c^{1/3}+{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b}","Not used",1,"((-1)^(1/6)*c^(4/3)*atan(((-1)^(5/6)*(c*cot(a + b*x))^(1/3)*1i)/c^(1/3))*1i)/b - (3*c*(c*cot(a + b*x))^(1/3))/b - ((-1)^(1/6)*c^(4/3)*log((-1)^(1/6)*c^(1/3) - 2*(c*cot(a + b*x))^(1/3) + (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/2 + 1/2))/(2*b) - ((-1)^(1/6)*c^(4/3)*log(2*(c*cot(a + b*x))^(1/3) + (-1)^(1/6)*c^(1/3) - (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/2 - 1/2))/(2*b) + ((-1)^(1/6)*c^(4/3)*log(2*(c*cot(a + b*x))^(1/3) + (-1)^(1/6)*c^(1/3) + (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/4 + 1/4))/b + ((-1)^(1/6)*c^(4/3)*log(2*(c*cot(a + b*x))^(1/3) - (-1)^(1/6)*c^(1/3) + (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/4 - 1/4))/b","B"
18,1,260,225,0.816412,"\text{Not used}","int((c*cot(a + b*x))^(2/3),x)","-\frac{{\left(-1\right)}^{1/6}\,c^{2/3}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{2/3}\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{c^{1/3}}\right)\,1{}\mathrm{i}}{b}-\frac{{\left(-1\right)}^{1/6}\,c^{2/3}\,\ln\left(\frac{972\,c^9}{b^3}-\frac{486\,{\left(-1\right)}^{1/6}\,c^{26/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{b^3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b}-\frac{{\left(-1\right)}^{1/6}\,c^{2/3}\,\ln\left(\frac{972\,c^9}{b^3}-\frac{486\,{\left(-1\right)}^{1/6}\,c^{26/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{b^3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b}+\frac{{\left(-1\right)}^{1/6}\,c^{2/3}\,\ln\left(\frac{972\,c^9}{b^3}+\frac{486\,{\left(-1\right)}^{1/6}\,c^{26/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{b^3}\right)\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b}+\frac{{\left(-1\right)}^{1/6}\,c^{2/3}\,\ln\left(\frac{972\,c^9}{b^3}+\frac{486\,{\left(-1\right)}^{1/6}\,c^{26/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{b^3}\right)\,\left(\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b}","Not used",1,"((-1)^(1/6)*c^(2/3)*log((972*c^9)/b^3 + (486*(-1)^(1/6)*c^(26/3)*(3^(1/2)*1i - 1)*(c*cot(a + b*x))^(1/3))/b^3)*((3^(1/2)*1i)/4 - 1/4))/b - ((-1)^(1/6)*c^(2/3)*log((972*c^9)/b^3 - (486*(-1)^(1/6)*c^(26/3)*(3^(1/2)*1i - 1)*(c*cot(a + b*x))^(1/3))/b^3)*((3^(1/2)*1i)/2 - 1/2))/(2*b) - ((-1)^(1/6)*c^(2/3)*log((972*c^9)/b^3 - (486*(-1)^(1/6)*c^(26/3)*(3^(1/2)*1i + 1)*(c*cot(a + b*x))^(1/3))/b^3)*((3^(1/2)*1i)/2 + 1/2))/(2*b) - ((-1)^(1/6)*c^(2/3)*atan(((-1)^(2/3)*(c*cot(a + b*x))^(1/3))/c^(1/3))*1i)/b + ((-1)^(1/6)*c^(2/3)*log((972*c^9)/b^3 + (486*(-1)^(1/6)*c^(26/3)*(3^(1/2)*1i + 1)*(c*cot(a + b*x))^(1/3))/b^3)*((3^(1/2)*1i)/4 + 1/4))/b","B"
19,1,134,131,0.519636,"\text{Not used}","int((c*cot(a + b*x))^(1/3),x)","\frac{c^{1/3}\,\ln\left(81\,c^{16/3}\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{2/3}+81\,c^6\right)}{2\,b}-\frac{c^{1/3}\,\ln\left(\frac{81\,c^6}{b^4}-\frac{81\,c^{16/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{2/3}}{b^4}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b}+\frac{c^{1/3}\,\ln\left(\frac{81\,c^6}{b^4}+\frac{162\,c^{16/3}\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{2/3}}{b^4}\right)\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b}","Not used",1,"(c^(1/3)*log(81*c^(16/3)*(c*cot(a + b*x))^(2/3) + 81*c^6))/(2*b) - (c^(1/3)*log((81*c^6)/b^4 - (81*c^(16/3)*((3^(1/2)*1i)/2 + 1/2)*(c*cot(a + b*x))^(2/3))/b^4)*((3^(1/2)*1i)/2 + 1/2))/(2*b) + (c^(1/3)*log((81*c^6)/b^4 + (162*c^(16/3)*((3^(1/2)*1i)/4 - 1/4)*(c*cot(a + b*x))^(2/3))/b^4)*((3^(1/2)*1i)/4 - 1/4))/b","B"
