1,0,0,42,2.502000," ","int((a+I*a*cot(d*x+c))^n,x)","\int \left(a +i a \cot \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+I*a*cot(d*x+c))^n,x)","F"
2,1,388,95,0.495000," ","int((e*cot(d*x+c))^(5/2)*(a+cot(d*x+c)*a),x)","-\frac{2 a \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}-\frac{2 a e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{2 a \,e^{2} \sqrt{e \cot \left(d x +c \right)}}{d}-\frac{a \,e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d}-\frac{a \,e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}+\frac{a \,e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}+\frac{a \,e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \,e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \,e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5*a*(e*cot(d*x+c))^(5/2)/d-2/3*a*e*(e*cot(d*x+c))^(3/2)/d+2*a*e^2*(e*cot(d*x+c))^(1/2)/d-1/4*a/d*e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2*a/d*e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2*a/d*e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4*a/d*e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d*e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d*e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
3,1,363,77,0.427000," ","int((e*cot(d*x+c))^(3/2)*(a+cot(d*x+c)*a),x)","-\frac{2 a \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{2 a e \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d}+\frac{a e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{a e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}+\frac{a \,e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \,e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \,e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*a*(e*cot(d*x+c))^(3/2)/d-2*a*e*(e*cot(d*x+c))^(1/2)/d+1/4*a/d*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4*a/d*e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d*e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d*e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
4,1,337,58,0.431000," ","int((e*cot(d*x+c))^(1/2)*(a+cot(d*x+c)*a),x)","-\frac{2 a \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{a e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*a*(e*cot(d*x+c))^(1/2)/d+1/4*a/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4*a/d*e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2*a/d*e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2*a/d*e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
5,1,327,40,0.430000," ","int((a+cot(d*x+c)*a)/(e*cot(d*x+c))^(1/2),x)","-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}-\frac{a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4*a/d/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2*a/d/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2*a/d/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4*a/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2*a/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2*a/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
6,1,355,62,0.359000," ","int((a+cot(d*x+c)*a)/(e*cot(d*x+c))^(3/2),x)","-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{2}}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2}}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2}}+\frac{a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a}{d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-1/4*a/d/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2*a/d/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2*a/d/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4*a/d/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2*a/d/e/(e*cot(d*x+c))^(1/2)","B"
7,1,374,82,0.356000," ","int((a+cot(d*x+c)*a)/(e*cot(d*x+c))^(5/2),x)","\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{3}}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3}}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3}}+\frac{a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a}{d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}+\frac{2 a}{3 d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/4*a/d/e^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d/e^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d/e^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4*a/d/e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d/e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d/e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2*a/d/e^2/(e*cot(d*x+c))^(1/2)+2/3*a/d/e/(e*cot(d*x+c))^(3/2)","B"
8,1,234,216,0.606000," ","int((e*cot(d*x+c))^(5/2)*(a+cot(d*x+c)*a)^2,x)","-\frac{2 a^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d e}-\frac{4 a^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}+\frac{4 a^{2} e^{2} \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a^{2} e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{a^{2} e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d}-\frac{a^{2} e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}"," ",0,"-2/7*a^2*(e*cot(d*x+c))^(7/2)/d/e-4/5*a^2*(e*cot(d*x+c))^(5/2)/d+4*a^2*e^2*(e*cot(d*x+c))^(1/2)/d+1/d*a^2*e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*a^2*e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^2*e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
9,1,213,195,0.613000," ","int((e*cot(d*x+c))^(3/2)*(a+cot(d*x+c)*a)^2,x)","-\frac{2 a^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d e}-\frac{4 a^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{a^{2} e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5*a^2*(e*cot(d*x+c))^(5/2)/d/e-4/3*a^2*(e*cot(d*x+c))^(3/2)/d+1/2/d*a^2*e^2/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^2*e^2/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^2*e^2/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
10,1,204,195,0.592000," ","int((e*cot(d*x+c))^(1/2)*(a+cot(d*x+c)*a)^2,x)","-\frac{2 a^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d e}-\frac{4 a^{2} \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}+\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d}"," ",0,"-2/3*a^2*(e*cot(d*x+c))^(3/2)/d/e-4*a^2*(e*cot(d*x+c))^(1/2)/d+1/d*a^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*a^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))","A"
11,1,186,177,0.535000," ","int((a+cot(d*x+c)*a)^2/(e*cot(d*x+c))^(1/2),x)","-\frac{2 a^{2} \sqrt{e \cot \left(d x +c \right)}}{d e}-\frac{a^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*a^2*(e*cot(d*x+c))^(1/2)/d/e-1/2/d*a^2/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^2/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^2/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
12,1,195,177,0.484000," ","int((a+cot(d*x+c)*a)^2/(e*cot(d*x+c))^(3/2),x)","-\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{2}}-\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2}}+\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2}}+\frac{2 a^{2}}{d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-1/2/d*a^2/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^2/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^2/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2*a^2/d/e/(e*cot(d*x+c))^(1/2)","A"
13,1,216,198,0.467000," ","int((a+cot(d*x+c)*a)^2/(e*cot(d*x+c))^(5/2),x)","\frac{a^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{2}}{3 d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{4 a^{2}}{d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/2/d*a^2/e^2/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^2/e^2/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^2/e^2/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3*a^2/d/e/(e*cot(d*x+c))^(3/2)+4*a^2/d/e^2/(e*cot(d*x+c))^(1/2)","A"
14,1,216,198,0.460000," ","int((a+cot(d*x+c)*a)^2/(e*cot(d*x+c))^(7/2),x)","\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{4}}+\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{4}}-\frac{a^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{4}}+\frac{2 a^{2}}{5 d e \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{4 a^{2}}{3 d \,e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/d*a^2/e^4*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^2/e^4*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^2/e^4*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/5*a^2/d/e/(e*cot(d*x+c))^(5/2)+4/3*a^2/d/e^2/(e*cot(d*x+c))^(3/2)","A"
15,1,446,157,0.791000," ","int((e*cot(d*x+c))^(5/2)*(a+cot(d*x+c)*a)^3,x)","-\frac{2 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{9}{2}}}{9 d \,e^{2}}-\frac{6 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d e}-\frac{4 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}+\frac{4 a^{3} e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{4 a^{3} e^{2} \sqrt{e \cot \left(d x +c \right)}}{d}-\frac{a^{3} e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d}-\frac{a^{3} e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}+\frac{a^{3} e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{a^{3} e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/9/d*a^3/e^2*(e*cot(d*x+c))^(9/2)-6/7*a^3*(e*cot(d*x+c))^(7/2)/d/e-4/5*a^3*(e*cot(d*x+c))^(5/2)/d+4/3*a^3*e*(e*cot(d*x+c))^(3/2)/d+4*a^3*e^2*(e*cot(d*x+c))^(1/2)/d-1/2/d*a^3*e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3*e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3*e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*a^3*e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3*e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3*e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
16,1,419,135,0.869000," ","int((e*cot(d*x+c))^(3/2)*(a+cot(d*x+c)*a)^3,x)","-\frac{2 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d \,e^{2}}-\frac{6 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d e}-\frac{4 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{4 a^{3} e \sqrt{e \cot \left(d x +c \right)}}{d}-\frac{a^{3} e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d}-\frac{a^{3} e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}+\frac{a^{3} e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}+\frac{a^{3} e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/7/d*a^3/e^2*(e*cot(d*x+c))^(7/2)-6/5*a^3*(e*cot(d*x+c))^(5/2)/d/e-4/3*a^3*(e*cot(d*x+c))^(3/2)/d+4*a^3*e*(e*cot(d*x+c))^(1/2)/d-1/2/d*a^3*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*a^3*e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3*e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3*e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
17,1,391,117,0.960000," ","int((e*cot(d*x+c))^(1/2)*(a+cot(d*x+c)*a)^3,x)","-\frac{2 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,e^{2}}-\frac{2 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{d e}-\frac{4 a^{3} \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}+\frac{a^{3} e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5/d*a^3/e^2*(e*cot(d*x+c))^(5/2)-2*a^3*(e*cot(d*x+c))^(3/2)/d/e-4*a^3*(e*cot(d*x+c))^(1/2)/d+1/2/d*a^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*a^3*e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3*e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3*e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
18,1,379,98,0.568000," ","int((a+cot(d*x+c)*a)^3/(e*cot(d*x+c))^(1/2),x)","-\frac{2 a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,e^{2}}-\frac{6 a^{3} \sqrt{e \cot \left(d x +c \right)}}{d e}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d e}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d e}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d e}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3/d*a^3/e^2*(e*cot(d*x+c))^(3/2)-6*a^3*(e*cot(d*x+c))^(1/2)/d/e+1/2/d*a^3/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*a^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
19,1,388,99,0.479000," ","int((a+cot(d*x+c)*a)^3/(e*cot(d*x+c))^(3/2),x)","-\frac{2 a^{3} \sqrt{e \cot \left(d x +c \right)}}{d \,e^{2}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{2}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2}}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2}}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-2*a^3*(e*cot(d*x+c))^(1/2)/d/e^2-1/2/d*a^3/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*a^3/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/d*a^3/e/(e*cot(d*x+c))^(1/2)","B"
20,1,388,98,0.498000," ","int((a+cot(d*x+c)*a)^3/(e*cot(d*x+c))^(5/2),x)","-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{3}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{3}}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{3}}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{3 d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{6 a^{3}}{d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-1/2/d*a^3/e^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3/e^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3/e^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*a^3/e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3/e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3/e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3/d*a^3/e/(e*cot(d*x+c))^(3/2)+6*a^3/d/e^2/(e*cot(d*x+c))^(1/2)","B"
21,1,409,120,0.526000," ","int((a+cot(d*x+c)*a)^3/(e*cot(d*x+c))^(7/2),x)","\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{4}}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{4}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{4}}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{5 d e \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{2 a^{3}}{d \,e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{4 a^{3}}{d \,e^{3} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/2/d*a^3/e^4*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3/e^4*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3/e^4*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*a^3/e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3/e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3/e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/5/d*a^3/e/(e*cot(d*x+c))^(5/2)+2*a^3/d/e^2/(e*cot(d*x+c))^(3/2)+4*a^3/d/e^3/(e*cot(d*x+c))^(1/2)","B"
22,1,430,140,0.536000," ","int((a+cot(d*x+c)*a)^3/(e*cot(d*x+c))^(9/2),x)","\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{5}}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{5}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{5}}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{7 d e \left(e \cot \left(d x +c \right)\right)^{\frac{7}{2}}}+\frac{6 a^{3}}{5 d \,e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{4 a^{3}}{d \,e^{4} \sqrt{e \cot \left(d x +c \right)}}+\frac{4 a^{3}}{3 d \,e^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/d*a^3/e^5*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a^3/e^5*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a^3/e^5*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*a^3/e^4*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a^3/e^4*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a^3/e^4*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/7/d*a^3/e/(e*cot(d*x+c))^(7/2)+6/5*a^3/d/e^2/(e*cot(d*x+c))^(5/2)-4*a^3/d/e^4/(e*cot(d*x+c))^(1/2)+4/3*a^3/d/e^3/(e*cot(d*x+c))^(3/2)","B"
