1,0,-1,49,0.000000,"\text{Not used}","int((a + a*cot(c + d*x)*1i)^n,x)","\int {\left(a+a\,\mathrm{cot}\left(c+d\,x\right)\,1{}\mathrm{i}\right)}^n \,d x","Not used",1,"int((a + a*cot(c + d*x)*1i)^n, x)","F"
2,1,144,116,1.978114,"\text{Not used}","int((e*cot(c + d*x))^(5/2)*(a + a*cot(c + d*x)),x)","\frac{2\,a\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{2\,a\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{2\,a\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d}+\frac{{\left(-1\right)}^{1/4}\,a\,e^{5/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}}{\sqrt{e}}\right)}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,e^{5/2}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d}+\frac{{\left(-1\right)}^{1/4}\,a\,e^{5/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(1+1{}\mathrm{i}\right)}{d}","Not used",1,"(2*a*e^2*(e*cot(c + d*x))^(1/2))/d - (2*a*e*(e*cot(c + d*x))^(3/2))/(3*d) - (2*a*(e*cot(c + d*x))^(5/2))/(5*d) + ((-1)^(1/4)*a*e^(5/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 + 1i))/d + ((-1)^(1/4)*a*e^(5/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2)*1i)/e^(1/2)))/d - ((-1)^(1/4)*a*e^(5/2)*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/d","B"
3,1,98,94,1.161004,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + a*cot(c + d*x)),x)","-\frac{2\,a\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{2\,a\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}+\frac{{\left(-1\right)}^{1/4}\,a\,e^{3/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(1-\mathrm{i}\right)}{d}+\frac{{\left(-1\right)}^{1/4}\,a\,e^{3/2}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(-1-\mathrm{i}\right)}{d}","Not used",1,"((-1)^(1/4)*a*e^(3/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 - 1i))/d - (2*a*e*(e*cot(c + d*x))^(1/2))/d - (2*a*(e*cot(c + d*x))^(3/2))/(3*d) - ((-1)^(1/4)*a*e^(3/2)*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 + 1i))/d","B"
4,1,128,71,0.776518,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + a*cot(c + d*x)),x)","-\frac{2\,a\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,\sqrt{e}\,\left(\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)-\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\right)}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,\sqrt{e}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,\sqrt{e}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d}","Not used",1,"- (2*a*(e*cot(c + d*x))^(1/2))/d - ((-1)^(1/4)*a*e^(1/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/d - ((-1)^(1/4)*a*e^(1/2)*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/d - ((-1)^(1/4)*a*e^(1/2)*(atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)) - atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))))/d","B"
5,1,65,49,0.727911,"\text{Not used}","int((a + a*cot(c + d*x))/(e*cot(c + d*x))^(1/2),x)","\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(-1+1{}\mathrm{i}\right)}{d\,\sqrt{e}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(1+1{}\mathrm{i}\right)}{d\,\sqrt{e}}","Not used",1,"((-1)^(1/4)*a*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 + 1i))/(d*e^(1/2)) - ((-1)^(1/4)*a*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 - 1i))/(d*e^(1/2))","B"