20,1,128,131,0.579304,"\text{Not used}","int(1/(c*cot(a + b*x))^(1/3),x)","-\frac{\ln\left({\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{2/3}+c^{2/3}\right)}{2\,b\,c^{1/3}}-\frac{\ln\left(\frac{81\,c^{11/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{b^3}+\frac{162\,c^3\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{2/3}}{b^3}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{4\,b\,c^{1/3}}+\frac{\ln\left(\frac{81\,c^{11/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{b^3}-\frac{162\,c^3\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{2/3}}{b^3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{4\,b\,c^{1/3}}","Not used",1,"(log((81*c^(11/3)*(3^(1/2)*1i + 1))/b^3 - (162*c^3*(c*cot(a + b*x))^(2/3))/b^3)*(3^(1/2)*1i + 1))/(4*b*c^(1/3)) - (log((81*c^(11/3)*(3^(1/2)*1i - 1))/b^3 + (162*c^3*(c*cot(a + b*x))^(2/3))/b^3)*(3^(1/2)*1i - 1))/(4*b*c^(1/3)) - log((c*cot(a + b*x))^(2/3) + c^(2/3))/(2*b*c^(1/3))","B"
21,1,231,225,0.545662,"\text{Not used}","int(1/(c*cot(a + b*x))^(2/3),x)","-\frac{{\left(-1\right)}^{1/6}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{5/6}\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}\,1{}\mathrm{i}}{c^{1/3}}\right)\,1{}\mathrm{i}}{b\,c^{2/3}}-\frac{{\left(-1\right)}^{1/6}\,\ln\left(2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}+{\left(-1\right)}^{1/6}\,c^{1/3}+{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b\,c^{2/3}}-\frac{{\left(-1\right)}^{1/6}\,\ln\left(2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}-{\left(-1\right)}^{1/6}\,c^{1/3}+{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b\,c^{2/3}}+\frac{{\left(-1\right)}^{1/6}\,\ln\left({\left(-1\right)}^{1/6}\,c^{1/3}-2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}+{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b\,c^{2/3}}+\frac{{\left(-1\right)}^{1/6}\,\ln\left(2\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}+{\left(-1\right)}^{1/6}\,c^{1/3}-{\left(-1\right)}^{2/3}\,\sqrt{3}\,c^{1/3}\right)\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b\,c^{2/3}}","Not used",1,"((-1)^(1/6)*log((-1)^(1/6)*c^(1/3) - 2*(c*cot(a + b*x))^(1/3) + (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/4 + 1/4))/(b*c^(2/3)) - ((-1)^(1/6)*log(2*(c*cot(a + b*x))^(1/3) + (-1)^(1/6)*c^(1/3) + (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/2 + 1/2))/(2*b*c^(2/3)) - ((-1)^(1/6)*log(2*(c*cot(a + b*x))^(1/3) - (-1)^(1/6)*c^(1/3) + (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/2 - 1/2))/(2*b*c^(2/3)) - ((-1)^(1/6)*atan(((-1)^(5/6)*(c*cot(a + b*x))^(1/3)*1i)/c^(1/3))*1i)/(b*c^(2/3)) + ((-1)^(1/6)*log(2*(c*cot(a + b*x))^(1/3) + (-1)^(1/6)*c^(1/3) - (-1)^(2/3)*3^(1/2)*c^(1/3))*((3^(1/2)*1i)/4 - 1/4))/(b*c^(2/3))","B"