23,1,394,92,0.730000," ","int((e*cot(d*x+c))^(5/2)/(a+cot(d*x+c)*a),x)","-\frac{2 e^{2} \sqrt{e \cot \left(d x +c \right)}}{d a}+\frac{e^{\frac{5}{2}} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{d a}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a}-\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a}+\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*e^2*(e*cot(d*x+c))^(1/2)/d/a+e^(5/2)*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/d/a+1/8/d/a*e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a*e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a*e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a*e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a*e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a*e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
24,1,368,71,0.732000," ","int((e*cot(d*x+c))^(3/2)/(a+cot(d*x+c)*a),x)","-\frac{e^{\frac{3}{2}} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{d a}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a}-\frac{e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-e^(3/2)*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/d/a+1/8/d/a*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a*e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a*e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a*e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
25,1,358,71,0.812000," ","int((e*cot(d*x+c))^(1/2)/(a+cot(d*x+c)*a),x)","\frac{\arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e}}{d a}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a}-\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"arctan((e*cot(d*x+c))^(1/2)/e^(1/2))*e^(1/2)/d/a-1/8/d/a*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a*e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a*e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a*e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
26,1,365,68,0.877000," ","int(1/(e*cot(d*x+c))^(1/2)/(a+cot(d*x+c)*a),x)","-\frac{\arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{a d \sqrt{e}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a e}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a e}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a e}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a/d/e^(1/2)-1/8/d/a/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
27,1,394,92,0.810000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+cot(d*x+c)*a),x)","\frac{\arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{a d \,e^{\frac{3}{2}}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \,e^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \,e^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \,e^{2}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{a d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a/d/e^(3/2)+1/8/d/a/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/a/d/e/(e*cot(d*x+c))^(1/2)","B"
28,1,416,113,0.758000," ","int(1/(e*cot(d*x+c))^(5/2)/(a+cot(d*x+c)*a),x)","-\frac{\arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{a d \,e^{\frac{5}{2}}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \,e^{3}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \,e^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \,e^{3}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d a \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d a \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{3 a d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{2}{a d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a/d/e^(5/2)+1/8/d/a/e^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a/e^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a/e^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a/e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a/e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a/e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3/a/d/e/(e*cot(d*x+c))^(3/2)-2/a/d/e^2/(e*cot(d*x+c))^(1/2)","B"
29,1,234,217,0.829000," ","int((e*cot(d*x+c))^(5/2)/(a+cot(d*x+c)*a)^2,x)","\frac{e^{3} \sqrt{e \cot \left(d x +c \right)}}{2 d \,a^{2} \left(e \cot \left(d x +c \right)+e \right)}-\frac{3 e^{\frac{5}{2}} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{2 a^{2} d}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d \,a^{2}}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2}}-\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2}}"," ",0,"1/2/d/a^2*e^3*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)+e)-3/2*e^(5/2)*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^2/d+1/8/d/a^2*e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a^2*e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a^2*e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
30,1,234,215,0.745000," ","int((e*cot(d*x+c))^(3/2)/(a+cot(d*x+c)*a)^2,x)","-\frac{e^{2} \sqrt{e \cot \left(d x +c \right)}}{2 d \,a^{2} \left(e \cot \left(d x +c \right)+e \right)}+\frac{e^{\frac{3}{2}} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{2 a^{2} d}-\frac{e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d \,a^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/2/d/a^2*e^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)+e)+1/2*e^(3/2)*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^2/d-1/8/d/a^2*e^2/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a^2*e^2/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a^2*e^2/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
31,1,223,214,0.792000," ","int((e*cot(d*x+c))^(1/2)/(a+cot(d*x+c)*a)^2,x)","-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d \,a^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2}}+\frac{e \sqrt{e \cot \left(d x +c \right)}}{2 d \,a^{2} \left(e \cot \left(d x +c \right)+e \right)}+\frac{\arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e}}{2 a^{2} d}"," ",0,"-1/8/d/a^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d/a^2*e*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)+e)+1/2*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))*e^(1/2)/a^2/d","A"
32,1,222,217,0.714000," ","int(1/(e*cot(d*x+c))^(1/2)/(a+cot(d*x+c)*a)^2,x)","-\frac{\sqrt{e \cot \left(d x +c \right)}}{2 d \,a^{2} \left(e \cot \left(d x +c \right)+e \right)}-\frac{3 \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{2 a^{2} d \sqrt{e}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d \,a^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/2/d/a^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)+e)-3/2*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^2/d/e^(1/2)+1/8/d/a^2/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a^2/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a^2/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
33,1,255,238,0.654000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+cot(d*x+c)*a)^2,x)","\frac{\sqrt{e \cot \left(d x +c \right)}}{2 d \,a^{2} e \left(e \cot \left(d x +c \right)+e \right)}+\frac{5 \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{2 a^{2} d \,e^{\frac{3}{2}}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d \,a^{2} e^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} e^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} e^{2}}+\frac{2}{a^{2} d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/2/d/a^2/e*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)+e)+5/2*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^2/d/e^(3/2)+1/8/d/a^2/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/4/d/a^2/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/a^2/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/a^2/d/e/(e*cot(d*x+c))^(1/2)","A"
34,1,276,259,0.666000," ","int(1/(e*cot(d*x+c))^(5/2)/(a+cot(d*x+c)*a)^2,x)","-\frac{\sqrt{e \cot \left(d x +c \right)}}{2 d \,a^{2} e^{2} \left(e \cot \left(d x +c \right)+e \right)}-\frac{7 \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{2 a^{2} d \,e^{\frac{5}{2}}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{8 d \,a^{2} e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{4 d \,a^{2} e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{3 a^{2} d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{4}{a^{2} d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-1/2/d/a^2/e^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)+e)-7/2*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^2/d/e^(5/2)-1/8/d/a^2/e^2/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/4/d/a^2/e^2/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/a^2/e^2/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3/a^2/d/e/(e*cot(d*x+c))^(3/2)-4/a^2/d/e^2/(e*cot(d*x+c))^(1/2)","A"
35,1,440,135,0.831000," ","int((e*cot(d*x+c))^(5/2)/(a+cot(d*x+c)*a)^3,x)","-\frac{5 e^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{3 e^{4} \sqrt{e \cot \left(d x +c \right)}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{e^{\frac{5}{2}} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{8 a^{3} d}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3}}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3}}-\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3}}-\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-5/8/d/a^3*e^3/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(3/2)-3/8/d/a^3*e^4/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(1/2)-1/8*e^(5/2)*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^3/d+1/16/d/a^3*e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/8/d/a^3*e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a^3*e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/16/d/a^3*e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3*e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3*e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
36,1,434,135,0.845000," ","int((e*cot(d*x+c))^(3/2)/(a+cot(d*x+c)*a)^3,x)","\frac{e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{e^{3} \sqrt{e \cot \left(d x +c \right)}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}+\frac{5 e^{\frac{3}{2}} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{8 a^{3} d}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3}}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3}}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3}}-\frac{e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"1/8/d/a^3*e^2/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(3/2)-1/8/d/a^3*e^3/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(1/2)+5/8*e^(3/2)*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^3/d-1/16/d/a^3*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/16/d/a^3*e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3*e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3*e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
37,1,423,132,0.856000," ","int((e*cot(d*x+c))^(1/2)/(a+cot(d*x+c)*a)^3,x)","\frac{3 e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}+\frac{5 e^{2} \sqrt{e \cot \left(d x +c \right)}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{\arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right) \sqrt{e}}{8 a^{3} d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3}}+\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"3/8/d/a^3*e/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(3/2)+5/8/d/a^3*e^2/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(1/2)-1/8*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))*e^(1/2)/a^3/d-1/16/d/a^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/16/d/a^3*e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/8/d/a^3*e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a^3*e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
38,1,426,136,0.833000," ","int(1/(e*cot(d*x+c))^(1/2)/(a+cot(d*x+c)*a)^3,x)","-\frac{7 \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{9 e \sqrt{e \cot \left(d x +c \right)}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{11 \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{8 a^{3} d \sqrt{e}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} e}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-7/8/d/a^3/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(3/2)-9/8/d/a^3*e/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(1/2)-11/8*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^3/d/e^(1/2)+1/16/d/a^3/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/8/d/a^3/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a^3/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/16/d/a^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/8/d/a^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
39,1,458,156,0.795000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+cot(d*x+c)*a)^3,x)","\frac{11 \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \,a^{3} e \left(e \cot \left(d x +c \right)+e \right)^{2}}+\frac{13 \sqrt{e \cot \left(d x +c \right)}}{8 d \,a^{3} \left(e \cot \left(d x +c \right)+e \right)^{2}}+\frac{31 \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{8 a^{3} d \,e^{\frac{3}{2}}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} e^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e^{2}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{a^{3} d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"11/8/d/a^3/e/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(3/2)+13/8/d/a^3/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(1/2)+31/8*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^3/d/e^(3/2)+1/16/d/a^3/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/8/d/a^3/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/8/d/a^3/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/16/d/a^3/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/a^3/d/e/(e*cot(d*x+c))^(1/2)","B"
40,1,482,178,0.855000," ","int(1/(e*cot(d*x+c))^(5/2)/(a+cot(d*x+c)*a)^3,x)","-\frac{15 \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \,a^{3} e^{2} \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{17 \sqrt{e \cot \left(d x +c \right)}}{8 d \,a^{3} e \left(e \cot \left(d x +c \right)+e \right)^{2}}-\frac{59 \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}}{\sqrt{e}}\right)}{8 a^{3} d \,e^{\frac{5}{2}}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} e^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e^{3}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e^{3}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{16 d \,a^{3} e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{8 d \,a^{3} e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{3 a^{3} d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{6}{a^{3} d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-15/8/d/a^3/e^2/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(3/2)-17/8/d/a^3/e/(e*cot(d*x+c)+e)^2*(e*cot(d*x+c))^(1/2)-59/8*arctan((e*cot(d*x+c))^(1/2)/e^(1/2))/a^3/d/e^(5/2)-1/16/d/a^3/e^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3/e^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3/e^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/16/d/a^3/e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/8/d/a^3/e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/8/d/a^3/e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3/a^3/d/e/(e*cot(d*x+c))^(3/2)-6/a^3/d/e^2/(e*cot(d*x+c))^(1/2)","B"