6,1,84,75,0.960122,"\text{Not used}","int((a + a*cot(c + d*x))/(e*cot(c + d*x))^(3/2),x)","\frac{2\,a}{d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(1+1{}\mathrm{i}\right)}{d\,e^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(-1+1{}\mathrm{i}\right)}{d\,e^{3/2}}","Not used",1,"(2*a)/(d*e*(e*cot(c + d*x))^(1/2)) + ((-1)^(1/4)*a*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 + 1i))/(d*e^(3/2)) - ((-1)^(1/4)*a*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 - 1i))/(d*e^(3/2))","B"
7,1,103,99,1.483248,"\text{Not used}","int((a + a*cot(c + d*x))/(e*cot(c + d*x))^(5/2),x)","\frac{2\,a}{d\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{2\,a}{3\,d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(1-\mathrm{i}\right)}{d\,e^{5/2}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,\left(-1-\mathrm{i}\right)}{d\,e^{5/2}}","Not used",1,"(2*a)/(d*e^2*(e*cot(c + d*x))^(1/2)) + (2*a)/(3*d*e*(e*cot(c + d*x))^(3/2)) + ((-1)^(1/4)*a*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 - 1i))/(d*e^(5/2)) - ((-1)^(1/4)*a*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*(1 + 1i))/(d*e^(5/2))","B"
8,1,125,269,1.728178,"\text{Not used}","int((e*cot(c + d*x))^(5/2)*(a + a*cot(c + d*x))^2,x)","\frac{4\,a^2\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{4\,a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d}-\frac{2\,a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}}{7\,d\,e}+\frac{{\left(-1\right)}^{1/4}\,a^2\,e^{5/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d}+\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,e^{5/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}}{\sqrt{e}}\right)}{d}","Not used",1,"(4*a^2*e^2*(e*cot(c + d*x))^(1/2))/d - (4*a^2*(e*cot(c + d*x))^(5/2))/(5*d) - (2*a^2*(e*cot(c + d*x))^(7/2))/(7*d*e) + ((-1)^(1/4)*a^2*e^(5/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*2i)/d + (2*(-1)^(1/4)*a^2*e^(5/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2)*1i)/e^(1/2)))/d","B"
9,1,104,246,0.948285,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + a*cot(c + d*x))^2,x)","\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,e^{3/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d}-\frac{2\,a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d\,e}-\frac{4\,a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}+\frac{{\left(-1\right)}^{1/4}\,a^2\,e^{3/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(2*(-1)^(1/4)*a^2*e^(3/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/d - (2*a^2*(e*cot(c + d*x))^(5/2))/(5*d*e) - (4*a^2*(e*cot(c + d*x))^(3/2))/(3*d) + ((-1)^(1/4)*a^2*e^(3/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2)*1i)/e^(1/2))*2i)/d","B"
10,1,104,244,0.697219,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + a*cot(c + d*x))^2,x)","-\frac{4\,a^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{2\,a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d\,e}-\frac{{\left(-1\right)}^{1/4}\,a^2\,\sqrt{e}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d}-\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,\sqrt{e}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}}{\sqrt{e}}\right)}{d}","Not used",1,"- (4*a^2*(e*cot(c + d*x))^(1/2))/d - (2*a^2*(e*cot(c + d*x))^(3/2))/(3*d*e) - ((-1)^(1/4)*a^2*e^(1/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*2i)/d - (2*(-1)^(1/4)*a^2*e^(1/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2)*1i)/e^(1/2)))/d","B"