22,1,277,244,0.433563,"\text{Not used}","int(1/(c*cot(a + b*x))^(4/3),x)","\frac{3}{b\,c\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}+\frac{{\left(-1\right)}^{1/6}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{2/3}\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}}{c^{1/3}}\right)\,1{}\mathrm{i}}{b\,c^{4/3}}-\frac{{\left(-1\right)}^{1/6}\,\ln\left(972\,b^6\,c^{12}+972\,{\left(-1\right)}^{1/6}\,b^6\,c^{35/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b\,c^{4/3}}-\frac{{\left(-1\right)}^{1/6}\,\ln\left(972\,b^6\,c^{12}+972\,{\left(-1\right)}^{1/6}\,b^6\,c^{35/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2\,b\,c^{4/3}}+\frac{{\left(-1\right)}^{1/6}\,\ln\left(972\,b^6\,c^{12}-1944\,{\left(-1\right)}^{1/6}\,b^6\,c^{35/3}\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}\right)\,\left(-\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b\,c^{4/3}}+\frac{{\left(-1\right)}^{1/6}\,\ln\left(972\,b^6\,c^{12}-1944\,{\left(-1\right)}^{1/6}\,b^6\,c^{35/3}\,\left(\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)\,{\left(c\,\mathrm{cot}\left(a+b\,x\right)\right)}^{1/3}\right)\,\left(\frac{1}{4}+\frac{\sqrt{3}\,1{}\mathrm{i}}{4}\right)}{b\,c^{4/3}}","Not used",1,"3/(b*c*(c*cot(a + b*x))^(1/3)) + ((-1)^(1/6)*atan(((-1)^(2/3)*(c*cot(a + b*x))^(1/3))/c^(1/3))*1i)/(b*c^(4/3)) - ((-1)^(1/6)*log(972*b^6*c^12 + 972*(-1)^(1/6)*b^6*c^(35/3)*((3^(1/2)*1i)/2 - 1/2)*(c*cot(a + b*x))^(1/3))*((3^(1/2)*1i)/2 - 1/2))/(2*b*c^(4/3)) - ((-1)^(1/6)*log(972*b^6*c^12 + 972*(-1)^(1/6)*b^6*c^(35/3)*((3^(1/2)*1i)/2 + 1/2)*(c*cot(a + b*x))^(1/3))*((3^(1/2)*1i)/2 + 1/2))/(2*b*c^(4/3)) + ((-1)^(1/6)*log(972*b^6*c^12 - 1944*(-1)^(1/6)*b^6*c^(35/3)*((3^(1/2)*1i)/4 - 1/4)*(c*cot(a + b*x))^(1/3))*((3^(1/2)*1i)/4 - 1/4))/(b*c^(4/3)) + ((-1)^(1/6)*log(972*b^6*c^12 - 1944*(-1)^(1/6)*b^6*c^(35/3)*((3^(1/2)*1i)/4 + 1/4)*(c*cot(a + b*x))^(1/3))*((3^(1/2)*1i)/4 + 1/4))/(b*c^(4/3))","B"
23,0,-1,46,0.000000,"\text{Not used}","int(cot(a + b*x)^n,x)","\int {\mathrm{cot}\left(a+b\,x\right)}^n \,d x","Not used",1,"int(cot(a + b*x)^n, x)","F"
24,0,-1,51,0.000000,"\text{Not used}","int((b*cot(c + d*x))^n,x)","\int {\left(b\,\mathrm{cot}\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((b*cot(c + d*x))^n, x)","F"
25,0,-1,36,0.000000,"\text{Not used}","int((a*cot(x)^2)^(3/2),x)","\int {\left(a\,{\mathrm{cot}\left(x\right)}^2\right)}^{3/2} \,d x","Not used",1,"int((a*cot(x)^2)^(3/2), x)","F"
26,0,-1,16,0.000000,"\text{Not used}","int((a*cot(x)^2)^(1/2),x)","\int \sqrt{a\,{\mathrm{cot}\left(x\right)}^2} \,d x","Not used",1,"int((a*cot(x)^2)^(1/2), x)","F"
27,1,25,17,0.289969,"\text{Not used}","int(1/(a*cot(x)^2)^(1/2),x)","-\frac{\mathrm{atan}\left(\frac{\sqrt{-a}\,\mathrm{cot}\left(x\right)}{\sqrt{a}\,\sqrt{{\mathrm{cot}\left(x\right)}^2}}\right)}{\sqrt{-a}}","Not used",1,"-atan(((-a)^(1/2)*cot(x))/(a^(1/2)*(cot(x)^2)^(1/2)))/(-a)^(1/2)","B"
28,0,-1,39,0.000000,"\text{Not used}","int(1/(a*cot(x)^2)^(3/2),x)","\int \frac{1}{{\left(a\,{\mathrm{cot}\left(x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*cot(x)^2)^(3/2), x)","F"
29,0,-1,200,0.000000,"\text{Not used}","int((a*cot(x)^3)^(3/2),x)","\int {\left(a\,{\mathrm{cot}\left(x\right)}^3\right)}^{3/2} \,d x","Not used",1,"int((a*cot(x)^3)^(3/2), x)","F"