41,1,356,160,0.269000," ","int(cot(x)^2*(1+cot(x))^(1/2),x)","-\frac{2 \left(1+\cot \left(x \right)\right)^{\frac{3}{2}}}{3}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}+\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}+\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}"," ",0,"-2/3*(1+cot(x))^(3/2)+1/4*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/2*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/2*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
42,1,249,99,0.132000," ","int(cot(x)*(1+cot(x))^(1/2),x)","-2 \sqrt{1+\cot \left(x \right)}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}"," ",0,"-2*(1+cot(x))^(1/2)-1/4*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","B"
43,1,265,101,0.175000," ","int(cot(x)^2*(1+cot(x))^(3/2),x)","-\frac{2 \left(1+\cot \left(x \right)\right)^{\frac{5}{2}}}{5}+2 \sqrt{1+\cot \left(x \right)}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}"," ",0,"-2/5*(1+cot(x))^(5/2)+2*(1+cot(x))^(1/2)+1/4*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
44,1,452,159,0.117000," ","int(cot(x)*(1+cot(x))^(3/2),x)","-\frac{2 \left(1+\cot \left(x \right)\right)^{\frac{3}{2}}}{3}-2 \sqrt{1+\cot \left(x \right)}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{2}+\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{2}+\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{2 \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}"," ",0,"-2/3*(1+cot(x))^(3/2)-2*(1+cot(x))^(1/2)+1/4*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/2*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/4*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","B"
45,1,442,152,0.224000," ","int(cot(x)^2/(1+cot(x))^(1/2),x)","-2 \sqrt{1+\cot \left(x \right)}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{4}-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-2+2 \sqrt{2}}}"," ",0,"-2*(1+cot(x))^(1/2)-1/4*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/8*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/4*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/2*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/4*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/8*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/4*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/2*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","B"
46,1,249,85,0.161000," ","int(cot(x)/(1+cot(x))^(1/2),x)","-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}"," ",0,"-1/8*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
47,1,249,97,0.186000," ","int(cot(x)^2/(1+cot(x))^(3/2),x)","-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{1}{\sqrt{1+\cot \left(x \right)}}"," ",0,"-1/8*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/(1+cot(x))^(1/2)","B"
48,1,356,160,0.126000," ","int(cot(x)/(1+cot(x))^(3/2),x)","-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}-\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}-\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}+\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{1}{\sqrt{1+\cot \left(x \right)}}"," ",0,"-1/8*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/4*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/4*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/4*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/8*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/4*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/(1+cot(x))^(1/2)","B"
49,1,265,101,0.193000," ","int(cot(x)^2/(1+cot(x))^(5/2),x)","-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{16}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{16}+\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{1}{3 \left(1+\cot \left(x \right)\right)^{\frac{3}{2}}}-\frac{1}{\sqrt{1+\cot \left(x \right)}}"," ",0,"-1/16*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/4/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/16*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/4/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/3/(1+cot(x))^(3/2)-1/(1+cot(x))^(1/2)","B"
50,1,444,152,0.134000," ","int(cot(x)/(1+cot(x))^(5/2),x)","-\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{16}+\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}-\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}-\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{8 \sqrt{-2+2 \sqrt{2}}}+\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}-\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2 \sqrt{2}+2}\, \sqrt{2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{16}-\frac{\sqrt{2 \sqrt{2}+2}\, \ln \left(1+\cot \left(x \right)+\sqrt{2}+\sqrt{1+\cot \left(x \right)}\, \sqrt{2 \sqrt{2}+2}\right)}{8}-\frac{\sqrt{2}\, \left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{8 \sqrt{-2+2 \sqrt{2}}}+\frac{\left(2 \sqrt{2}+2\right) \arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\arctan \left(\frac{2 \sqrt{1+\cot \left(x \right)}+\sqrt{2 \sqrt{2}+2}}{\sqrt{-2+2 \sqrt{2}}}\right) \sqrt{2}}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{1}{3 \left(1+\cot \left(x \right)\right)^{\frac{3}{2}}}"," ",0,"-1/16*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))+1/8*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)-(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/8*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)-(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/16*(2*2^(1/2)+2)^(1/2)*2^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/8*(2*2^(1/2)+2)^(1/2)*ln(1+cot(x)+2^(1/2)+(1+cot(x))^(1/2)*(2*2^(1/2)+2)^(1/2))-1/8*2^(1/2)*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4*(2*2^(1/2)+2)/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))-1/2/(-2+2*2^(1/2))^(1/2)*arctan((2*(1+cot(x))^(1/2)+(2*2^(1/2)+2)^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/3/(1+cot(x))^(3/2)","B"
51,1,363,194,0.367000," ","int((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c)),x)","-\frac{2 b \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{2 a e \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d}+\frac{a e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{a e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}+\frac{e^{2} b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*b*(e*cot(d*x+c))^(3/2)/d-2*a*e*(e*cot(d*x+c))^(1/2)/d+1/4*a/d*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d*e^2*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*e^2*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*e^2*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
52,1,337,177,0.355000," ","int((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c)),x)","-\frac{2 b \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d}+\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{e a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*b*(e*cot(d*x+c))^(1/2)/d+1/4/d*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d*e*a/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d*e*a/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*e*a/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
53,1,327,161,0.406000," ","int((a+b*cot(d*x+c))/(e*cot(d*x+c))^(1/2),x)","-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}-\frac{b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4*a/d/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2*a/d/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2*a/d/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
54,1,355,180,0.372000," ","int((a+b*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x)","-\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{2}}-\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2}}+\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2}}+\frac{a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a}{d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-1/4/d/e^2*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d/e^2*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d/e^2*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4*a/d/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2*a/d/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2*a/d/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2*a/d/e/(e*cot(d*x+c))^(1/2)","A"
55,1,374,199,0.482000," ","int((a+b*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x)","\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{3}}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3}}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3}}+\frac{b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a}{3 d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{2 b}{d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/4/d/e^3*a*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d/e^3*a*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d/e^3*a*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/e^2*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d/e^2*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d/e^2*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3*a/d/e/(e*cot(d*x+c))^(3/2)+2*b/d/e^2/(e*cot(d*x+c))^(1/2)","A"
56,1,581,260,0.650000," ","int((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^2,x)","-\frac{2 b^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d e}-\frac{4 a b \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{2 e \,a^{2} \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{2 e \,b^{2} \sqrt{e \cot \left(d x +c \right)}}{d}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d}+\frac{e^{2} a b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} a b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} a b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5*b^2*(e*cot(d*x+c))^(5/2)/d/e-4/3*a*b*(e*cot(d*x+c))^(3/2)/d-2*e/d*a^2*(e*cot(d*x+c))^(1/2)+2*e/d*b^2*(e*cot(d*x+c))^(1/2)-1/2*e/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2*e/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/4*e/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2-1/4*e/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+1/2*e/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2*e/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/2*e^2/d*a*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+e^2/d*a*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-e^2/d*a*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
57,1,534,235,0.539000," ","int((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c))^2,x)","-\frac{2 b^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d e}-\frac{4 a b \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d}-\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3*b^2*(e*cot(d*x+c))^(3/2)/d/e-4*a*b*(e*cot(d*x+c))^(1/2)/d+1/2/d*a*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*a*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*a*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4*e/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2+1/4*e/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+1/2*e/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2*e/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2*e/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2*e/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2","B"
58,1,529,218,0.520000," ","int((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(1/2),x)","-\frac{2 b^{2} \sqrt{e \cot \left(d x +c \right)}}{d e}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 e d}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 e d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e d}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e d}-\frac{a b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*b^2*(e*cot(d*x+c))^(1/2)/d/e+1/2/e/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/e/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/4/e/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2+1/4/e/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2-1/2/e/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/e/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/d*a*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*a*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*a*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
59,1,538,218,0.456000," ","int((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x)","-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 e^{2} d}-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{e^{2} d}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{e^{2} d}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 e d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 e d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{2}}{d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-1/2/e^2/d*a*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/e^2/d*a*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/e^2/d*a*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/e/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/e/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/e/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/e/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/4/e/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2-1/4/e/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+2*a^2/d/e/(e*cot(d*x+c))^(1/2)","B"
60,1,558,238,0.466000," ","int((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x)","\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e^{3} d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e^{3} d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e^{3} d}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e^{3} d}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 e^{3} d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 e^{3} d}+\frac{a b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 e^{2} d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{e^{2} d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{e^{2} d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{2}}{3 d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{4 a b}{d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/2/e^3/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/e^3/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/e^3/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/e^3/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/4/e^3/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2-1/4/e^3/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+1/2/e^2/d*a*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/e^2/d*a*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/e^2/d*a*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3*a^2/d/e/(e*cot(d*x+c))^(3/2)+4*a*b/d/e^2/(e*cot(d*x+c))^(1/2)","B"
61,1,600,265,0.449000," ","int((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x)","\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 e^{4} d}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{e^{4} d}-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{e^{4} d}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 e^{3} d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 e^{3} d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e^{3} d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e^{3} d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 e^{3} d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 e^{3} d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{2}}{5 d e \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{2 a^{2}}{e^{3} d \sqrt{e \cot \left(d x +c \right)}}+\frac{2 b^{2}}{e^{3} d \sqrt{e \cot \left(d x +c \right)}}+\frac{4 a b}{3 d \,e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/e^4/d*a*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/e^4/d*a*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/e^4/d*a*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/e^3/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2+1/4/e^3/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2-1/2/e^3/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/e^3/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/2/e^3/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/e^3/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+2/5*a^2/d/e/(e*cot(d*x+c))^(5/2)-2/e^3/d/(e*cot(d*x+c))^(1/2)*a^2+2/e^3/d/(e*cot(d*x+c))^(1/2)*b^2+4/3*a*b/d/e^2/(e*cot(d*x+c))^(3/2)","B"