11,1,86,222,0.444912,"\text{Not used}","int((a + a*cot(c + d*x))^2/(e*cot(c + d*x))^(1/2),x)","\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,\sqrt{e}}-\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,\sqrt{e}}-\frac{2\,a^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d\,e}","Not used",1,"(2*(-1)^(1/4)*a^2*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(1/2)) - (2*(-1)^(1/4)*a^2*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(1/2)) - (2*a^2*(e*cot(c + d*x))^(1/2))/(d*e)","B"
12,1,86,222,0.592702,"\text{Not used}","int((a + a*cot(c + d*x))^2/(e*cot(c + d*x))^(3/2),x)","\frac{2\,a^2}{d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d\,e^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d\,e^{3/2}}","Not used",1,"(2*a^2)/(d*e*(e*cot(c + d*x))^(1/2)) + ((-1)^(1/4)*a^2*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*2i)/(d*e^(3/2)) + ((-1)^(1/4)*a^2*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*2i)/(d*e^(3/2))","B"
13,1,99,247,0.701196,"\text{Not used}","int((a + a*cot(c + d*x))^2/(e*cot(c + d*x))^(5/2),x)","\frac{4\,a^2\,\mathrm{cot}\left(c+d\,x\right)+\frac{2\,a^2}{3}}{d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}+\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,e^{5/2}}-\frac{2\,{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,e^{5/2}}","Not used",1,"(4*a^2*cot(c + d*x) + (2*a^2)/3)/(d*e*(e*cot(c + d*x))^(3/2)) + (2*(-1)^(1/4)*a^2*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(5/2)) - (2*(-1)^(1/4)*a^2*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(5/2))","B"
14,1,99,249,1.291601,"\text{Not used}","int((a + a*cot(c + d*x))^2/(e*cot(c + d*x))^(7/2),x)","\frac{\frac{4\,a^2\,\mathrm{cot}\left(c+d\,x\right)}{3}+\frac{2\,a^2}{5}}{d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d\,e^{7/2}}-\frac{{\left(-1\right)}^{1/4}\,a^2\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,2{}\mathrm{i}}{d\,e^{7/2}}","Not used",1,"((4*a^2*cot(c + d*x))/3 + (2*a^2)/5)/(d*e*(e*cot(c + d*x))^(5/2)) - ((-1)^(1/4)*a^2*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*2i)/(d*e^(7/2)) - ((-1)^(1/4)*a^2*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*2i)/(d*e^(7/2))","B"
15,1,177,186,2.440288,"\text{Not used}","int((e*cot(c + d*x))^(5/2)*(a + a*cot(c + d*x))^3,x)","\frac{4\,a^3\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{4\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d}-\frac{6\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}}{7\,d\,e}-\frac{2\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{9/2}}{9\,d\,e^2}+\frac{4\,a^3\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{\sqrt{2}\,a^3\,e^{5/2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{d}","Not used",1,"(4*a^3*e^2*(e*cot(c + d*x))^(1/2))/d - (4*a^3*(e*cot(c + d*x))^(5/2))/(5*d) - (6*a^3*(e*cot(c + d*x))^(7/2))/(7*d*e) - (2*a^3*(e*cot(c + d*x))^(9/2))/(9*d*e^2) + (4*a^3*e*(e*cot(c + d*x))^(3/2))/(3*d) - (2^(1/2)*a^3*e^(5/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/d","B"
16,1,143,160,1.616908,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + a*cot(c + d*x))^3,x)","\frac{4\,a^3\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{6\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d\,e}-\frac{2\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}}{7\,d\,e^2}-\frac{4\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}+\frac{\sqrt{2}\,a^3\,e^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,a^6\,e^{9/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,32{}\mathrm{i}}{32\,a^6\,e^5+32\,a^6\,e^5\,\mathrm{cot}\left(c+d\,x\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(4*a^3*e*(e*cot(c + d*x))^(1/2))/d - (6*a^3*(e*cot(c + d*x))^(5/2))/(5*d*e) - (2*a^3*(e*cot(c + d*x))^(7/2))/(7*d*e^2) - (4*a^3*(e*cot(c + d*x))^(3/2))/(3*d) + (2^(1/2)*a^3*e^(3/2)*atan((2^(1/2)*a^6*e^(9/2)*(e*cot(c + d*x))^(1/2)*32i)/(32*a^6*e^5 + 32*a^6*e^5*cot(c + d*x)))*2i)/d","B"
