1,0,0,0,0.000000," ","integrate((a+I*a*cot(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \cot\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((I*a*cot(d*x + c) + a)^n, x)","F",0
2,1,149,0,0.760122," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(15 \, a e^{2} {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - \frac{4 \, {\left(15 \, a e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}} - 5 \, a e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} - 3 \, a \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}\right)}}{e}\right)} e}{30 \, d}"," ",0,"-1/30*(15*a*e^2*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 4*(15*a*e^2*sqrt(e/tan(d*x + c)) - 5*a*e*(e/tan(d*x + c))^(3/2) - 3*a*(e/tan(d*x + c))^(5/2))/e)*e/d","A",0
3,1,124,0,0.616131," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, a e {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)} - \frac{2 \, {\left(3 \, a e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + a \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e}\right)} e}{3 \, d}"," ",0,"1/3*(3*a*e*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e)) - 2*(3*a*e*sqrt(e/tan(d*x + c)) + a*(e/tan(d*x + c))^(3/2))/e)*e/d","A",0
4,1,108,0,0.896124," ","integrate((e*cot(d*x+c))^(1/2)*(a+a*cot(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(a {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - \frac{4 \, a \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{e}\right)} e}{2 \, d}"," ",0,"1/2*(a*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 4*a*sqrt(e/tan(d*x + c))/e)*e/d","A",0
5,1,83,0,0.691562," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{a {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{d}"," ",0,"-a*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/d","B",0
6,1,111,0,0.718577," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{a {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{2}} - \frac{4 \, a}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)}}{2 \, d}"," ",0,"-1/2*e*(a*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^2 - 4*a/(e^2*sqrt(e/tan(d*x + c))))/d","A",0
7,1,123,0,0.598774," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{3 \, a {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{e^{3}} + \frac{2 \, {\left(a e + \frac{3 \, a e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{3 \, d}"," ",0,"1/3*e*(3*a*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/e^3 + 2*(a*e + 3*a*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
8,1,232,0,0.594861," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(35 \, {\left(2 \, \sqrt{2} e^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} e^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} e^{\frac{3}{2}} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right) - \sqrt{2} e^{\frac{3}{2}} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)\right)} a^{2} - \frac{4 \, {\left(70 \, a^{2} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} - 14 \, a^{2} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} - 5 \, a^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}}\right)}}{e^{2}}\right)} e}{70 \, d}"," ",0,"-1/70*(35*(2*sqrt(2)*e^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*e^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + sqrt(2)*e^(3/2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)) - sqrt(2)*e^(3/2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)))*a^2 - 4*(70*a^2*e^3*sqrt(e/tan(d*x + c)) - 14*a^2*e*(e/tan(d*x + c))^(5/2) - 5*a^2*(e/tan(d*x + c))^(7/2))/e^2)*e/d","A",0
9,1,213,0,0.601090," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(15 \, a^{2} e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - \frac{4 \, {\left(10 \, a^{2} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + 3 \, a^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}\right)}}{e^{2}}\right)} e}{30 \, d}"," ",0,"1/30*(15*a^2*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 4*(10*a^2*e*(e/tan(d*x + c))^(3/2) + 3*a^2*(e/tan(d*x + c))^(5/2))/e^2)*e/d","A",0
10,1,211,0,0.704760," ","integrate((e*cot(d*x+c))^(1/2)*(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - \frac{4 \, {\left(6 \, a^{2} e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + a^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e^{2}}\right)} e}{6 \, d}"," ",0,"1/6*(3*a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 4*(6*a^2*e*sqrt(e/tan(d*x + c)) + a^2*(e/tan(d*x + c))^(3/2))/e^2)*e/d","A",0
11,1,193,0,0.786751," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\frac{a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e} + \frac{4 \, a^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{e^{2}}\right)} e}{2 \, d}"," ",0,"-1/2*(a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e + 4*a^2*sqrt(e/tan(d*x + c))/e^2)*e/d","A",0
12,1,202,0,0.460850," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{\frac{2 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{\sqrt{2} a^{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}} - \frac{\sqrt{2} a^{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}}}{e} - \frac{4 \, a^{2}}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)}}{2 \, d}"," ",0,"-1/2*e*((2*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + 2*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + sqrt(2)*a^2*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2) - sqrt(2)*a^2*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2))/e - 4*a^2/(e^2*sqrt(e/tan(d*x + c))))/d","A",0
13,1,211,0,0.540300," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{3 \, a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{3}} + \frac{4 \, {\left(a^{2} e + \frac{6 \, a^{2} e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{6 \, d}"," ",0,"1/6*e*(3*a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^3 + 4*(a^2*e + 6*a^2*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
14,1,221,0,0.689656," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{15 \, {\left(\frac{2 \, \sqrt{2} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{\sqrt{2} a^{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}} - \frac{\sqrt{2} a^{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}}\right)}}{e^{3}} + \frac{4 \, {\left(3 \, a^{2} e + \frac{10 \, a^{2} e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}}\right)}}{30 \, d}"," ",0,"1/30*e*(15*(2*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + 2*sqrt(2)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + sqrt(2)*a^2*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2) - sqrt(2)*a^2*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2))/e^3 + 4*(3*a^2*e + 10*a^2*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(5/2)))/d","A",0