62,1,807,311,0.753000," ","int((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^3,x)","-\frac{2 \left(e \cot \left(d x +c \right)\right)^{\frac{7}{2}} b^{3}}{7 d \,e^{2}}-\frac{6 a \,b^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d e}-\frac{2 a^{2} b \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{d}+\frac{2 \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}} b^{3}}{3 d}-\frac{2 a^{3} e \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{6 e a \,b^{2} \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d}-\frac{3 e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d}+\frac{3 e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d}-\frac{3 e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d}+\frac{3 e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/7/d/e^2*(e*cot(d*x+c))^(7/2)*b^3-6/5*a*b^2*(e*cot(d*x+c))^(5/2)/d/e-2/d*a^2*b*(e*cot(d*x+c))^(3/2)+2/3/d*(e*cot(d*x+c))^(3/2)*b^3-2*a^3*e*(e*cot(d*x+c))^(1/2)/d+6/d*e*a*b^2*(e*cot(d*x+c))^(1/2)+1/4/d*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3-3/4/d*e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-1/2/d*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+1/2/d*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+3/4/d*e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d*e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3-3/2/d*e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/2/d*e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3","B"
63,1,750,285,0.722000," ","int((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c))^3,x)","-\frac{2 b^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d \,e^{2}}-\frac{2 a \,b^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{d e}-\frac{6 \sqrt{e \cot \left(d x +c \right)}\, a^{2} b}{d}+\frac{2 b^{3} \sqrt{e \cot \left(d x +c \right)}}{d}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d}-\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/5/d/e^2*b^3*(e*cot(d*x+c))^(5/2)-2*a*b^2*(e*cot(d*x+c))^(3/2)/d/e-6/d*(e*cot(d*x+c))^(1/2)*a^2*b+2/d*b^3*(e*cot(d*x+c))^(1/2)+3/4/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3-3/2/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/2/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-1/4/d*e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3+3/4/d*e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2+1/2/d*e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/2/d*e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2","B"
64,1,725,258,0.607000," ","int((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(1/2),x)","-\frac{2 b^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \,e^{2}}-\frac{6 a \,b^{2} \sqrt{e \cot \left(d x +c \right)}}{d e}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d e}+\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/3/d/e^2*b^3*(e*cot(d*x+c))^(3/2)-6*a*b^2*(e*cot(d*x+c))^(1/2)/d/e+1/2/d*a^3/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-3/2/d/e*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/2/d*a^3/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+3/2/d/e*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/4/d*a^3/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+3/4/d/e*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2+3/2/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/4/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b+1/4/d*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3-3/2/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3","B"
65,1,742,262,0.467000," ","int((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x)","-\frac{2 b^{3} \sqrt{e \cot \left(d x +c \right)}}{d \,e^{2}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{2}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \,e^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \,e^{2}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{2}}+\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-2/d/e^2*b^3*(e*cot(d*x+c))^(1/2)+3/2/d/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/e^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/4/d/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b+1/4/d/e^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3-3/2/d/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/e^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+1/4/d*a^3/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-3/4/d/e*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-1/2/d*a^3/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+3/2/d/e*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+1/2/d*a^3/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-3/2/d/e*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+2/d*a^3/e/(e*cot(d*x+c))^(1/2)","B"
66,1,743,258,0.459000," ","int((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x)","\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \,e^{3}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \,e^{3}}+\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \,e^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \,e^{3}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \,e^{3}}+\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{3 d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{6 a^{2} b}{d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/4/d/e^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3-3/4/d/e^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2+1/2/d*a^3/e^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-3/2/d/e^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/2/d/e^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d/e^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+3/4/d/e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d/e^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3+3/2/d/e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/e^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/2/d/e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/e^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+2/3/d/e*a^3/(e*cot(d*x+c))^(3/2)+6*a^2*b/d/e^2/(e*cot(d*x+c))^(1/2)","B"
67,1,786,286,0.463000," ","int((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x)","-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{4}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{4}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \,e^{4}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \,e^{4}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{4}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{4}}-\frac{a^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \,e^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{5 d e \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{2 a^{2} b}{d \,e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{2 a^{3}}{d \,e^{3} \sqrt{e \cot \left(d x +c \right)}}+\frac{6 a \,b^{2}}{d \,e^{3} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-3/2/d/e^4*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/e^4*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/4/d/e^4*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d/e^4*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3+3/2/d/e^4*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/e^4*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-1/4/d*a^3/e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+3/4/d/e^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2+1/2/d*a^3/e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-3/2/d/e^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/2/d*a^3/e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+3/2/d/e^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+2/5/d*a^3/e/(e*cot(d*x+c))^(5/2)+2*a^2*b/d/e^2/(e*cot(d*x+c))^(3/2)-2*a^3/d/e^3/(e*cot(d*x+c))^(1/2)+6/d/e^3*a/(e*cot(d*x+c))^(1/2)*b^2","B"
68,1,829,316,0.451000," ","int((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x)","\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{5}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \,e^{5}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{5}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \,e^{5}}-\frac{a^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{5}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \,e^{5}}-\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{4} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2 a^{3}}{7 d e \left(e \cot \left(d x +c \right)\right)^{\frac{7}{2}}}+\frac{6 a^{2} b}{5 d \,e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{2 a^{3}}{3 d \,e^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{2 a \,b^{2}}{d \,e^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{6 b \,a^{2}}{d \,e^{4} \sqrt{e \cot \left(d x +c \right)}}+\frac{2 b^{3}}{d \,e^{4} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/2/d*a^3/e^5*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-3/2/d/e^5*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/4/d*a^3/e^5*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+3/4/d/e^5*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-1/2/d*a^3/e^5*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+3/2/d/e^5*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-3/4/d/e^4*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b+1/4/d/e^4*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3+3/2/d/e^4*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/e^4*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/2/d/e^4*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/e^4*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+2/7/d*a^3/e/(e*cot(d*x+c))^(7/2)+6/5*a^2*b/d/e^2/(e*cot(d*x+c))^(5/2)-2/3*a^3/d/e^3/(e*cot(d*x+c))^(3/2)+2/d/e^3*a/(e*cot(d*x+c))^(3/2)*b^2-6/d/e^4*b/(e*cot(d*x+c))^(1/2)*a^2+2/d/e^4*b^3/(e*cot(d*x+c))^(1/2)","B"
69,1,459,262,0.673000," ","int((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x)","-\frac{2 e^{2} \sqrt{e \cot \left(d x +c \right)}}{b d}+\frac{2 e^{3} a^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d b \left(a^{2}+b^{2}\right) \sqrt{a e b}}+\frac{e^{2} b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right)}+\frac{e^{2} b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{e^{2} b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{e^{3} a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{3} a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2*e^2*(e*cot(d*x+c))^(1/2)/b/d+2/d*e^3/b*a^3/(a^2+b^2)/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/4/d*e^2/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*e^2/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*e^2/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d*e^3/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*e^3/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*e^3/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
70,1,429,241,0.687000," ","int((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x)","-\frac{2 e^{2} a^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{a e b}}+\frac{e a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right)}+\frac{e a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{e a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{e^{2} b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/d*e^2*a^2/(a^2+b^2)/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/4/d*e/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d*e/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d*e/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d*e^2/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d*e^2/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*e^2/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
71,1,417,241,0.790000," ","int((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c)),x)","\frac{2 e a b \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{a e b}}-\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right)}-\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right)}-\frac{e a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"2/d*e*a*b/(a^2+b^2)/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/4/d/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d*e/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d*e/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*e/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
72,1,423,241,0.712000," ","int(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c)),x)","-\frac{2 b^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{a e b}}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e \left(a^{2}+b^{2}\right)}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(a^{2}+b^{2}\right)}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(a^{2}+b^{2}\right)}+\frac{b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/d*b^2/(a^2+b^2)/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/4/d/e/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d/e/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d/e/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","A"
73,1,459,262,0.614000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x)","\frac{2 b^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d e a \left(a^{2}+b^{2}\right) \sqrt{a e b}}+\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{2} \left(a^{2}+b^{2}\right)}+\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(a^{2}+b^{2}\right)}-\frac{b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(a^{2}+b^{2}\right)}+\frac{a \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d e \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{a d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"2/d/e/a*b^3/(a^2+b^2)/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/4/d/e^2/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d/e^2/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d/e^2/(a^2+b^2)*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d/e/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d/e/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d/e/(a^2+b^2)*a/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/a/d/e/(e*cot(d*x+c))^(1/2)","A"