17,1,136,138,0.989547,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + a*cot(c + d*x))^3,x)","\frac{\sqrt{2}\,a^3\,\sqrt{e}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{d}-\frac{2\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{d\,e}-\frac{2\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d\,e^2}-\frac{4\,a^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}","Not used",1,"(2^(1/2)*a^3*e^(1/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/d - (2*a^3*(e*cot(c + d*x))^(3/2))/(d*e) - (2*a^3*(e*cot(c + d*x))^(5/2))/(5*d*e^2) - (4*a^3*(e*cot(c + d*x))^(1/2))/d","B"
18,1,100,117,0.621330,"\text{Not used}","int((a + a*cot(c + d*x))^3/(e*cot(c + d*x))^(1/2),x)","\frac{2\,\sqrt{2}\,a^3\,\mathrm{atanh}\left(\frac{32\,\sqrt{2}\,a^6\,\sqrt{e}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{32\,a^6\,e+32\,a^6\,e\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d\,\sqrt{e}}-\frac{2\,a^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d\,e^2}-\frac{6\,a^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d\,e}","Not used",1,"(2*2^(1/2)*a^3*atanh((32*2^(1/2)*a^6*e^(1/2)*(e*cot(c + d*x))^(1/2))/(32*a^6*e + 32*a^6*e*cot(c + d*x))))/(d*e^(1/2)) - (2*a^3*(e*cot(c + d*x))^(3/2))/(3*d*e^2) - (6*a^3*(e*cot(c + d*x))^(1/2))/(d*e)","B"
19,1,119,114,0.576194,"\text{Not used}","int((a + a*cot(c + d*x))^3/(e*cot(c + d*x))^(3/2),x)","\frac{2\,a^3}{d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}-\frac{2\,a^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d\,e^2}-\frac{\sqrt{2}\,a^3\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{d\,e^{3/2}}","Not used",1,"(2*a^3)/(d*e*(e*cot(c + d*x))^(1/2)) - (2*a^3*(e*cot(c + d*x))^(1/2))/(d*e^2) - (2^(1/2)*a^3*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(d*e^(3/2))","B"
20,1,101,117,0.705093,"\text{Not used}","int((a + a*cot(c + d*x))^3/(e*cot(c + d*x))^(5/2),x)","\frac{\frac{2\,a^3\,e}{3}+6\,a^3\,e\,\mathrm{cot}\left(c+d\,x\right)}{d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-\frac{2\,\sqrt{2}\,a^3\,\mathrm{atanh}\left(\frac{32\,\sqrt{2}\,a^6\,d\,e^{5/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{32\,a^6\,d\,e^3+32\,a^6\,d\,e^3\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d\,e^{5/2}}","Not used",1,"((2*a^3*e)/3 + 6*a^3*e*cot(c + d*x))/(d*e^2*(e*cot(c + d*x))^(3/2)) - (2*2^(1/2)*a^3*atanh((32*2^(1/2)*a^6*d*e^(5/2)*(e*cot(c + d*x))^(1/2))/(32*a^6*d*e^3 + 32*a^6*d*e^3*cot(c + d*x))))/(d*e^(5/2))","B"
21,1,126,141,1.261248,"\text{Not used}","int((a + a*cot(c + d*x))^3/(e*cot(c + d*x))^(7/2),x)","\frac{4\,e\,a^3\,{\mathrm{cot}\left(c+d\,x\right)}^2+2\,e\,a^3\,\mathrm{cot}\left(c+d\,x\right)+\frac{2\,e\,a^3}{5}}{d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}+\frac{\sqrt{2}\,a^3\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{d\,e^{7/2}}","Not used",1,"((2*a^3*e)/5 + 4*a^3*e*cot(c + d*x)^2 + 2*a^3*e*cot(c + d*x))/(d*e^2*(e*cot(c + d*x))^(5/2)) + (2^(1/2)*a^3*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(d*e^(7/2))","B"