15,1,193,0,0.499651," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(315 \, a^{3} e^{2} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)} - \frac{630 \, a^{3} e^{4} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 210 \, a^{3} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} - 126 \, a^{3} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} - 135 \, a^{3} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}} - 35 \, a^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{9}{2}}}{e^{3}}\right)} e}{315 \, d}"," ",0,"-2/315*(315*a^3*e^2*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e)) - (630*a^3*e^4*sqrt(e/tan(d*x + c)) + 210*a^3*e^3*(e/tan(d*x + c))^(3/2) - 126*a^3*e^2*(e/tan(d*x + c))^(5/2) - 135*a^3*e*(e/tan(d*x + c))^(7/2) - 35*a^3*(e/tan(d*x + c))^(9/2))/e^3)*e/d","A",0
16,1,175,0,0.465875," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(105 \, a^{3} e {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - \frac{2 \, {\left(210 \, a^{3} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} - 70 \, a^{3} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} - 63 \, a^{3} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} - 15 \, a^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}}\right)}}{e^{3}}\right)} e}{105 \, d}"," ",0,"-1/105*(105*a^3*e*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 2*(210*a^3*e^3*sqrt(e/tan(d*x + c)) - 70*a^3*e^2*(e/tan(d*x + c))^(3/2) - 63*a^3*e*(e/tan(d*x + c))^(5/2) - 15*a^3*(e/tan(d*x + c))^(7/2))/e^3)*e/d","A",0
17,1,149,0,0.759505," ","integrate((e*cot(d*x+c))^(1/2)*(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)} - \frac{10 \, a^{3} e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 5 \, a^{3} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + a^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}}{e^{3}}\right)} e}{5 \, d}"," ",0,"2/5*(5*a^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e)) - (10*a^3*e^2*sqrt(e/tan(d*x + c)) + 5*a^3*e*(e/tan(d*x + c))^(3/2) + a^3*(e/tan(d*x + c))^(5/2))/e^3)*e/d","A",0
18,1,136,0,0.550947," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\frac{3 \, a^{3} {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e} - \frac{2 \, {\left(9 \, a^{3} e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + a^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e^{3}}\right)} e}{3 \, d}"," ",0,"1/3*(3*a^3*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e - 2*(9*a^3*e*sqrt(e/tan(d*x + c)) + a^3*(e/tan(d*x + c))^(3/2))/e^3)*e/d","A",0
19,1,130,0,0.680147," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{a^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{e^{2}} - \frac{a^{3}}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}} + \frac{a^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{e^{3}}\right)} e}{d}"," ",0,"-2*(a^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/e^2 - a^3/(e^2*sqrt(e/tan(d*x + c))) + a^3*sqrt(e/tan(d*x + c))/e^3)*e/d","A",0
20,1,133,0,0.790622," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{3 \, a^{3} {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{3}} - \frac{2 \, {\left(a^{3} e + \frac{9 \, a^{3} e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{3 \, d}"," ",0,"-1/3*e*(3*a^3*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^3 - 2*(a^3*e + 9*a^3*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
21,1,148,0,0.773480," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, e {\left(\frac{5 \, a^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{e^{4}} + \frac{a^{3} e^{2} + \frac{5 \, a^{3} e^{2}}{\tan\left(d x + c\right)} + \frac{10 \, a^{3} e^{2}}{\tan\left(d x + c\right)^{2}}}{e^{4} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}}\right)}}{5 \, d}"," ",0,"2/5*e*(5*a^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/e^4 + (a^3*e^2 + 5*a^3*e^2/tan(d*x + c) + 10*a^3*e^2/tan(d*x + c)^2)/(e^4*(e/tan(d*x + c))^(5/2)))/d","A",0
22,1,170,0,0.854792," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{105 \, a^{3} {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{5}} + \frac{2 \, {\left(15 \, a^{3} e^{3} + \frac{63 \, a^{3} e^{3}}{\tan\left(d x + c\right)} + \frac{70 \, a^{3} e^{3}}{\tan\left(d x + c\right)^{2}} - \frac{210 \, a^{3} e^{3}}{\tan\left(d x + c\right)^{3}}\right)}}{e^{5} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}}}\right)}}{105 \, d}"," ",0,"1/105*e*(105*a^3*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^5 + 2*(15*a^3*e^3 + 63*a^3*e^3/tan(d*x + c) + 70*a^3*e^3/tan(d*x + c)^2 - 210*a^3*e^3/tan(d*x + c)^3)/(e^5*(e/tan(d*x + c))^(7/2)))/d","A",0
23,1,134,0,1.566516," ","integrate((e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\frac{e^{2} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{a} + \frac{2 \, e^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a} - \frac{4 \, e \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{a}\right)} e}{2 \, d}"," ",0,"1/2*(e^2*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/a + 2*e^(3/2)*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/a - 4*e*sqrt(e/tan(d*x + c))/a)*e/d","A",0
24,1,118,0,0.702552," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c)),x, algorithm=""maxima"")","\frac{e {\left(\frac{e {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{a} - \frac{4 \, \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a}\right)}}{4 \, d}"," ",0,"1/4*e*(e*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/a - 4*sqrt(e)*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/a)/d","A",0
25,1,113,0,0.808543," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{e {\left(\frac{\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}}{a} - \frac{2 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a \sqrt{e}}\right)}}{2 \, d}"," ",0,"-1/2*e*((sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/a - 2*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a*sqrt(e)))/d","A",0
26,1,120,0,0.631764," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{e {\left(\frac{\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a e} + \frac{4 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a e^{\frac{3}{2}}}\right)}}{4 \, d}"," ",0,"-1/4*e*((sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a*e) + 4*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a*e^(3/2)))/d","A",0
27,1,136,0,1.644991," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c)),x, algorithm=""maxima"")","\frac{e {\left(\frac{\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}}{a e^{2}} + \frac{2 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a e^{\frac{5}{2}}} + \frac{4}{a e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)}}{2 \, d}"," ",0,"1/2*e*((sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/(a*e^2) + 2*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a*e^(5/2)) + 4/(a*e^2*sqrt(e/tan(d*x + c))))/d","A",0
28,1,154,0,0.444485," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c)),x, algorithm=""maxima"")","\frac{e {\left(\frac{3 \, {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{a e^{3}} - \frac{12 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a e^{\frac{7}{2}}} + \frac{8 \, {\left(e - \frac{3 \, e}{\tan\left(d x + c\right)}\right)}}{a e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{12 \, d}"," ",0,"1/12*e*(3*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a*e^3) - 12*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a*e^(7/2)) + 8*(e - 3*e/tan(d*x + c))/(a*e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