74,1,481,284,0.629000," ","int(1/(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x)","-\frac{2 b^{4} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \,e^{2} a^{2} \left(a^{2}+b^{2}\right) \sqrt{a e b}}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{3} \left(a^{2}+b^{2}\right)}+\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3} \left(a^{2}+b^{2}\right)}-\frac{a \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3} \left(a^{2}+b^{2}\right)}-\frac{b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{4 d \,e^{2} \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{2} \left(a^{2}+b^{2}\right) \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{3 a d e \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{2 b}{a^{2} d \,e^{2} \sqrt{e \cot \left(d x +c \right)}}"," ",0,"-2/d/e^2/a^2*b^4/(a^2+b^2)/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/4/d/e^3/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/2/d/e^3/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/2/d/e^3/(a^2+b^2)*a*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/4/d/e^2/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/2/d/e^2/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d/e^2/(a^2+b^2)*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+2/3/a/d/e/(e*cot(d*x+c))^(3/2)-2*b/a^2/d/e^2/(e*cot(d*x+c))^(1/2)","A"
75,1,805,372,0.831000," ","int((e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^2,x)","-\frac{2 e^{3} \sqrt{e \cot \left(d x +c \right)}}{d \,b^{2}}-\frac{e^{4} a^{5} \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} b^{2} \left(e \cot \left(d x +c \right) b +a e \right)}-\frac{e^{4} a^{3} \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}+\frac{3 e^{4} a^{5} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} b^{2} \sqrt{a e b}}+\frac{7 e^{4} a^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}+\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e^{4} a b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{4} a b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{4} a b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/d*e^3/b^2*(e*cot(d*x+c))^(1/2)-1/d*e^4*a^5/(a^2+b^2)^2/b^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)-1/d*e^4*a^3/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)+3/d*e^4*a^5/(a^2+b^2)^2/b^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+7/d*e^4*a^3/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/2/d*e^3/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/d*e^3/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/4/d*e^3/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2+1/4/d*e^3/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2-1/2/d*e^3/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/d*e^3/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/2/d*e^4/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*e^4/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*e^4/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
76,1,784,330,0.781000," ","int((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^2,x)","\frac{e^{3} a^{4} \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} b \left(e \cot \left(d x +c \right) b +a e \right)}+\frac{e^{3} a^{2} b \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}-\frac{e^{3} a^{4} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} b \sqrt{a e b}}-\frac{5 e^{3} a^{2} b \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}+\frac{e^{2} a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e^{2} a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{e^{2} a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"1/d*e^3*a^4/(a^2+b^2)^2/b*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)+1/d*e^3*a^2/(a^2+b^2)^2*b*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)-1/d*e^3*a^4/(a^2+b^2)^2/b/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-5/d*e^3*a^2/(a^2+b^2)^2*b/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/2/d*e^2/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d*e^2/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d*e^2/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/4/d*e^3/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2-1/4/d*e^3/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+1/2/d*e^3/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/d*e^3/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/d*e^3/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/d*e^3/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2","B"
77,1,768,324,0.757000," ","int((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x)","-\frac{e^{2} a^{3} \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}-\frac{e^{2} a \sqrt{e \cot \left(d x +c \right)}\, b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}-\frac{e^{2} a^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}+\frac{3 e^{2} a \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2}}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{e^{2} a b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} a b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} a b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/d*e^2*a^3/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)-1/d*e^2*a/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)*b^2-1/d*e^2*a^3/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+3/d*e^2*a/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))*b^2-1/2/d*e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/d*e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/4/d*e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2-1/4/d*e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+1/2/d*e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/d*e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/d*e^2/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d*e^2/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d*e^2/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
78,1,749,323,0.823000," ","int((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^2,x)","\frac{e b \sqrt{e \cot \left(d x +c \right)}\, a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}+\frac{e \,b^{3} \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}+\frac{3 e b \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}-\frac{e \,b^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"1/d*e*b/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)*a^2+1/d*e*b^3/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)+3/d*e*b/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))*a^2-1/d*e*b^3/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/2/d/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))-1/d/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/d/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d*e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/d*e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/d*e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/d*e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/4/d*e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2+1/4/d*e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2","B"
79,1,765,331,0.846000," ","int(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^2,x)","-\frac{b^{2} a \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}-\frac{b^{4} \sqrt{e \cot \left(d x +c \right)}}{d \left(a^{2}+b^{2}\right)^{2} a \left(e \cot \left(d x +c \right) b +a e \right)}-\frac{5 b^{2} a \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}-\frac{b^{4} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d \left(a^{2}+b^{2}\right)^{2} a \sqrt{a e b}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d e \left(a^{2}+b^{2}\right)^{2}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d e \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{a b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{a b \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/d*b^2/(a^2+b^2)^2*a*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)-1/d*b^4/(a^2+b^2)^2/a*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)-5/d*b^2/(a^2+b^2)^2*a/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/d*b^4/(a^2+b^2)^2/a/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/2/d/e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/d/e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/2/d/e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/d/e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/4/d/e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2+1/4/d/e/(a^2+b^2)^2*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+1/2/d/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d/(a^2+b^2)^2*a*b/(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)","B"
80,1,803,372,0.763000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x)","\frac{b^{3} \sqrt{e \cot \left(d x +c \right)}}{d e \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}+\frac{b^{5} \sqrt{e \cot \left(d x +c \right)}}{d e \,a^{2} \left(a^{2}+b^{2}\right)^{2} \left(e \cot \left(d x +c \right) b +a e \right)}+\frac{7 b^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d e \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}+\frac{3 b^{5} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{d e \,a^{2} \left(a^{2}+b^{2}\right)^{2} \sqrt{a e b}}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right)}{2 d \,e^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2} \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right)}{d \,e^{2} \left(a^{2}+b^{2}\right)^{2}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2}}{4 d e \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{2}}{4 d e \left(a^{2}+b^{2}\right)^{2} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{a^{2} d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"1/d/e*b^3/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)+1/d/e*b^5/a^2/(a^2+b^2)^2*(e*cot(d*x+c))^(1/2)/(e*cot(d*x+c)*b+a*e)+7/d/e*b^3/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+3/d/e*b^5/a^2/(a^2+b^2)^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/2/d/e^2/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))+1/d/e^2/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)-1/d/e^2/(a^2+b^2)^2*a*b*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)+1/2/d/e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2-1/2/d/e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2-1/2/d/e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2+1/2/d/e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^2+1/4/d/e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2-1/4/d/e/(a^2+b^2)^2*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^2+2/a^2/d/e/(e*cot(d*x+c))^(1/2)","B"
81,1,1254,454,0.853000," ","int((e*cot(d*x+c))^(9/2)/(a+b*cot(d*x+c))^3,x)","-\frac{2 e^{4} \sqrt{e \cot \left(d x +c \right)}}{d \,b^{3}}-\frac{9 e^{5} a^{7} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \,b^{2} \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{13 e^{5} a^{5} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{17 e^{5} a^{3} b^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{7 e^{6} a^{8} \sqrt{e \cot \left(d x +c \right)}}{4 d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{11 e^{6} a^{6} \sqrt{e \cot \left(d x +c \right)}}{2 d b \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{15 e^{6} a^{4} b \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{15 e^{5} a^{7} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \,b^{3} \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{23 e^{5} a^{5} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{2 d b \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{63 e^{5} a^{3} b \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{3 e^{4} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e^{4} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e^{4} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{e^{4} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 e^{4} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e^{4} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{5} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e^{5} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{5} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{5} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-2/d*e^4/b^3*(e*cot(d*x+c))^(1/2)-9/4/d*e^5*a^7/b^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)-13/2/d*e^5*a^5/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)-17/4/d*e^5*a^3*b^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)-7/4/d*e^6*a^8/b^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)-11/2/d*e^6*a^6/b/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)-15/4/d*e^6*a^4*b/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)+15/4/d*e^5*a^7/b^3/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+23/2/d*e^5*a^5/b/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+63/4/d*e^5*a^3*b/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-3/2/d*e^4/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*e^4/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/2/d*e^4/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*e^4/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/4/d*e^4/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b+1/4/d*e^4/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3-1/2/d*e^5/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e^5/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/4/d*e^5/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3+3/4/d*e^5/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2+1/2/d*e^5/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e^5/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2","B"
82,1,1232,405,0.880000," ","int((e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^3,x)","\frac{5 e^{4} a^{6} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2} b}+\frac{9 e^{4} a^{4} b \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{13 e^{4} a^{2} b^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{3 e^{5} a^{7} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2} b^{2}}+\frac{7 e^{5} a^{5} \sqrt{e \cot \left(d x +c \right)}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{11 e^{5} a^{3} b^{2} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{3 e^{4} a^{6} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} b^{2} \sqrt{a e b}}-\frac{3 e^{4} a^{4} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{35 e^{4} a^{2} b^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 e^{3} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e^{4} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{4} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{4} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{4} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{4} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"5/4/d*e^4*a^6/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2/b*(e*cot(d*x+c))^(3/2)+9/2/d*e^4*a^4/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*b*(e*cot(d*x+c))^(3/2)+13/4/d*e^4*a^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*b^3*(e*cot(d*x+c))^(3/2)+3/4/d*e^5*a^7/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2/b^2*(e*cot(d*x+c))^(1/2)+7/2/d*e^5*a^5/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)+11/4/d*e^5*a^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*b^2*(e*cot(d*x+c))^(1/2)-3/4/d*e^4*a^6/(a^2+b^2)^3/b^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-3/2/d*e^4*a^4/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-35/4/d*e^4*a^2/(a^2+b^2)^3*b^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/4/d*e^3/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3+3/4/d*e^3/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-1/2/d*e^3/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e^3/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+1/2/d*e^3/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e^3/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+3/4/d*e^4/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d*e^4/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3+3/2/d*e^4/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*e^4/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/2/d*e^4/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*e^4/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3","B"