22,1,129,165,1.923559,"\text{Not used}","int((a + a*cot(c + d*x))^3/(e*cot(c + d*x))^(9/2),x)","\frac{-4\,e\,a^3\,{\mathrm{cot}\left(c+d\,x\right)}^3+\frac{4\,e\,a^3\,{\mathrm{cot}\left(c+d\,x\right)}^2}{3}+\frac{6\,e\,a^3\,\mathrm{cot}\left(c+d\,x\right)}{5}+\frac{2\,e\,a^3}{7}}{d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}}+\frac{2\,\sqrt{2}\,a^3\,\mathrm{atanh}\left(\frac{32\,\sqrt{2}\,a^6\,d\,e^{9/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{32\,a^6\,d\,e^5+32\,a^6\,d\,e^5\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d\,e^{9/2}}","Not used",1,"((2*a^3*e)/7 + (4*a^3*e*cot(c + d*x)^2)/3 - 4*a^3*e*cot(c + d*x)^3 + (6*a^3*e*cot(c + d*x))/5)/(d*e^2*(e*cot(c + d*x))^(7/2)) + (2*2^(1/2)*a^3*atanh((32*2^(1/2)*a^6*d*e^(9/2)*(e*cot(c + d*x))^(1/2))/(32*a^6*d*e^5 + 32*a^6*d*e^5*cot(c + d*x))))/(d*e^(9/2))","B"
23,1,123,111,0.681555,"\text{Not used}","int((e*cot(c + d*x))^(5/2)/(a + a*cot(c + d*x)),x)","\frac{e^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{a\,d}-\frac{2\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{a\,d}+\frac{\sqrt{2}\,e^{5/2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{4\,a\,d}","Not used",1,"(e^(5/2)*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(a*d) - (2*e^2*(e*cot(c + d*x))^(1/2))/(a*d) + (2^(1/2)*e^(5/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(4*a*d)","B"
24,1,79,87,0.492339,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + a*cot(c + d*x)),x)","\frac{\sqrt{2}\,e^{3/2}\,\mathrm{atanh}\left(\frac{12\,\sqrt{2}\,e^{25/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{12\,e^{13}\,\mathrm{cot}\left(c+d\,x\right)+12\,e^{13}}\right)}{2\,a\,d}-\frac{e^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{a\,d}","Not used",1,"(2^(1/2)*e^(3/2)*atanh((12*2^(1/2)*e^(25/2)*(e*cot(c + d*x))^(1/2))/(12*e^13*cot(c + d*x) + 12*e^13)))/(2*a*d) - (e^(3/2)*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(a*d)","B"
25,1,102,87,0.367702,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + a*cot(c + d*x)),x)","\frac{\sqrt{e}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{a\,d}-\frac{\sqrt{2}\,\sqrt{e}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{4\,a\,d}","Not used",1,"(e^(1/2)*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(a*d) - (2^(1/2)*e^(1/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(4*a*d)","B"
26,1,79,83,0.522961,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + a*cot(c + d*x))),x)","-\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{a\,d\,\sqrt{e}}-\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{12\,\sqrt{2}\,e^{9/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{12\,e^5\,\mathrm{cot}\left(c+d\,x\right)+12\,e^5}\right)}{2\,a\,d\,\sqrt{e}}","Not used",1,"- atan((e*cot(c + d*x))^(1/2)/e^(1/2))/(a*d*e^(1/2)) - (2^(1/2)*atanh((12*2^(1/2)*e^(9/2)*(e*cot(c + d*x))^(1/2))/(12*e^5*cot(c + d*x) + 12*e^5)))/(2*a*d*e^(1/2))","B"
27,1,123,111,0.643648,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + a*cot(c + d*x))),x)","\frac{2}{a\,d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{a\,d\,e^{3/2}}+\frac{\sqrt{2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{4\,a\,d\,e^{3/2}}","Not used",1,"2/(a*d*e*(e*cot(c + d*x))^(1/2)) + atan((e*cot(c + d*x))^(1/2)/e^(1/2))/(a*d*e^(3/2)) + (2^(1/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(4*a*d*e^(3/2))","B"