29,1,233,0,0.437845," ","integrate((e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(\frac{4 \, e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{a^{2} e + \frac{a^{2} e}{\tan\left(d x + c\right)}} - \frac{12 \, e^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{2}} + \frac{2 \, \sqrt{2} e^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} e^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} e^{\frac{3}{2}} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right) - \sqrt{2} e^{\frac{3}{2}} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{a^{2}}\right)} e}{8 \, d}"," ",0,"1/8*(4*e^2*sqrt(e/tan(d*x + c))/(a^2*e + a^2*e/tan(d*x + c)) - 12*e^(3/2)*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/a^2 + (2*sqrt(2)*e^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*e^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + sqrt(2)*e^(3/2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)) - sqrt(2)*e^(3/2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)))/a^2)*e/d","A",0
30,1,232,0,0.490558," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{e {\left(\frac{4 \, e \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{a^{2} e + \frac{a^{2} e}{\tan\left(d x + c\right)}} + \frac{e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{a^{2}} - \frac{4 \, \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{2}}\right)}}{8 \, d}"," ",0,"-1/8*e*(4*e*sqrt(e/tan(d*x + c))/(a^2*e + a^2*e/tan(d*x + c)) + e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/a^2 - 4*sqrt(e)*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/a^2)/d","A",0
31,1,231,0,0.584607," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{e {\left(\frac{4 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{a^{2} e + \frac{a^{2} e}{\tan\left(d x + c\right)}} - \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{2}} + \frac{4 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{2} \sqrt{e}}\right)}}{8 \, d}"," ",0,"1/8*e*(4*sqrt(e/tan(d*x + c))/(a^2*e + a^2*e/tan(d*x + c)) - (2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/a^2 + 4*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^2*sqrt(e)))/d","A",0
32,1,238,0,0.545120," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{e {\left(\frac{4 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{a^{2} e^{2} + \frac{a^{2} e^{2}}{\tan\left(d x + c\right)}} - \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{2} e} + \frac{12 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{2} e^{\frac{3}{2}}}\right)}}{8 \, d}"," ",0,"-1/8*e*(4*sqrt(e/tan(d*x + c))/(a^2*e^2 + a^2*e^2/tan(d*x + c)) - (2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a^2*e) + 12*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^2*e^(3/2)))/d","A",0
33,1,256,0,0.869865," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{e {\left(\frac{4 \, {\left(4 \, e + \frac{5 \, e}{\tan\left(d x + c\right)}\right)}}{a^{2} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + a^{2} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}} + \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}}}{a^{2} e} + \frac{20 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{2} e^{\frac{5}{2}}}\right)}}{8 \, d}"," ",0,"1/8*e*(4*(4*e + 5*e/tan(d*x + c))/(a^2*e^3*sqrt(e/tan(d*x + c)) + a^2*e^2*(e/tan(d*x + c))^(3/2)) + (2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2))/(a^2*e) + 20*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^2*e^(5/2)))/d","A",0
34,1,274,0,1.012899," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{e {\left(\frac{4 \, {\left(4 \, e^{2} - \frac{20 \, e^{2}}{\tan\left(d x + c\right)} - \frac{27 \, e^{2}}{\tan\left(d x + c\right)^{2}}\right)}}{a^{2} e^{4} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + a^{2} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}} - \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{a^{2} e^{3}} - \frac{84 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{2} e^{\frac{7}{2}}}\right)}}{24 \, d}"," ",0,"1/24*e*(4*(4*e^2 - 20*e^2/tan(d*x + c) - 27*e^2/tan(d*x + c)^2)/(a^2*e^4*(e/tan(d*x + c))^(3/2) + a^2*e^3*(e/tan(d*x + c))^(5/2)) - 3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a^2*e^3) - 84*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^2*e^(7/2)))/d","A",0
35,1,197,0,0.455609," ","integrate((e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{e {\left(\frac{3 \, e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 5 \, e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{a^{3} e^{2} + \frac{2 \, a^{3} e^{2}}{\tan\left(d x + c\right)} + \frac{a^{3} e^{2}}{\tan\left(d x + c\right)^{2}}} - \frac{e^{2} {\left(\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{a^{3}} + \frac{e^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{3}}\right)}}{8 \, d}"," ",0,"-1/8*e*((3*e^3*sqrt(e/tan(d*x + c)) + 5*e^2*(e/tan(d*x + c))^(3/2))/(a^3*e^2 + 2*a^3*e^2/tan(d*x + c) + a^3*e^2/tan(d*x + c)^2) - e^2*(sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/a^3 + e^(3/2)*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/a^3)/d","A",0
36,1,189,0,0.917881," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{e {\left(\frac{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}} - e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{a^{3} e^{2} + \frac{2 \, a^{3} e^{2}}{\tan\left(d x + c\right)} + \frac{a^{3} e^{2}}{\tan\left(d x + c\right)^{2}}} + \frac{2 \, e {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{a^{3}} - \frac{5 \, \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{3}}\right)}}{8 \, d}"," ",0,"-1/8*e*((e^2*sqrt(e/tan(d*x + c)) - e*(e/tan(d*x + c))^(3/2))/(a^3*e^2 + 2*a^3*e^2/tan(d*x + c) + a^3*e^2/tan(d*x + c)^2) + 2*e*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/a^3 - 5*sqrt(e)*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/a^3)/d","A",0
37,1,190,0,0.601385," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{e {\left(\frac{5 \, e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 3 \, \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{a^{3} e^{2} + \frac{2 \, a^{3} e^{2}}{\tan\left(d x + c\right)} + \frac{a^{3} e^{2}}{\tan\left(d x + c\right)^{2}}} - \frac{\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{3}} - \frac{\arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{3} \sqrt{e}}\right)}}{8 \, d}"," ",0,"1/8*e*((5*e*sqrt(e/tan(d*x + c)) + 3*(e/tan(d*x + c))^(3/2))/(a^3*e^2 + 2*a^3*e^2/tan(d*x + c) + a^3*e^2/tan(d*x + c)^2) - (sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/a^3 - arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^3*sqrt(e)))/d","A",0
38,1,189,0,0.512463," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{e {\left(\frac{9 \, e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 7 \, \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{a^{3} e^{3} + \frac{2 \, a^{3} e^{3}}{\tan\left(d x + c\right)} + \frac{a^{3} e^{3}}{\tan\left(d x + c\right)^{2}}} - \frac{2 \, {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{a^{3} e} + \frac{11 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{3} e^{\frac{3}{2}}}\right)}}{8 \, d}"," ",0,"-1/8*e*((9*e*sqrt(e/tan(d*x + c)) + 7*(e/tan(d*x + c))^(3/2))/(a^3*e^3 + 2*a^3*e^3/tan(d*x + c) + a^3*e^3/tan(d*x + c)^2) - 2*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/(a^3*e) + 11*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^3*e^(3/2)))/d","A",0