30,0,-1,176,0.000000,"\text{Not used}","int((a*cot(x)^3)^(1/2),x)","\int \sqrt{a\,{\mathrm{cot}\left(x\right)}^3} \,d x","Not used",1,"int((a*cot(x)^3)^(1/2), x)","F"
31,0,-1,176,0.000000,"\text{Not used}","int(1/(a*cot(x)^3)^(1/2),x)","\int \frac{1}{\sqrt{a\,{\mathrm{cot}\left(x\right)}^3}} \,d x","Not used",1,"int(1/(a*cot(x)^3)^(1/2), x)","F"
32,0,-1,212,0.000000,"\text{Not used}","int(1/(a*cot(x)^3)^(3/2),x)","\int \frac{1}{{\left(a\,{\mathrm{cot}\left(x\right)}^3\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*cot(x)^3)^(3/2), x)","F"
33,0,-1,70,0.000000,"\text{Not used}","int((a*cot(x)^4)^(3/2),x)","\int {\left(a\,{\mathrm{cot}\left(x\right)}^4\right)}^{3/2} \,d x","Not used",1,"int((a*cot(x)^4)^(3/2), x)","F"
34,0,-1,32,0.000000,"\text{Not used}","int((a*cot(x)^4)^(1/2),x)","\int \sqrt{a\,{\mathrm{cot}\left(x\right)}^4} \,d x","Not used",1,"int((a*cot(x)^4)^(1/2), x)","F"
35,0,-1,31,0.000000,"\text{Not used}","int(1/(a*cot(x)^4)^(1/2),x)","\int \frac{1}{\sqrt{a\,{\mathrm{cot}\left(x\right)}^4}} \,d x","Not used",1,"int(1/(a*cot(x)^4)^(1/2), x)","F"
36,0,-1,77,0.000000,"\text{Not used}","int(1/(a*cot(x)^4)^(3/2),x)","\int \frac{1}{{\left(a\,{\mathrm{cot}\left(x\right)}^4\right)}^{3/2}} \,d x","Not used",1,"int(1/(a*cot(x)^4)^(3/2), x)","F"
37,0,-1,60,0.000000,"\text{Not used}","int((b*cot(c + d*x)^p)^n,x)","\int {\left(b\,{\mathrm{cot}\left(c+d\,x\right)}^p\right)}^n \,d x","Not used",1,"int((b*cot(c + d*x)^p)^n, x)","F"
38,0,-1,62,0.000000,"\text{Not used}","int((a*(b*cot(c + d*x))^p)^n,x)","\int {\left(a\,{\left(b\,\mathrm{cot}\left(c+d\,x\right)\right)}^p\right)}^n \,d x","Not used",1,"int((a*(b*cot(c + d*x))^p)^n, x)","F"
39,0,-1,87,0.000000,"\text{Not used}","int((b*cot(e + f*x))^n*(a*sin(e + f*x))^m,x)","\int {\left(b\,\mathrm{cot}\left(e+f\,x\right)\right)}^n\,{\left(a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((b*cot(e + f*x))^n*(a*sin(e + f*x))^m, x)","F"
40,0,-1,84,0.000000,"\text{Not used}","int((a*cos(e + f*x))^m*(b*cot(e + f*x))^n,x)","\int {\left(a\,\cos\left(e+f\,x\right)\right)}^m\,{\left(b\,\mathrm{cot}\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a*cos(e + f*x))^m*(b*cot(e + f*x))^n, x)","F"
41,0,-1,64,0.000000,"\text{Not used}","int((a*cot(e + f*x))^m*(b*cot(e + f*x))^n,x)","\int {\left(a\,\mathrm{cot}\left(e+f\,x\right)\right)}^m\,{\left(b\,\mathrm{cot}\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a*cot(e + f*x))^m*(b*cot(e + f*x))^n, x)","F"
42,0,-1,90,0.000000,"\text{Not used}","int((b*cot(e + f*x))^n*(a/cos(e + f*x))^m,x)","\int {\left(b\,\mathrm{cot}\left(e+f\,x\right)\right)}^n\,{\left(\frac{a}{\cos\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int((b*cot(e + f*x))^n*(a/cos(e + f*x))^m, x)","F"