28,1,132,135,0.929395,"\text{Not used}","int(1/((e*cot(c + d*x))^(5/2)*(a + a*cot(c + d*x))),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{12\,\sqrt{2}\,a^3\,d^3\,e^{21/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{12\,a^3\,d^3\,e^{11}+12\,a^3\,d^3\,e^{11}\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,a\,d\,e^{5/2}}-\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{a\,d\,e^{5/2}}-\frac{\frac{2\,\mathrm{cot}\left(c+d\,x\right)}{e}-\frac{2}{3\,e}}{a\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}","Not used",1,"(2^(1/2)*atanh((12*2^(1/2)*a^3*d^3*e^(21/2)*(e*cot(c + d*x))^(1/2))/(12*a^3*d^3*e^11 + 12*a^3*d^3*e^11*cot(c + d*x))))/(2*a*d*e^(5/2)) - atan((e*cot(c + d*x))^(1/2)/e^(1/2))/(a*d*e^(5/2)) - ((2*cot(c + d*x))/e - 2/(3*e))/(a*d*(e*cot(c + d*x))^(3/2))","B"
29,1,375,281,0.898436,"\text{Not used}","int((e*cot(c + d*x))^(5/2)/(a + a*cot(c + d*x))^2,x)","\frac{e^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\left(a^2\,d\,e+a^2\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)}-\mathrm{atan}\left(\frac{e^{20}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^{10}}{256\,a^8\,d^4}\right)}^{1/4}\,16{}\mathrm{i}}{\frac{36\,e^{23}}{a^2\,d}+64\,a^2\,d\,e^{18}\,\sqrt{-\frac{e^{10}}{256\,a^8\,d^4}}}-\frac{e^{15}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^{10}}{256\,a^8\,d^4}\right)}^{3/4}\,2304{}\mathrm{i}}{\frac{36\,e^{23}}{a^6\,d^3}+\frac{64\,e^{18}\,\sqrt{-\frac{e^{10}}{256\,a^8\,d^4}}}{a^2\,d}}\right)\,{\left(-\frac{e^{10}}{256\,a^8\,d^4}\right)}^{1/4}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{4\,e^{20}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^{10}}{a^8\,d^4}\right)}^{1/4}}{\frac{36\,e^{23}}{a^2\,d}-4\,a^2\,d\,e^{18}\,\sqrt{-\frac{e^{10}}{a^8\,d^4}}}+\frac{36\,e^{15}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^{10}}{a^8\,d^4}\right)}^{3/4}}{\frac{36\,e^{23}}{a^6\,d^3}-\frac{4\,e^{18}\,\sqrt{-\frac{e^{10}}{a^8\,d^4}}}{a^2\,d}}\right)\,{\left(-\frac{e^{10}}{a^8\,d^4}\right)}^{1/4}}{2}-\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-e^5}\,1{}\mathrm{i}}{e^3}\right)\,\sqrt{-e^5}\,3{}\mathrm{i}}{2\,a^2\,d}","Not used",1,"(e^3*(e*cot(c + d*x))^(1/2))/(2*(a^2*d*e + a^2*d*e*cot(c + d*x))) - atan((e^20*(e*cot(c + d*x))^(1/2)*(-e^10/(256*a^8*d^4))^(1/4)*16i)/((36*e^23)/(a^2*d) + 64*a^2*d*e^18*(-e^10/(256*a^8*d^4))^(1/2)) - (e^15*(e*cot(c + d*x))^(1/2)*(-e^10/(256*a^8*d^4))^(3/4)*2304i)/((36*e^23)/(a^6*d^3) + (64*e^18*(-e^10/(256*a^8*d^4))^(1/2))/(a^2*d)))*(-e^10/(256*a^8*d^4))^(1/4)*2i - (atan((4*e^20*(e*cot(c + d*x))^(1/2)*(-e^10/(a^8*d^4))^(1/4))/((36*e^23)/(a^2*d) - 4*a^2*d*e^18*(-e^10/(a^8*d^4))^(1/2)) + (36*e^15*(e*cot(c + d*x))^(1/2)*(-e^10/(a^8*d^4))^(3/4))/((36*e^23)/(a^6*d^3) - (4*e^18*(-e^10/(a^8*d^4))^(1/2))/(a^2*d)))*(-e^10/(a^8*d^4))^(1/4))/2 - (atan(((e*cot(c + d*x))^(1/2)*(-e^5)^(1/2)*1i)/e^3)*(-e^5)^(1/2)*3i)/(2*a^2*d)","B"
30,1,376,279,0.822874,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + a*cot(c + d*x))^2,x)","-\frac{\mathrm{atan}\left(\frac{4\,e^{16}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^6}{a^8\,d^4}\right)}^{1/4}}{\frac{4\,e^{18}}{a^2\,d}+4\,a^2\,d\,e^{15}\,\sqrt{-\frac{e^6}{a^8\,d^4}}}+\frac{4\,e^{13}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^6}{a^8\,d^4}\right)}^{3/4}}{\frac{4\,e^{18}}{a^6\,d^3}+\frac{4\,e^{15}\,\sqrt{-\frac{e^6}{a^8\,d^4}}}{a^2\,d}}\right)\,{\left(-\frac{e^6}{a^8\,d^4}\right)}^{1/4}}{2}-\mathrm{atan}\left(\frac{e^{16}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^6}{256\,a^8\,d^4}\right)}^{1/4}\,16{}\mathrm{i}}{\frac{4\,e^{18}}{a^2\,d}-64\,a^2\,d\,e^{15}\,\sqrt{-\frac{e^6}{256\,a^8\,d^4}}}-\frac{e^{13}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^6}{256\,a^8\,d^4}\right)}^{3/4}\,256{}\mathrm{i}}{\frac{4\,e^{18}}{a^6\,d^3}-\frac{64\,e^{15}\,\sqrt{-\frac{e^6}{256\,a^8\,d^4}}}{a^2\,d}}\right)\,{\left(-\frac{e^6}{256\,a^8\,d^4}\right)}^{1/4}\,2{}\mathrm{i}-\frac{e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\left(a^2\,d\,e+a^2\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-e^3}\,1{}\mathrm{i}}{e^2}\right)\,\sqrt{-e^3}\,1{}\mathrm{i}}{2\,a^2\,d}","Not