39,1,214,0,0.713022," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{e {\left(\frac{16 \, e^{2} + \frac{45 \, e^{2}}{\tan\left(d x + c\right)} + \frac{27 \, e^{2}}{\tan\left(d x + c\right)^{2}}}{a^{3} e^{4} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 2 \, a^{3} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + a^{3} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}} + \frac{\frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{3} e^{2}} + \frac{31 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{3} e^{\frac{5}{2}}}\right)}}{8 \, d}"," ",0,"1/8*e*((16*e^2 + 45*e^2/tan(d*x + c) + 27*e^2/tan(d*x + c)^2)/(a^3*e^4*sqrt(e/tan(d*x + c)) + 2*a^3*e^3*(e/tan(d*x + c))^(3/2) + a^3*e^2*(e/tan(d*x + c))^(5/2)) + (sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a^3*e^2) + 31*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^3*e^(5/2)))/d","A",0
40,1,224,0,0.777806," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{e {\left(\frac{16 \, e^{3} - \frac{112 \, e^{3}}{\tan\left(d x + c\right)} - \frac{323 \, e^{3}}{\tan\left(d x + c\right)^{2}} - \frac{189 \, e^{3}}{\tan\left(d x + c\right)^{3}}}{a^{3} e^{5} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + 2 \, a^{3} e^{4} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} + a^{3} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}}} - \frac{6 \, {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}}\right)}}{a^{3} e^{3}} - \frac{177 \, \arctan\left(\frac{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{e}}\right)}{a^{3} e^{\frac{7}{2}}}\right)}}{24 \, d}"," ",0,"1/24*e*((16*e^3 - 112*e^3/tan(d*x + c) - 323*e^3/tan(d*x + c)^2 - 189*e^3/tan(d*x + c)^3)/(a^3*e^5*(e/tan(d*x + c))^(3/2) + 2*a^3*e^4*(e/tan(d*x + c))^(5/2) + a^3*e^3*(e/tan(d*x + c))^(7/2)) - 6*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e))/(a^3*e^3) - 177*arctan(sqrt(e/tan(d*x + c))/sqrt(e))/(a^3*e^(7/2)))/d","A",0
41,0,0,0,0.000000," ","integrate(cot(x)^2*(1+cot(x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\cot\left(x\right) + 1} \cot\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(cot(x) + 1)*cot(x)^2, x)","F",0
42,0,0,0,0.000000," ","integrate(cot(x)*(1+cot(x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\cot\left(x\right) + 1} \cot\left(x\right)\,{d x}"," ",0,"integrate(sqrt(cot(x) + 1)*cot(x), x)","F",0
43,-1,0,0,0.000000," ","integrate(cot(x)^2*(1+cot(x))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,0.000000," ","integrate(cot(x)*(1+cot(x))^(3/2),x, algorithm=""maxima"")","\int {\left(\cot\left(x\right) + 1\right)}^{\frac{3}{2}} \cot\left(x\right)\,{d x}"," ",0,"integrate((cot(x) + 1)^(3/2)*cot(x), x)","F",0
45,0,0,0,0.000000," ","integrate(cot(x)^2/(1+cot(x))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)^{2}}{\sqrt{\cot\left(x\right) + 1}}\,{d x}"," ",0,"integrate(cot(x)^2/sqrt(cot(x) + 1), x)","F",0
46,0,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{\sqrt{\cot\left(x\right) + 1}}\,{d x}"," ",0,"integrate(cot(x)/sqrt(cot(x) + 1), x)","F",0
47,0,0,0,0.000000," ","integrate(cot(x)^2/(1+cot(x))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)^{2}}{{\left(\cot\left(x\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(x)^2/(cot(x) + 1)^(3/2), x)","F",0
48,0,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{{\left(\cot\left(x\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(x)/(cot(x) + 1)^(3/2), x)","F",0
49,0,0,0,0.000000," ","integrate(cot(x)^2/(1+cot(x))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)^{2}}{{\left(\cot\left(x\right) + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(x)^2/(cot(x) + 1)^(5/2), x)","F",0
50,0,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{{\left(\cot\left(x\right) + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(x)/(cot(x) + 1)^(5/2), x)","F",0
51,1,221,0,0.852025," ","integrate((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, {\left(\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e - \frac{8 \, {\left(3 \, a e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + b \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e}\right)} e}{12 \, d}"," ",0,"1/12*(3*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a - b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e - 8*(3*a*e*sqrt(e/tan(d*x + c)) + b*(e/tan(d*x + c))^(3/2))/e)*e/d","A",0
52,1,199,0,0.728332," ","integrate((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{8 \, b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{e}\right)} e}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a + b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + 8*b*sqrt(e/tan(d*x + c))/e)*e/d","A",0
53,1,180,0,0.749677," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a - b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/d","A",0
54,1,204,0,0.692259," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{e^{2}} + \frac{8 \, a}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)}}{4 \, d}"," ",0,"1/4*e*((2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a + b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^2 + 8*a/(e^2*sqrt(e/tan(d*x + c))))/d","A",0
55,1,220,0,0.704093," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{3}} + \frac{8 \, {\left(a e + \frac{3 \, b e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{12 \, d}"," ",0,"1/12*e*(3*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a - b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^3 + 8*(a*e + 3*b*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
56,1,287,0,0.584827," ","integrate((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(15 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e - \frac{8 \, {\left(10 \, a b e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + 3 \, b^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} + 15 \, {\left(a^{2} - b^{2}\right)} e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{e^{2}}\right)} e}{60 \, d}"," ",0,"1/60*(15*(2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e - 8*(10*a*b*e*(e/tan(d*x + c))^(3/2) + 3*b^2*(e/tan(d*x + c))^(5/2) + 15*(a^2 - b^2)*e^2*sqrt(e/tan(d*x + c)))/e^2)*e/d","A",0
57,1,257,0,0.450521," ","integrate((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{6 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{6 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{3 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{3 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{8 \, {\left(6 \, a b e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + b^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e^{2}}\right)} e}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 6*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - 3*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + 3*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + 8*(6*a*b*e*sqrt(e/tan(d*x + c)) + b^2*(e/tan(d*x + c))^(3/2))/e^2)*e/d","A",0