83,1,1229,399,0.995000," ","int((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^3,x)","-\frac{e^{3} a^{5} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{5 e^{3} a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{9 e^{3} a \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}} b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{e^{4} a^{6} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2} b}-\frac{3 e^{4} a^{4} b \sqrt{e \cot \left(d x +c \right)}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{7 e^{4} a^{2} b^{3} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{e^{3} a^{5} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} b \sqrt{a e b}}-\frac{9 e^{3} a^{3} b \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{15 e^{3} a \,b^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{3 e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{e^{2} \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e^{3} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{3} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-1/4/d*e^3*a^5/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)-5/2/d*e^3*a^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)*b^2-9/4/d*e^3*a/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)*b^4+1/4/d*e^4*a^6/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2/b*(e*cot(d*x+c))^(1/2)-3/2/d*e^4*a^4/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*b*(e*cot(d*x+c))^(1/2)-7/4/d*e^4*a^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*b^3*(e*cot(d*x+c))^(1/2)-1/4/d*e^3*a^5/(a^2+b^2)^3/b/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-9/2/d*e^3*a^3/(a^2+b^2)^3*b/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+15/4/d*e^3*a/(a^2+b^2)^3*b^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+3/2/d*e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/2/d*e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/4/d*e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d*e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3+1/2/d*e^3/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e^3/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/2/d*e^3/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e^3/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+1/4/d*e^3/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3-3/4/d*e^3/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2","B"
84,1,1212,390,0.870000," ","int((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x)","-\frac{3 e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}} b \,a^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}} a^{2} b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{5 e^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}} b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{5 e^{3} \sqrt{e \cot \left(d x +c \right)}\, a^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{e^{3} \sqrt{e \cot \left(d x +c \right)}\, a^{3} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{3 e^{3} \sqrt{e \cot \left(d x +c \right)}\, a \,b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{3 e^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right) a^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{13 e^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right) a^{2} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{3 e^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right) b^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 e \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e^{2} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{e^{2} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-3/4/d*e^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)*b*a^4+1/2/d*e^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)*a^2*b^3+5/4/d*e^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)*b^5-5/4/d*e^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)*a^5-1/2/d*e^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)*a^3*b^2+3/4/d*e^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)*a*b^4-3/4/d*e^2/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))*a^4+13/2/d*e^2/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))*a^2*b^2-3/4/d*e^2/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))*b^4-1/2/d*e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+1/4/d*e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3-3/4/d*e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2+1/2/d*e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+3/2/d*e^2/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d*e^2/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/2/d*e^2/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d*e^2/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/4/d*e^2/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b+1/4/d*e^2/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3","B"
85,1,1187,392,0.972000," ","int((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^3,x)","\frac{7 e \,b^{2} a^{3} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{3 e \,b^{4} a \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{e \,b^{6} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2} a}+\frac{9 e^{2} b \sqrt{e \cot \left(d x +c \right)}\, a^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{5 e^{2} b^{3} \sqrt{e \cot \left(d x +c \right)}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{e^{2} b^{5} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{15 e b \,a^{3} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{9 e \,b^{3} a \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{e \,b^{5} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a \sqrt{a e b}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 e \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"7/4/d*e*b^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*a^3*(e*cot(d*x+c))^(3/2)+3/2/d*e*b^4/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*a*(e*cot(d*x+c))^(3/2)-1/4/d*e*b^6/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2/a*(e*cot(d*x+c))^(3/2)+9/4/d*e^2*b/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)*a^4+5/2/d*e^2*b^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)*a^2+1/4/d*e^2*b^5/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)+15/4/d*e*b/(a^2+b^2)^3*a^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-9/2/d*e*b^3/(a^2+b^2)^3*a/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-1/4/d*e*b^5/(a^2+b^2)^3/a/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+3/2/d/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3-3/4/d/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b+1/4/d/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3-3/2/d/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+1/2/d*e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d*e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/4/d*e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3+3/4/d*e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-1/2/d*e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d*e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2","B"
86,1,1190,405,0.845000," ","int(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^3,x)","-\frac{11 b^{3} a^{2} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{7 b^{5} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{3 b^{7} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2} a^{2}}-\frac{13 e \,b^{2} a^{3} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{9 e \,b^{4} a \sqrt{e \cot \left(d x +c \right)}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}-\frac{5 e \,b^{6} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2} a}-\frac{35 b^{2} a^{2} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{3 b^{4} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{2 d \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{3 b^{6} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d \left(a^{2}+b^{2}\right)^{3} a^{2} \sqrt{a e b}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d e \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d e \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d e \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d e \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}"," ",0,"-11/4/d*b^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*a^2*(e*cot(d*x+c))^(3/2)-7/2/d*b^5/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)-3/4/d*b^7/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2/a^2*(e*cot(d*x+c))^(3/2)-13/4/d*e*b^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*a^3*(e*cot(d*x+c))^(1/2)-9/2/d*e*b^4/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*a*(e*cot(d*x+c))^(1/2)-5/4/d*e*b^6/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2/a*(e*cot(d*x+c))^(1/2)-35/4/d*b^2/(a^2+b^2)^3*a^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-3/2/d*b^4/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-3/4/d*b^6/(a^2+b^2)^3/a^2/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+1/2/d/e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d/e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/2/d/e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d/e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2-1/4/d/e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3+3/4/d/e/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-3/2/d/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/2/d/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/4/d/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3","B"
87,1,1245,454,0.795000," ","int(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x)","\frac{15 b^{4} a \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d e \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{11 b^{6} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d e a \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{7 b^{8} \left(e \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{4 d e \,a^{3} \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{17 b^{3} a^{2} \sqrt{e \cot \left(d x +c \right)}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{13 b^{5} \sqrt{e \cot \left(d x +c \right)}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{9 b^{7} \sqrt{e \cot \left(d x +c \right)}}{4 d \,a^{2} \left(a^{2}+b^{2}\right)^{3} \left(e \cot \left(d x +c \right) b +a e \right)^{2}}+\frac{63 b^{3} a \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d e \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{23 b^{5} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{2 d e a \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}+\frac{15 b^{7} \arctan \left(\frac{\sqrt{e \cot \left(d x +c \right)}\, b}{\sqrt{a e b}}\right)}{4 d e \,a^{3} \left(a^{2}+b^{2}\right)^{3} \sqrt{a e b}}-\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{2} \left(a^{2}+b^{2}\right)^{3}}+\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{2} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{2} b}{4 d \,e^{2} \left(a^{2}+b^{2}\right)^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) b^{3}}{4 d \,e^{2} \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{2} b}{2 d \,e^{2} \left(a^{2}+b^{2}\right)^{3}}-\frac{\left(e^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) b^{3}}{2 d \,e^{2} \left(a^{2}+b^{2}\right)^{3}}+\frac{\sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a^{3}}{4 d e \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \ln \left(\frac{e \cot \left(d x +c \right)-\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}{e \cot \left(d x +c \right)+\left(e^{2}\right)^{\frac{1}{4}} \sqrt{e \cot \left(d x +c \right)}\, \sqrt{2}+\sqrt{e^{2}}}\right) a \,b^{2}}{4 d e \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d e \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a^{3}}{2 d e \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \cot \left(d x +c \right)}}{\left(e^{2}\right)^{\frac{1}{4}}}+1\right) a \,b^{2}}{2 d e \left(a^{2}+b^{2}\right)^{3} \left(e^{2}\right)^{\frac{1}{4}}}+\frac{2}{a^{3} d e \sqrt{e \cot \left(d x +c \right)}}"," ",0,"15/4/d/e*b^4*a/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)+11/2/d/e*b^6/a/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)+7/4/d/e*b^8/a^3/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(3/2)+17/4/d*b^3*a^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)+13/2/d*b^5/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)+9/4/d*b^7/a^2/(a^2+b^2)^3/(e*cot(d*x+c)*b+a*e)^2*(e*cot(d*x+c))^(1/2)+63/4/d/e*b^3*a/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+23/2/d/e*b^5/a/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))+15/4/d/e*b^7/a^3/(a^2+b^2)^3/(a*e*b)^(1/2)*arctan((e*cot(d*x+c))^(1/2)*b/(a*e*b)^(1/2))-3/2/d/e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b+1/2/d/e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+3/4/d/e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^2*b-1/4/d/e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*ln((e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*b^3+3/2/d/e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^2*b-1/2/d/e^2/(a^2+b^2)^3*(e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*b^3+1/4/d/e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a^3-3/4/d/e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*ln((e*cot(d*x+c)-(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2))/(e*cot(d*x+c)+(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)*2^(1/2)+(e^2)^(1/2)))*a*b^2-1/2/d/e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3+3/2/d/e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(-2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+1/2/d/e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a^3-3/2/d/e/(a^2+b^2)^3*2^(1/2)/(e^2)^(1/4)*arctan(2^(1/2)/(e^2)^(1/4)*(e*cot(d*x+c))^(1/2)+1)*a*b^2+2/a^3/d/e/(e*cot(d*x+c))^(1/2)","B"
88,0,0,155,1.235000," ","int((a+b*cot(d*x+c))^n,x)","\int \left(a +b \cot \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+b*cot(d*x+c))^n,x)","F"
89,0,0,187,2.421000," ","int((a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n,x)","\int \left(a +b \cot \left(f x +e \right)\right)^{m} \left(d \tan \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n,x)","F"