43,1,123,76,1.575798,"\text{Not used}","int((d*cot(e + f*x))^n/sin(e + f*x)^6,x)","-\frac{{\left(\frac{d\,\cos\left(e+f\,x\right)}{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}^n\,\left(5\,\cos\left(e+f\,x\right)-\frac{5\,\cos\left(3\,e+3\,f\,x\right)}{2}+\frac{\cos\left(5\,e+5\,f\,x\right)}{2}+5\,n\,\cos\left(e+f\,x\right)-n\,\cos\left(3\,e+3\,f\,x\right)+n^2\,\cos\left(e+f\,x\right)\right)}{f\,{\sin\left(e+f\,x\right)}^5\,\left(n+1\right)\,\left(n+3\right)\,\left(n+5\right)}","Not used",1,"-(((d*cos(e + f*x))/(2*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)))^n*(5*cos(e + f*x) - (5*cos(3*e + 3*f*x))/2 + cos(5*e + 5*f*x)/2 + 5*n*cos(e + f*x) - n*cos(3*e + 3*f*x) + n^2*cos(e + f*x)))/(f*sin(e + f*x)^5*(n + 1)*(n + 3)*(n + 5))","B"
44,1,84,51,0.670481,"\text{Not used}","int((d*cot(e + f*x))^n/sin(e + f*x)^4,x)","-\frac{\left(\frac{3\,\cos\left(e+f\,x\right)}{2}-\frac{\cos\left(3\,e+3\,f\,x\right)}{2}+n\,\cos\left(e+f\,x\right)\right)\,{\left(\frac{d\,\cos\left(e+f\,x\right)}{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}^n}{f\,{\sin\left(e+f\,x\right)}^3\,\left(n+1\right)\,\left(n+3\right)}","Not used",1,"-(((3*cos(e + f*x))/2 - cos(3*e + 3*f*x)/2 + n*cos(e + f*x))*((d*cos(e + f*x))/(2*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)))^n)/(f*sin(e + f*x)^3*(n + 1)*(n + 3))","B"
45,1,73,25,0.340688,"\text{Not used}","int((d*cot(e + f*x))^n/sin(e + f*x)^2,x)","\frac{\left(\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{2\,n+2}-\frac{1}{2\,n+2}\right)\,{\left(-\frac{d\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}^n}{f\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}","Not used",1,"((tan(e/2 + (f*x)/2)^2/(2*n + 2) - 1/(2*n + 2))*(-(d*(tan(e/2 + (f*x)/2)^2 - 1))/(2*tan(e/2 + (f*x)/2)))^n)/(f*tan(e/2 + (f*x)/2))","B"
46,0,-1,51,0.000000,"\text{Not used}","int(sin(e + f*x)^2*(d*cot(e + f*x))^n,x)","\int {\sin\left(e+f\,x\right)}^2\,{\left(d\,\mathrm{cot}\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(sin(e + f*x)^2*(d*cot(e + f*x))^n, x)","F"
47,0,-1,51,0.000000,"\text{Not used}","int(sin(e + f*x)^4*(d*cot(e + f*x))^n,x)","\int {\sin\left(e+f\,x\right)}^4\,{\left(d\,\mathrm{cot}\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(sin(e + f*x)^4*(d*cot(e + f*x))^n, x)","F"
48,0,-1,79,0.000000,"\text{Not used}","int((d*cot(e + f*x))^n/sin(e + f*x)^3,x)","\int \frac{{\left(d\,\mathrm{cot}\left(e+f\,x\right)\right)}^n}{{\sin\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((d*cot(e + f*x))^n/sin(e + f*x)^3, x)","F"
49,0,-1,77,0.000000,"\text{Not used}","int((d*cot(e + f*x))^n/sin(e + f*x),x)","\int \frac{{\left(d\,\mathrm{cot}\left(e+f\,x\right)\right)}^n}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((d*cot(e + f*x))^n/sin(e + f*x), x)","F"
50,0,-1,73,0.000000,"\text{Not used}","int(sin(e + f*x)*(d*cot(e + f*x))^n,x)","\int \sin\left(e+f\,x\right)\,{\left(d\,\mathrm{cot}\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(sin(e + f*x)*(d*cot(e + f*x))^n, x)","F"
51,0,-1,79,0.000000,"\text{Not used}","int(sin(e + f*x)^3*(d*cot(e + f*x))^n,x)","\int {\sin\left(e+f\,x\right)}^3\,{\left(d\,\mathrm{cot}\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int(sin(e + f*x)^3*(d*cot(e + f*x))^n, x)","F"
52,0,-1,83,0.000000,"\text{Not used}","int((b*cot(e + f*x))^n*(a/sin(e + f*x))^m,x)","\int {\left(b\,\mathrm{cot}\left(e+f\,x\right)\right)}^n\,{\left(\frac{a}{\sin\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int((b*cot(e + f*x))^n*(a/sin(e + f*x))^m, x)","F"