58,1,242,0,0.796655," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{8 \, b^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{e^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{e}\right)}}{4 \, d}"," ",0,"-1/4*e*(8*b^2*sqrt(e/tan(d*x + c))/e^2 + (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e)/d","A",0
59,1,242,0,0.899973," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{8 \, a^{2}}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}} + \frac{\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{e^{2}}\right)}}{4 \, d}"," ",0,"1/4*e*(8*a^2/(e^2*sqrt(e/tan(d*x + c))) + (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^2)/d","A",0
60,1,259,0,0.625732," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{3}} + \frac{8 \, {\left(a^{2} e + \frac{6 \, a b e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{12 \, d}"," ",0,"1/12*e*(3*(2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^3 + 8*(a^2*e + 6*a*b*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
61,1,286,0,0.530456," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{15 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{4}} - \frac{8 \, {\left(3 \, a^{2} e^{2} + \frac{10 \, a b e^{2}}{\tan\left(d x + c\right)} - \frac{15 \, {\left(a^{2} - b^{2}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}\right)}}{e^{4} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}}\right)}}{60 \, d}"," ",0,"-1/60*e*(15*(2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^4 - 8*(3*a^2*e^2 + 10*a*b*e^2/tan(d*x + c) - 15*(a^2 - b^2)*e^2/tan(d*x + c)^2)/(e^4*(e/tan(d*x + c))^(5/2)))/d","A",0
62,1,347,0,0.440173," ","integrate((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(105 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e - \frac{8 \, {\left(63 \, a b^{2} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} + 15 \, b^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}} + 105 \, {\left(a^{3} - 3 \, a b^{2}\right)} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 35 \, {\left(3 \, a^{2} b - b^{3}\right)} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e^{3}}\right)} e}{420 \, d}"," ",0,"1/420*(105*(2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e - 8*(63*a*b^2*e*(e/tan(d*x + c))^(5/2) + 15*b^3*(e/tan(d*x + c))^(7/2) + 105*(a^3 - 3*a*b^2)*e^3*sqrt(e/tan(d*x + c)) + 35*(3*a^2*b - b^3)*e^2*(e/tan(d*x + c))^(3/2))/e^3)*e/d","A",0
63,1,316,0,0.437183," ","integrate((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{8 \, {\left(5 \, a b^{2} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + b^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} + 5 \, {\left(3 \, a^{2} b - b^{3}\right)} e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{e^{3}}\right)} e}{20 \, d}"," ",0,"-1/20*(10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + 8*(5*a*b^2*e*(e/tan(d*x + c))^(3/2) + b^3*(e/tan(d*x + c))^(5/2) + 5*(3*a^2*b - b^3)*e^2*sqrt(e/tan(d*x + c)))/e^3)*e/d","A",0
64,1,292,0,0.517390," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e} + \frac{8 \, {\left(9 \, a b^{2} e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + b^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)}}{e^{3}}\right)}}{12 \, d}"," ",0,"-1/12*e*(3*(2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e + 8*(9*a*b^2*e*sqrt(e/tan(d*x + c)) + b^3*(e/tan(d*x + c))^(3/2))/e^3)/d","A",0
65,1,290,0,0.652836," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{8 \, a^{3}}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}} - \frac{8 \, b^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{e^{3}} + \frac{\frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{e^{2}}\right)}}{4 \, d}"," ",0,"1/4*e*(8*a^3/(e^2*sqrt(e/tan(d*x + c))) - 8*b^3*sqrt(e/tan(d*x + c))/e^3 + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^2)/d","A",0
66,1,289,0,0.692656," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{e {\left(\frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{3}} + \frac{8 \, {\left(a^{3} e + \frac{9 \, a^{2} b e}{\tan\left(d x + c\right)}\right)}}{e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{12 \, d}"," ",0,"1/12*e*(3*(2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^3 + 8*(a^3*e + 9*a^2*b*e/tan(d*x + c))/(e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
67,1,316,0,0.710958," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{5 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{4}} - \frac{8 \, {\left(a^{3} e^{2} + \frac{5 \, a^{2} b e^{2}}{\tan\left(d x + c\right)} - \frac{5 \, {\left(a^{3} - 3 \, a b^{2}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}\right)}}{e^{4} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}}\right)}}{20 \, d}"," ",0,"-1/20*e*(5*(2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^4 - 8*(a^3*e^2 + 5*a^2*b*e^2/tan(d*x + c) - 5*(a^3 - 3*a*b^2)*e^2/tan(d*x + c)^2)/(e^4*(e/tan(d*x + c))^(5/2)))/d","A",0
68,1,342,0,0.766048," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x, algorithm=""maxima"")","-\frac{e {\left(\frac{105 \, {\left(\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{e^{5}} - \frac{8 \, {\left(15 \, a^{3} e^{3} + \frac{63 \, a^{2} b e^{3}}{\tan\left(d x + c\right)} - \frac{35 \, {\left(a^{3} - 3 \, a b^{2}\right)} e^{3}}{\tan\left(d x + c\right)^{2}} - \frac{105 \, {\left(3 \, a^{2} b - b^{3}\right)} e^{3}}{\tan\left(d x + c\right)^{3}}\right)}}{e^{5} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{7}{2}}}\right)}}{420 \, d}"," ",0,"-1/420*e*(105*(2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^5 - 8*(15*a^3*e^3 + 63*a^2*b*e^3/tan(d*x + c) - 35*(a^3 - 3*a*b^2)*e^3/tan(d*x + c)^2 - 105*(3*a^2*b - b^3)*e^3/tan(d*x + c)^3)/(e^5*(e/tan(d*x + c))^(7/2)))/d","A",0
69,1,259,0,0.538085," ","integrate((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\frac{8 \, a^{3} e^{2} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{2} b + b^{3}\right)} \sqrt{a b e}} + \frac{{\left(\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e^{2}}{a^{2} + b^{2}} - \frac{8 \, e \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{b}\right)} e}{4 \, d}"," ",0,"1/4*(8*a^3*e^2*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^2*b + b^3)*sqrt(a*b*e)) + (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e^2/(a^2 + b^2) - 8*e*sqrt(e/tan(d*x + c))/b)*e/d","A",0
70,1,236,0,0.494349," ","integrate((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(\frac{8 \, a^{2} e \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{\sqrt{a b e} {\left(a^{2} + b^{2}\right)}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e}{a^{2} + b^{2}}\right)} e}{4 \, d}"," ",0,"-1/4*(8*a^2*e*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/(sqrt(a*b*e)*(a^2 + b^2)) - (2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e/(a^2 + b^2))*e/d","A",0