90,1,1622,36,0.457000," ","int((1+I*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x)","\frac{i \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}-\frac{i \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{2}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a \,b^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2} b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{3}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{2}}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a b}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2} b}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{3}}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"I/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*b-I/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*b^2-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b-I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a^2-I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a^3-I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a*b^2+1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a*b+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a^2*b+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*b^3+I/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^2+1/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*b+1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*b+1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^3","B"
91,1,1622,36,0.538000," ","int((1-I*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x)","\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a \,b^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{i \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}-\frac{i \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{2}}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{2}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}+\frac{i \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) a^{2} b}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) b^{3}}{2 d \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right)}-\frac{i \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a b}{d \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2} b}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) b^{3}}{d \sqrt{a^{2}+b^{2}}\, \left(\sqrt{a^{2}+b^{2}}\, a +a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a*b^2+I/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*b-I/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^2+I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a^3-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b+1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*b^2-1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a+I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a^2-1/2*I/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a*b+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*a^2*b+1/2/d/(2*(a^2+b^2)^(1/2)+2*a)^(1/2)/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*b^3-I/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*b+1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*b+1/d/(a^2+b^2)^(1/2)/((a^2+b^2)^(1/2)*a+a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*b^3","B"
92,1,187,59,0.419000," ","int((A+B*cot(d*x+c))/(a+b*cot(d*x+c)),x)","-\frac{\ln \left(a +b \cot \left(d x +c \right)\right) A b}{d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(a +b \cot \left(d x +c \right)\right) a B}{d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) A b}{2 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) a B}{2 d \left(a^{2}+b^{2}\right)}-\frac{A \pi  a}{2 d \left(a^{2}+b^{2}\right)}-\frac{B \pi  b}{2 d \left(a^{2}+b^{2}\right)}+\frac{A \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) a}{d \left(a^{2}+b^{2}\right)}+\frac{B \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) b}{d \left(a^{2}+b^{2}\right)}"," ",0,"-1/d/(a^2+b^2)*ln(a+b*cot(d*x+c))*A*b+1/d/(a^2+b^2)*ln(a+b*cot(d*x+c))*a*B+1/2/d/(a^2+b^2)*ln(cot(d*x+c)^2+1)*A*b-1/2/d/(a^2+b^2)*ln(cot(d*x+c)^2+1)*a*B-1/2/d/(a^2+b^2)*A*Pi*a-1/2/d/(a^2+b^2)*B*Pi*b+1/d/(a^2+b^2)*A*arccot(cot(d*x+c))*a+1/d/(a^2+b^2)*B*arccot(cot(d*x+c))*b","B"
93,1,356,111,0.370000," ","int((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^2,x)","\frac{A b}{d \left(a^{2}+b^{2}\right) \left(a +b \cot \left(d x +c \right)\right)}-\frac{a B}{d \left(a^{2}+b^{2}\right) \left(a +b \cot \left(d x +c \right)\right)}-\frac{2 \ln \left(a +b \cot \left(d x +c \right)\right) A a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \cot \left(d x +c \right)\right) a^{2} B}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(a +b \cot \left(d x +c \right)\right) b^{2} B}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) A a b}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) a^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) b^{2} B}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \pi  \,a^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \pi  \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{B \pi  a b}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{A \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{A \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{2 B \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) a b}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d/(a^2+b^2)/(a+b*cot(d*x+c))*A*b-1/d/(a^2+b^2)/(a+b*cot(d*x+c))*a*B-2/d/(a^2+b^2)^2*ln(a+b*cot(d*x+c))*A*a*b+1/d/(a^2+b^2)^2*ln(a+b*cot(d*x+c))*a^2*B-1/d/(a^2+b^2)^2*ln(a+b*cot(d*x+c))*b^2*B+1/d/(a^2+b^2)^2*ln(cot(d*x+c)^2+1)*A*a*b-1/2/d/(a^2+b^2)^2*ln(cot(d*x+c)^2+1)*a^2*B+1/2/d/(a^2+b^2)^2*ln(cot(d*x+c)^2+1)*b^2*B-1/2/d/(a^2+b^2)^2*A*Pi*a^2+1/2/d/(a^2+b^2)^2*A*Pi*b^2-1/d/(a^2+b^2)^2*B*Pi*a*b+1/d/(a^2+b^2)^2*A*arccot(cot(d*x+c))*a^2-1/d/(a^2+b^2)^2*A*arccot(cot(d*x+c))*b^2+2/d/(a^2+b^2)^2*B*arccot(cot(d*x+c))*a*b","B"
94,1,559,173,0.382000," ","int((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^3,x)","\frac{A b}{2 d \left(a^{2}+b^{2}\right) \left(a +b \cot \left(d x +c \right)\right)^{2}}-\frac{a B}{2 d \left(a^{2}+b^{2}\right) \left(a +b \cot \left(d x +c \right)\right)^{2}}+\frac{2 A a b}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \cot \left(d x +c \right)\right)}-\frac{a^{2} B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \cot \left(d x +c \right)\right)}+\frac{b^{2} B}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \cot \left(d x +c \right)\right)}-\frac{3 \ln \left(a +b \cot \left(d x +c \right)\right) A \,a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \cot \left(d x +c \right)\right) A \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(a +b \cot \left(d x +c \right)\right) a^{3} B}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(a +b \cot \left(d x +c \right)\right) B a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(\cot^{2}\left(d x +c \right)+1\right) A \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) A \,b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(\cot^{2}\left(d x +c \right)+1\right) a^{3} B}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(\cot^{2}\left(d x +c \right)+1\right) B a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{A \pi  \,a^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 A \pi  a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 B \pi  \,a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{B \pi  \,b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{A \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 A \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 B \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) a^{2} b}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{B \,\mathrm{arccot}\left(\cot \left(d x +c \right)\right) b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/2/d/(a^2+b^2)/(a+b*cot(d*x+c))^2*A*b-1/2/d/(a^2+b^2)/(a+b*cot(d*x+c))^2*a*B+2/d/(a^2+b^2)^2/(a+b*cot(d*x+c))*A*a*b-1/d/(a^2+b^2)^2/(a+b*cot(d*x+c))*a^2*B+1/d/(a^2+b^2)^2/(a+b*cot(d*x+c))*b^2*B-3/d/(a^2+b^2)^3*ln(a+b*cot(d*x+c))*A*a^2*b+1/d/(a^2+b^2)^3*ln(a+b*cot(d*x+c))*A*b^3+1/d/(a^2+b^2)^3*ln(a+b*cot(d*x+c))*a^3*B-3/d/(a^2+b^2)^3*ln(a+b*cot(d*x+c))*B*a*b^2+3/2/d/(a^2+b^2)^3*ln(cot(d*x+c)^2+1)*A*a^2*b-1/2/d/(a^2+b^2)^3*ln(cot(d*x+c)^2+1)*A*b^3-1/2/d/(a^2+b^2)^3*ln(cot(d*x+c)^2+1)*a^3*B+3/2/d/(a^2+b^2)^3*ln(cot(d*x+c)^2+1)*B*a*b^2-1/2/d/(a^2+b^2)^3*A*Pi*a^3+3/2/d/(a^2+b^2)^3*A*Pi*a*b^2-3/2/d/(a^2+b^2)^3*B*Pi*a^2*b+1/2/d/(a^2+b^2)^3*B*Pi*b^3+1/d/(a^2+b^2)^3*A*arccot(cot(d*x+c))*a^3-3/d/(a^2+b^2)^3*A*arccot(cot(d*x+c))*a*b^2+3/d/(a^2+b^2)^3*B*arccot(cot(d*x+c))*a^2*b-1/d/(a^2+b^2)^3*B*arccot(cot(d*x+c))*b^3","B"
95,1,2405,160,0.547000," ","int((a+b*cot(d*x+c))^(5/2)*(A+B*cot(d*x+c)),x)","\frac{3 \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}+\frac{b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b^{2} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}+\frac{3 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 B \left(a +b \cot \left(d x +c \right)\right)^{\frac{3}{2}} a}{3 d}-\frac{2 B \,a^{2} \sqrt{a +b \cot \left(d x +c \right)}}{d}+\frac{2 B \sqrt{a +b \cot \left(d x +c \right)}\, b^{2}}{d}-\frac{2 A \left(a +b \cot \left(d x +c \right)\right)^{\frac{3}{2}} b}{3 d}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 A \sqrt{a +b \cot \left(d x +c \right)}\, a b}{d}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 d b}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{2}}{4 d b}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{2} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b^{2} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{3 b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{2 d}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b}-\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{3 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{2} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b^{2} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d}+\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b}-\frac{2 B \left(a +b \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}"," ",0,"3/4/d*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a^2-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a^2+1/2/d*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-2/3/d*B*(a+b*cot(d*x+c))^(3/2)*a-2/d*B*a^2*(a+b*cot(d*x+c))^(1/2)+2/d*B*(a+b*cot(d*x+c))^(1/2)*b^2-2/3/d*A*(a+b*cot(d*x+c))^(3/2)*b-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-4/d*A*(a+b*cot(d*x+c))^(1/2)*a*b+1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2-1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^2-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)*a-3/4/d*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/4/d*b^2*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d*b^2*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-3/4/d*b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/2/d*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-3/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-1/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+3/d*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+3/4/d*b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-2/5*B*(a+b*cot(d*x+c))^(5/2)/d","B"
96,1,1665,126,0.539000," ","int((a+b*cot(d*x+c))^(3/2)*(A+B*cot(d*x+c)),x)","\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d b}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,b^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d b}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}\, a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{4 d b}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{2 d}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \,b^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 A b \sqrt{a +b \cot \left(d x +c \right)}}{d}-\frac{2 B \sqrt{a +b \cot \left(d x +c \right)}\, a}{d}-\frac{2 B \left(a +b \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}"," ",0,"1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*b^2+1/4/d*b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/4/d*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/2/d*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a-1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)*a-1/4/d*b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/4/d*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/2/d*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*b^2-2/d*A*b*(a+b*cot(d*x+c))^(1/2)-2/d*B*(a+b*cot(d*x+c))^(1/2)*a-2/3*B*(a+b*cot(d*x+c))^(3/2)/d","B"
97,1,968,102,0.531000," ","int((a+b*cot(d*x+c))^(1/2)*(A+B*cot(d*x+c)),x)","-\frac{2 B \sqrt{a +b \cot \left(d x +c \right)}}{d}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}}{4 d b}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) A \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d b}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) B \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) A}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) B a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-2*B*(a+b*cot(d*x+c))^(1/2)/d+1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)-1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*(a^2+b^2)^(1/2)+1/d/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a","B"
98,1,1375,127,0.555000," ","int((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(5/2),x)","-\frac{2 b \left(a +b \cot \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d}+\frac{2 b \,a^{2} \sqrt{a +b \cot \left(d x +c \right)}}{d}+\frac{2 b^{3} \sqrt{a +b \cot \left(d x +c \right)}}{d}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{3}}{4 d b}-\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b}-\frac{b^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}+\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a^{3}}{4 d b}+\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, a}{4 d}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b}+\frac{b^{3} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d}-\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}\, a^{2}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) \sqrt{a^{2}+b^{2}}}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-2/5*b*(a+b*cot(d*x+c))^(5/2)/d+2/d*b*a^2*(a+b*cot(d*x+c))^(1/2)+2/d*b^3*(a+b*cot(d*x+c))^(1/2)-1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^3-1/4/d*b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a+1/4/d/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/4/d*b^3*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+2/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)*a^2-1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)+1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a^3+1/4/d*b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*a-1/4/d/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/4/d*b^3*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-2/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)*a^2+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*(a^2+b^2)^(1/2)","B"