71,1,233,0,0.483924," ","integrate((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\frac{8 \, a b \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{\sqrt{a b e} {\left(a^{2} + b^{2}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{2} + b^{2}}\right)} e}{4 \, d}"," ",0,"1/4*(8*a*b*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/(sqrt(a*b*e)*(a^2 + b^2)) - (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a^2 + b^2))*e/d","A",0
72,1,239,0,0.525539," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{e {\left(\frac{8 \, b^{2} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{\sqrt{a b e} {\left(a^{2} + b^{2}\right)} e} + \frac{\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{{\left(a^{2} + b^{2}\right)} e}\right)}}{4 \, d}"," ",0,"-1/4*e*(8*b^2*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/(sqrt(a*b*e)*(a^2 + b^2)*e) + (2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^2 + b^2)*e))/d","A",0
73,1,261,0,0.909594," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","\frac{e {\left(\frac{8 \, b^{3} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{3} + a b^{2}\right)} \sqrt{a b e} e^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{{\left(a^{2} + b^{2}\right)} e^{2}} + \frac{8}{a e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)}}{4 \, d}"," ",0,"1/4*e*(8*b^3*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^3 + a*b^2)*sqrt(a*b*e)*e^2) + (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^2 + b^2)*e^2) + 8/(a*e^2*sqrt(e/tan(d*x + c))))/d","A",0
74,1,280,0,0.661747," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","-\frac{e {\left(\frac{24 \, b^{4} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{4} + a^{2} b^{2}\right)} \sqrt{a b e} e^{3}} - \frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{{\left(a^{2} + b^{2}\right)} e^{3}} - \frac{8 \, {\left(a e - \frac{3 \, b e}{\tan\left(d x + c\right)}\right)}}{a^{2} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}\right)}}{12 \, d}"," ",0,"-1/12*e*(24*b^4*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^4 + a^2*b^2)*sqrt(a*b*e)*e^3) - 3*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^2 + b^2)*e^3) - 8*(a*e - 3*b*e/tan(d*x + c))/(a^2*e^3*(e/tan(d*x + c))^(3/2)))/d","A",0
75,1,385,0,0.462480," ","integrate((e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{4 \, a^{3} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{{\left(a^{3} b^{2} + a b^{4}\right)} e + \frac{{\left(a^{2} b^{3} + b^{5}\right)} e}{\tan\left(d x + c\right)}} - \frac{4 \, {\left(3 \, a^{5} + 7 \, a^{3} b^{2}\right)} e^{3} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a b e}} + \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e^{3}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{8 \, e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{b^{2}}\right)} e}{4 \, d}"," ",0,"-1/4*(4*a^3*e^3*sqrt(e/tan(d*x + c))/((a^3*b^2 + a*b^4)*e + (a^2*b^3 + b^5)*e/tan(d*x + c)) - 4*(3*a^5 + 7*a^3*b^2)*e^3*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^4*b^2 + 2*a^2*b^4 + b^6)*sqrt(a*b*e)) + (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e^3/(a^4 + 2*a^2*b^2 + b^4) + 8*e^2*sqrt(e/tan(d*x + c))/b^2)*e/d","A",0
76,1,359,0,0.449027," ","integrate((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(\frac{4 \, a^{2} e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{{\left(a^{3} b + a b^{3}\right)} e + \frac{{\left(a^{2} b^{2} + b^{4}\right)} e}{\tan\left(d x + c\right)}} - \frac{4 \, {\left(a^{4} + 5 \, a^{2} b^{2}\right)} e^{2} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{a b e}} + \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e^{2}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}\right)} e}{4 \, d}"," ",0,"1/4*(4*a^2*e^2*sqrt(e/tan(d*x + c))/((a^3*b + a*b^3)*e + (a^2*b^2 + b^4)*e/tan(d*x + c)) - 4*(a^4 + 5*a^2*b^2)*e^2*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^4*b + 2*a^2*b^3 + b^5)*sqrt(a*b*e)) + (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e^2/(a^4 + 2*a^2*b^2 + b^4))*e/d","A",0
77,1,344,0,0.592005," ","integrate((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{4 \, a e \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{{\left(a^{3} + a b^{2}\right)} e + \frac{{\left(a^{2} b + b^{3}\right)} e}{\tan\left(d x + c\right)}} + \frac{4 \, {\left(a^{3} - 3 \, a b^{2}\right)} e \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a b e}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}\right)} e}{4 \, d}"," ",0,"-1/4*(4*a*e*sqrt(e/tan(d*x + c))/((a^3 + a*b^2)*e + (a^2*b + b^3)*e/tan(d*x + c)) + 4*(a^3 - 3*a*b^2)*e*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a*b*e)) - (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e/(a^4 + 2*a^2*b^2 + b^4))*e/d","A",0
78,1,343,0,0.668365," ","integrate((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{e {\left(\frac{4 \, b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{{\left(a^{3} + a b^{2}\right)} e + \frac{{\left(a^{2} b + b^{3}\right)} e}{\tan\left(d x + c\right)}} + \frac{4 \, {\left(3 \, a^{2} b - b^{3}\right)} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a b e}} - \frac{\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}\right)}}{4 \, d}"," ",0,"1/4*e*(4*b*sqrt(e/tan(d*x + c))/((a^3 + a*b^2)*e + (a^2*b + b^3)*e/tan(d*x + c)) + 4*(3*a^2*b - b^3)*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a*b*e)) - (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
79,1,360,0,0.534575," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{4 \, b^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{{\left(a^{4} + a^{2} b^{2}\right)} e^{2} + \frac{{\left(a^{3} b + a b^{3}\right)} e^{2}}{\tan\left(d x + c\right)}} + \frac{4 \, {\left(5 \, a^{2} b^{2} + b^{4}\right)} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{a b e} e} + \frac{\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} e}\right)} e}{4 \, d}"," ",0,"-1/4*(4*b^2*sqrt(e/tan(d*x + c))/((a^4 + a^2*b^2)*e^2 + (a^3*b + a*b^3)*e^2/tan(d*x + c)) + 4*(5*a^2*b^2 + b^4)*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(a*b*e)*e) + (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^4 + 2*a^2*b^2 + b^4)*e))*e/d","A",0
80,1,402,0,0.718035," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{e {\left(\frac{4 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} e + \frac{{\left(2 \, a^{2} b + 3 \, b^{3}\right)} e}{\tan\left(d x + c\right)}\right)}}{{\left(a^{5} + a^{3} b^{2}\right)} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + {\left(a^{4} b + a^{2} b^{3}\right)} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}} + \frac{4 \, {\left(7 \, a^{2} b^{3} + 3 \, b^{5}\right)} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{a b e} e^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} e^{2}}\right)}}{4 \, d}"," ",0,"1/4*e*(4*(2*(a^3 + a*b^2)*e + (2*a^2*b + 3*b^3)*e/tan(d*x + c))/((a^5 + a^3*b^2)*e^3*sqrt(e/tan(d*x + c)) + (a^4*b + a^2*b^3)*e^2*(e/tan(d*x + c))^(3/2)) + 4*(7*a^2*b^3 + 3*b^5)*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^6 + 2*a^4*b^2 + a^2*b^4)*sqrt(a*b*e)*e^2) + (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^4 + 2*a^2*b^2 + b^4)*e^2))/d","A",0
81,1,537,0,0.614952," ","integrate((e*cot(d*x+c))^(9/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(\frac{{\left(15 \, a^{7} + 46 \, a^{5} b^{2} + 63 \, a^{3} b^{4}\right)} e^{4} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \sqrt{a b e}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e^{4}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{8 \, e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{b^{3}} - \frac{{\left(7 \, a^{6} + 15 \, a^{4} b^{2}\right)} e^{5} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + {\left(9 \, a^{5} b + 17 \, a^{3} b^{3}\right)} e^{4} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{{\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} e^{2} + \frac{2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} e^{2}}{\tan\left(d x + c\right)} + \frac{{\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}}\right)} e}{4 \, d}"," ",0,"1/4*((15*a^7 + 46*a^5*b^2 + 63*a^3*b^4)*e^4*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*sqrt(a*b*e)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e^4/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 8*e^3*sqrt(e/tan(d*x + c))/b^3 - ((7*a^6 + 15*a^4*b^2)*e^5*sqrt(e/tan(d*x + c)) + (9*a^5*b + 17*a^3*b^3)*e^4*(e/tan(d*x + c))^(3/2))/((a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*e^2 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*e^2/tan(d*x + c) + (a^4*b^5 + 2*a^2*b^7 + b^9)*e^2/tan(d*x + c)^2))*e/d","A",0
82,1,516,0,0.754566," ","integrate((e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{{\left(3 \, a^{6} + 6 \, a^{4} b^{2} + 35 \, a^{2} b^{4}\right)} e^{3} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a b e}} + \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e^{3}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{5} + 11 \, a^{3} b^{2}\right)} e^{4} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + {\left(5 \, a^{4} b + 13 \, a^{2} b^{3}\right)} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{{\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} e^{2} + \frac{2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} e^{2}}{\tan\left(d x + c\right)} + \frac{{\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}}\right)} e}{4 \, d}"," ",0,"-1/4*((3*a^6 + 6*a^4*b^2 + 35*a^2*b^4)*e^3*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*sqrt(a*b*e)) + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e^3/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((3*a^5 + 11*a^3*b^2)*e^4*sqrt(e/tan(d*x + c)) + (5*a^4*b + 13*a^2*b^3)*e^3*(e/tan(d*x + c))^(3/2))/((a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*e^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*e^2/tan(d*x + c) + (a^4*b^4 + 2*a^2*b^6 + b^8)*e^2/tan(d*x + c)^2))*e/d","A",0
83,1,505,0,0.558214," ","integrate((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{{\left(a^{5} + 18 \, a^{3} b^{2} - 15 \, a b^{4}\right)} e^{2} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a b e}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e^{2}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(a^{4} - 7 \, a^{2} b^{2}\right)} e^{3} \sqrt{\frac{e}{\tan\left(d x + c\right)}} - {\left(a^{3} b + 9 \, a b^{3}\right)} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{{\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} e^{2} + \frac{2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} e^{2}}{\tan\left(d x + c\right)} + \frac{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}}\right)} e}{4 \, d}"," ",0,"-1/4*((a^5 + 18*a^3*b^2 - 15*a*b^4)*e^2*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sqrt(a*b*e)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e^2/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((a^4 - 7*a^2*b^2)*e^3*sqrt(e/tan(d*x + c)) - (a^3*b + 9*a*b^3)*e^2*(e/tan(d*x + c))^(3/2))/((a^6*b + 2*a^4*b^3 + a^2*b^5)*e^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*e^2/tan(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*e^2/tan(d*x + c)^2))*e/d","A",0
84,1,492,0,0.777591," ","integrate((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{{\left(3 \, a^{4} - 26 \, a^{2} b^{2} + 3 \, b^{4}\right)} e \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a b e}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} e}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(5 \, a^{3} - 3 \, a b^{2}\right)} e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + {\left(3 \, a^{2} b - 5 \, b^{3}\right)} e \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} e^{2} + \frac{2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} e^{2}}{\tan\left(d x + c\right)} + \frac{{\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}}\right)} e}{4 \, d}"," ",0,"-1/4*((3*a^4 - 26*a^2*b^2 + 3*b^4)*e*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a*b*e)) - (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))*e/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((5*a^3 - 3*a*b^2)*e^2*sqrt(e/tan(d*x + c)) + (3*a^2*b - 5*b^3)*e*(e/tan(d*x + c))^(3/2))/((a^6 + 2*a^4*b^2 + a^2*b^4)*e^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*e^2/tan(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*e^2/tan(d*x + c)^2))*e/d","A",0
85,1,496,0,0.841573," ","integrate((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{e {\left(\frac{{\left(15 \, a^{4} b - 18 \, a^{2} b^{3} - b^{5}\right)} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{a b e}} + \frac{{\left(9 \, a^{3} b + a b^{3}\right)} e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + {\left(7 \, a^{2} b^{2} - b^{4}\right)} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{{\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} e^{2} + \frac{2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} e^{2}}{\tan\left(d x + c\right)} + \frac{{\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}} - \frac{\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}\right)}}{4 \, d}"," ",0,"1/4*e*((15*a^4*b - 18*a^2*b^3 - b^5)*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt(a*b*e)) + ((9*a^3*b + a*b^3)*e*sqrt(e/tan(d*x + c)) + (7*a^2*b^2 - b^4)*(e/tan(d*x + c))^(3/2))/((a^7 + 2*a^5*b^2 + a^3*b^4)*e^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*e^2/tan(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*e^2/tan(d*x + c)^2) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6))/d","A",0
86,1,510,0,0.475208," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","-\frac{e {\left(\frac{{\left(13 \, a^{3} b^{2} + 5 \, a b^{4}\right)} e \sqrt{\frac{e}{\tan\left(d x + c\right)}} + {\left(11 \, a^{2} b^{3} + 3 \, b^{5}\right)} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}{{\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} e^{3} + \frac{2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} e^{3}}{\tan\left(d x + c\right)} + \frac{{\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} e^{3}}{\tan\left(d x + c\right)^{2}}} + \frac{{\left(35 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, b^{6}\right)} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sqrt{a b e} e} + \frac{\frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} e}\right)}}{4 \, d}"," ",0,"-1/4*e*(((13*a^3*b^2 + 5*a*b^4)*e*sqrt(e/tan(d*x + c)) + (11*a^2*b^3 + 3*b^5)*(e/tan(d*x + c))^(3/2))/((a^8 + 2*a^6*b^2 + a^4*b^4)*e^3 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*e^3/tan(d*x + c) + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*e^3/tan(d*x + c)^2) + (35*a^4*b^2 + 6*a^2*b^4 + 3*b^6)*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*sqrt(a*b*e)*e) + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*e))/d","A",0