99,1,972,333,0.510000," ","int((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(3/2),x)","-\frac{2 b \left(a +b \cot \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d b}+\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d}+\frac{b \,a^{2} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a^{2}}{4 d b}-\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3} \ln \left(b \cot \left(d x +c \right)+a -\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d b}-\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a \ln \left(b \cot \left(d x +c \right)+a -\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d}+\frac{b \,a^{2} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}-\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(b \cot \left(d x +c \right)+a -\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) a^{2}}{4 d b}+\frac{b \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, \sqrt{a^{2}+b^{2}}\, \ln \left(b \cot \left(d x +c \right)+a -\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right)}{4 d}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}-\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-2/3*b*(a+b*cot(d*x+c))^(3/2)/d+1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))+1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))+1/d*b*a^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a^2-1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3*ln(b*cot(d*x+c)+a-(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))-1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a*ln(b*cot(d*x+c)+a-(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))+1/d*b*a^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)-(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d/b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a-(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*a^2+1/4/d*b*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*(a^2+b^2)^(1/2)*ln(b*cot(d*x+c)+a-(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))+1/d*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)-(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))","B"
100,1,2285,341,0.540000," ","int((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(1/2),x)","\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{5} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b^{5} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)}+\frac{b^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)}-\frac{2 b \sqrt{a +b \cot \left(d x +c \right)}}{d}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{5 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{2}}{2 d \left(a^{2}+b^{2}\right)}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{5 b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{b^{3} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/d*b^3/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-2/d*b^5/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/d*b^3/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+2/d*b^5/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d*b^3/(a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/4/d*b^3/(a^2+b^2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*b*(a+b*cot(d*x+c))^(1/2)/d+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6+4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-2/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/4/d/b/(a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-1/2/d*b/(a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+2/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6-5/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/2/d*b/(a^2+b^2)^(3/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-1/4/d*b^3/(a^2+b^2)^(3/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)^(3/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5+1/4/d/b/(a^2+b^2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/2/d*b/(a^2+b^2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+5/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+1/2/d*b/(a^2+b^2)^(3/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b^3/(a^2+b^2)^(3/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a","B"
101,1,3976,84,0.490000," ","int((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/d/(a^2+b^2)/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4-1/4/d/(a^2+b^2)/b^2*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d/(a^2+b^2)^(3/2)*b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/(a^2+b^2)^(1/2)/b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2+1/d/(a^2+b^2)^(3/2)/b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4-1/4/d/(a^2+b^2)^(3/2)/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-3/d/(a^2+b^2)^(3/2)*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*A+1/d/(a^2+b^2)^(3/2)*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*B-1/d/(a^2+b^2)^(1/2)/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-1/d/(a^2+b^2)^(1/2)/b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^2-1/d/(a^2+b^2)^(3/2)*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a*B+1/4/d/(a^2+b^2)/b^2*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/d/(a^2+b^2)^(1/2)/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^3-1/4/d/(a^2+b^2)/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/d*(a^2+b^2)^(1/2)/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+3/d/(a^2+b^2)^(3/2)*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2*A-1/d/(a^2+b^2)^(3/2)/b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A*a^4+1/d/(a^2+b^2)/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^4+1/d*(a^2+b^2)^(1/2)/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a+1/4/d/(a^2+b^2)^(3/2)/b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d/(a^2+b^2)^(3/2)*b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/(a^2+b^2)/b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+2/d/(a^2+b^2)^(3/2)*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/(a^2+b^2)*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3*B+1/4/d/(a^2+b^2)*b*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+2/d/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2-1/4/d/(a^2+b^2)*b*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*A*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/4/d/(a^2+b^2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/(a^2+b^2)^(3/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-1/4/d/(a^2+b^2)^(3/2)*b^2*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-1/4/d/(a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/d/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3*B-1/4/d/b^2*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d/b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a^2+1/d/(a^2+b^2)*b^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B-1/d/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*B*a-2/d/(a^2+b^2)^(3/2)*b^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/4/d/b^2*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/(a^2+b^2)^(3/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/d/(a^2+b^2)^(1/2)*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A-1/d/(a^2+b^2)^(1/2)*b/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*A+1/4/d/(a^2+b^2)^(3/2)*b^2*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*B*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)","B"
102,1,7951,118,0.459000," ","int((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
103,1,12836,161,0.440000," ","int((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
104,1,1905,84,0.543000," ","int((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x)","\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)}+\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{b^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{4 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{4 d b \left(a^{2}+b^{2}\right)}-\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{b^{3} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d b \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \sqrt{a^{2}+b^{2}}\, \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{5}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{3 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"1/4/d/b/(a^2+b^2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d*b/(a^2+b^2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/4/d/b/(a^2+b^2)^(3/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/4/d*b^3/(a^2+b^2)^(3/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/d*b/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-1/d*b^3/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+3/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/4/d/b/(a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-1/4/d*b/(a^2+b^2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a+1/4/d/b/(a^2+b^2)^(3/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-1/4/d*b^3/(a^2+b^2)^(3/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+1/d/b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/d*b/(a^2+b^2)^(1/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d*b/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5+1/d*b^3/(a^2+b^2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-3/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-4/d*b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3","B"
105,1,2291,112,0.563000," ","int((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x)","-\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{4 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b^{3} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{2}}+\frac{2 b^{5} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{2 b^{5} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right)}{d \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{b^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{4 d \left(a^{2}+b^{2}\right)^{2}}-\frac{b \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{4}}{4 d b \left(a^{2}+b^{2}\right)^{2}}-\frac{3 b^{3} \ln \left(\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-b \cot \left(d x +c \right)-a -\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{3 b^{3} \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a}{4 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{2 b^{3} \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{6}}{d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{4 a b}{\left(a^{2}+b^{2}\right) d \sqrt{a +b \cot \left(d x +c \right)}}+\frac{2 b^{3} \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}-\frac{\ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{5}}{4 d b \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{4 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{\frac{5}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{b \ln \left(b \cot \left(d x +c \right)+a +\sqrt{a +b \cot \left(d x +c \right)}\, \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}+\sqrt{a^{2}+b^{2}}\right) \sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}\, a^{3}}{2 d \left(a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{2 b \arctan \left(\frac{2 \sqrt{a +b \cot \left(d x +c \right)}+\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{\arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{4}}{d b \left(a^{2}+b^{2}\right)^{\frac{3}{2}} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}+\frac{2 b \arctan \left(\frac{\sqrt{2 \sqrt{a^{2}+b^{2}}+2 a}-2 \sqrt{a +b \cot \left(d x +c \right)}}{\sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{2} \sqrt{2 \sqrt{a^{2}+b^{2}}-2 a}}"," ",0,"-1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6+1/4/d/b/(a^2+b^2)^(5/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-4/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+1/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+1/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+1/4/d*b^3/(a^2+b^2)^2*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-1/4/d/b/(a^2+b^2)^2*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+2/d*b^5/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-2/d*b^5/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/d*b^3/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-1/4/d*b^3/(a^2+b^2)^2*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/2/d*b/(a^2+b^2)^(5/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3+1/4/d/b/(a^2+b^2)^2*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4-3/4/d*b^3/(a^2+b^2)^(5/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-1/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+3/4/d*b^3/(a^2+b^2)^(5/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-2/d*b^3/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^6-4*a*b/(a^2+b^2)/d/(a+b*cot(d*x+c))^(1/2)+2/d*b^3/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-1/4/d/b/(a^2+b^2)^(5/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5+4/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+1/2/d*b/(a^2+b^2)^(5/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-2/d*b/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/d/b/(a^2+b^2)^(3/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4+2/d*b/(a^2+b^2)^2/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3","B"
106,1,3055,150,0.556000," ","int((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-1/2/d*b/(a^2+b^2)^3*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-2/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+5/4/d*b/(a^2+b^2)^(7/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+3/d*b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5+2/d*b^3/(a^2+b^2)^2/(a+b*cot(d*x+c))^(1/2)+1/d*b^5/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))-6/d*b/(a^2+b^2)^2/(a+b*cot(d*x+c))^(1/2)*a^2+1/4/d*b^5/(a^2+b^2)^(7/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+3/d*b/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-5/d*b^3/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/4/d*b^5/(a^2+b^2)^(7/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-1/d*b^5/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))+2/d*b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3+1/d/b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^7+1/4/d/b/(a^2+b^2)^(7/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^6-2/d*b^3/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2+3/4/d*b^3/(a^2+b^2)^3*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-3/4/d*b^3/(a^2+b^2)^3*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a-5/4/d*b^3/(a^2+b^2)^(7/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2-3/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+3/d*b^3/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+5/4/d*b^3/(a^2+b^2)^(7/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^2+1/4/d/b/(a^2+b^2)^3*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-1/4/d/b/(a^2+b^2)^3*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^5-3/d*b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-7/d*b^5/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a+5/d*b^3/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^3-1/d/b/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^7+7/d*b^5/(a^2+b^2)^(7/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a-5/4/d*b/(a^2+b^2)^(7/2)*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^4+1/2/d*b/(a^2+b^2)^3*ln((a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)-b*cot(d*x+c)-a-(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^3-4/3*a*b/(a^2+b^2)/d/(a+b*cot(d*x+c))^(3/2)+1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5-1/4/d/b/(a^2+b^2)^(7/2)*ln(b*cot(d*x+c)+a+(a+b*cot(d*x+c))^(1/2)*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)+(a^2+b^2)^(1/2))*(2*(a^2+b^2)^(1/2)+2*a)^(1/2)*a^6+2/d*b^3/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan(((2*(a^2+b^2)^(1/2)+2*a)^(1/2)-2*(a+b*cot(d*x+c))^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^2-3/d*b/(a^2+b^2)^3/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^4-1/d/b/(a^2+b^2)^(5/2)/(2*(a^2+b^2)^(1/2)-2*a)^(1/2)*arctan((2*(a+b*cot(d*x+c))^(1/2)+(2*(a^2+b^2)^(1/2)+2*a)^(1/2))/(2*(a^2+b^2)^(1/2)-2*a)^(1/2))*a^5","B"