87,1,565,0,0.453180," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{e {\left(\frac{8 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} e^{2} + \frac{{\left(16 \, a^{5} b + 49 \, a^{3} b^{3} + 25 \, a b^{5}\right)} e^{2}}{\tan\left(d x + c\right)} + \frac{{\left(8 \, a^{4} b^{2} + 31 \, a^{2} b^{4} + 15 \, b^{6}\right)} e^{2}}{\tan\left(d x + c\right)^{2}}}{{\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} e^{4} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} e^{3} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} + {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} e^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}}} + \frac{{\left(63 \, a^{4} b^{3} + 46 \, a^{2} b^{5} + 15 \, b^{7}\right)} \arctan\left(\frac{b \sqrt{\frac{e}{\tan\left(d x + c\right)}}}{\sqrt{a b e}}\right)}{{\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} \sqrt{a b e} e^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} e^{2}}\right)}}{4 \, d}"," ",0,"1/4*e*((8*(a^6 + 2*a^4*b^2 + a^2*b^4)*e^2 + (16*a^5*b + 49*a^3*b^3 + 25*a*b^5)*e^2/tan(d*x + c) + (8*a^4*b^2 + 31*a^2*b^4 + 15*b^6)*e^2/tan(d*x + c)^2)/((a^9 + 2*a^7*b^2 + a^5*b^4)*e^4*sqrt(e/tan(d*x + c)) + 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*e^3*(e/tan(d*x + c))^(3/2) + (a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*e^2*(e/tan(d*x + c))^(5/2)) + (63*a^4*b^3 + 46*a^2*b^5 + 15*b^7)*arctan(b*sqrt(e/tan(d*x + c))/sqrt(a*b*e))/((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*sqrt(a*b*e)*e^2) + (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*e^2))/d","A",0
88,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \cot\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*cot(d*x + c) + a)^n, x)","F",0
89,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \cot\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*cot(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
90,0,0,0,0.000000," ","integrate((1+I*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{i \, \cot\left(d x + c\right) + 1}{\sqrt{b \cot\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((I*cot(d*x + c) + 1)/sqrt(b*cot(d*x + c) + a), x)","F",0
91,0,0,0,0.000000," ","integrate((1-I*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{-i \, \cot\left(d x + c\right) + 1}{\sqrt{b \cot\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((-I*cot(d*x + c) + 1)/sqrt(b*cot(d*x + c) + a), x)","F",0
92,1,89,0,1.689718," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a + B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(B a - A b\right)} \log\left(a \tan\left(d x + c\right) + b\right)}{a^{2} + b^{2}} - \frac{{\left(B a - A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*(A*a + B*b)*(d*x + c)/(a^2 + b^2) + 2*(B*a - A*b)*log(a*tan(d*x + c) + b)/(a^2 + b^2) - (B*a - A*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
93,1,185,0,0.530277," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a^{2} + 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(a \tan\left(d x + c\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a b - A b^{2}\right)}}{a^{3} b + a b^{3} + {\left(a^{4} + a^{2} b^{2}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(A*a^2 + 2*B*a*b - A*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a^2 - 2*A*a*b - B*b^2)*log(a*tan(d*x + c) + b)/(a^4 + 2*a^2*b^2 + b^4) - (B*a^2 - 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a*b - A*b^2)/(a^3*b + a*b^3 + (a^4 + a^2*b^2)*tan(d*x + c)))/d","A",0
94,1,337,0,0.865677," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{2} - B b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A b^{3}\right)} \log\left(a \tan\left(d x + c\right) + b\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3} - B a b^{4} - A b^{5} + 2 \, {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - A a b^{4}\right)} \tan\left(d x + c\right)}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(A*a^3 + 3*B*a^2*b - 3*A*a*b^2 - B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(a*tan(d*x + c) + b)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*B*a^3*b^2 - 5*A*a^2*b^3 - B*a*b^4 - A*b^5 + 2*(2*B*a^4*b - 3*A*a^3*b^2 - A*a*b^4)*tan(d*x + c))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + (a^8 + 2*a^6*b^2 + a^4*b^4)*tan(d*x + c)^2 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*tan(d*x + c)))/d","A",0
95,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^(5/2)*(A+B*cot(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cot\left(d x + c\right) + A\right)} {\left(b \cot\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cot(d*x + c) + A)*(b*cot(d*x + c) + a)^(5/2), x)","F",0
96,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^(3/2)*(A+B*cot(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^(1/2)*(A+B*cot(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cot\left(d x + c\right) + A\right)} \sqrt{b \cot\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*cot(d*x + c) + A)*sqrt(b*cot(d*x + c) + a), x)","F",0
98,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cot\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(b \cot\left(d x + c\right) - a\right)}\,{d x}"," ",0,"integrate((b*cot(d*x + c) + a)^(5/2)*(b*cot(d*x + c) - a), x)","F",0
99,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cot\left(d x + c\right) + a} {\left(b \cot\left(d x + c\right) - a\right)}\,{d x}"," ",0,"integrate(sqrt(b*cot(d*x + c) + a)*(b*cot(d*x + c) - a), x)","F",0
101,0,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \cot\left(d x + c\right) + A}{\sqrt{b \cot\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*cot(d*x + c) + A)/sqrt(b*cot(d*x + c) + a), x)","F",0
102,0,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \cot\left(d x + c\right) + A}{{\left(b \cot\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cot(d*x + c) + A)/(b*cot(d*x + c) + a)^(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \cot\left(d x + c\right) + A}{{\left(b \cot\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cot(d*x + c) + A)/(b*cot(d*x + c) + a)^(5/2), x)","F",0
104,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{b \cot\left(d x + c\right) - a}{\sqrt{b \cot\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((b*cot(d*x + c) - a)/sqrt(b*cot(d*x + c) + a), x)","F",0
105,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{b \cot\left(d x + c\right) - a}{{\left(b \cot\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cot(d*x + c) - a)/(b*cot(d*x + c) + a)^(3/2), x)","F",0
106,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{b \cot\left(d x + c\right) - a}{{\left(b \cot\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cot(d*x + c) - a)/(b*cot(d*x + c) + a)^(5/2), x)","F",0