used",1,"(atan(((e*cot(c + d*x))^(1/2)*(-e^3)^(1/2)*1i)/e^2)*(-e^3)^(1/2)*1i)/(2*a^2*d) - atan((e^16*(e*cot(c + d*x))^(1/2)*(-e^6/(256*a^8*d^4))^(1/4)*16i)/((4*e^18)/(a^2*d) - 64*a^2*d*e^15*(-e^6/(256*a^8*d^4))^(1/2)) - (e^13*(e*cot(c + d*x))^(1/2)*(-e^6/(256*a^8*d^4))^(3/4)*256i)/((4*e^18)/(a^6*d^3) - (64*e^15*(-e^6/(256*a^8*d^4))^(1/2))/(a^2*d)))*(-e^6/(256*a^8*d^4))^(1/4)*2i - (e^2*(e*cot(c + d*x))^(1/2))/(2*(a^2*d*e + a^2*d*e*cot(c + d*x))) - (atan((4*e^16*(e*cot(c + d*x))^(1/2)*(-e^6/(a^8*d^4))^(1/4))/((4*e^18)/(a^2*d) + 4*a^2*d*e^15*(-e^6/(a^8*d^4))^(1/2)) + (4*e^13*(e*cot(c + d*x))^(1/2)*(-e^6/(a^8*d^4))^(3/4))/((4*e^18)/(a^6*d^3) + (4*e^15*(-e^6/(a^8*d^4))^(1/2))/(a^2*d)))*(-e^6/(a^8*d^4))^(1/4))/2","B"
31,1,366,278,0.722014,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + a*cot(c + d*x))^2,x)","\frac{\mathrm{atan}\left(\frac{4\,e^{12}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^2}{a^8\,d^4}\right)}^{1/4}}{\frac{4\,e^{13}}{a^2\,d}-4\,a^2\,d\,e^{12}\,\sqrt{-\frac{e^2}{a^8\,d^4}}}+\frac{4\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^2}{a^8\,d^4}\right)}^{3/4}}{\frac{4\,e^{13}}{a^6\,d^3}-\frac{4\,e^{12}\,\sqrt{-\frac{e^2}{a^8\,d^4}}}{a^2\,d}}\right)\,{\left(-\frac{e^2}{a^8\,d^4}\right)}^{1/4}}{2}+\mathrm{atan}\left(\frac{e^{12}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^2}{256\,a^8\,d^4}\right)}^{1/4}\,16{}\mathrm{i}}{\frac{4\,e^{13}}{a^2\,d}+64\,a^2\,d\,e^{12}\,\sqrt{-\frac{e^2}{256\,a^8\,d^4}}}-\frac{e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{e^2}{256\,a^8\,d^4}\right)}^{3/4}\,256{}\mathrm{i}}{\frac{4\,e^{13}}{a^6\,d^3}+\frac{64\,e^{12}\,\sqrt{-\frac{e^2}{256\,a^8\,d^4}}}{a^2\,d}}\right)\,{\left(-\frac{e^2}{256\,a^8\,d^4}\right)}^{1/4}\,2{}\mathrm{i}+\frac{e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\left(a^2\,d\,e+a^2\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)}-\frac{\sqrt{-e}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}}{\sqrt{-e}}\right)\,1{}\mathrm{i}}{2\,a^2\,d}","Not used",1,"(atan((4*e^12*(e*cot(c + d*x))^(1/2)*(-e^2/(a^8*d^4))^(1/4))/((4*e^13)/(a^2*d) - 4*a^2*d*e^12*(-e^2/(a^8*d^4))^(1/2)) + (4*e^11*(e*cot(c + d*x))^(1/2)*(-e^2/(a^8*d^4))^(3/4))/((4*e^13)/(a^6*d^3) - (4*e^12*(-e^2/(a^8*d^4))^(1/2))/(a^2*d)))*(-e^2/(a^8*d^4))^(1/4))/2 + atan((e^12*(e*cot(c + d*x))^(1/2)*(-e^2/(256*a^8*d^4))^(1/4)*16i)/((4*e^13)/(a^2*d) + 64*a^2*d*e^12*(-e^2/(256*a^8*d^4))^(1/2)) - (e^11*(e*cot(c + d*x))^(1/2)*(-e^2/(256*a^8*d^4))^(3/4)*256i)/((4*e^13)/(a^6*d^3) + (64*e^12*(-e^2/(256*a^8*d^4))^(1/2))/(a^2*d)))*(-e^2/(256*a^8*d^4))^(1/4)*2i + (e*(e*cot(c + d*x))^(1/2))/(2*(a^2*d*e + a^2*d*e*cot(c + d*x))) - ((-e)^(1/2)*atan(((e*cot(c + d*x))^(1/2)*1i)/(-e)^(1/2))*1i)/(2*a^2*d)","B"
32,1,366,281,0.812817,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + a*cot(c + d*x))^2),x)","\frac{\mathrm{atan}\left(\frac{4\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{a^8\,d^4\,e^2}\right)}^{1/4}}{\frac{4\,e^8}{a^2\,d}+36\,a^2\,d\,e^9\,\sqrt{-\frac{1}{a^8\,d^4\,e^2}}}+\frac{36\,e^9\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{a^8\,d^4\,e^2}\right)}^{3/4}}{\frac{4\,e^8}{a^6\,d^3}+\frac{36\,e^9\,\sqrt{-\frac{1}{a^8\,d^4\,e^2}}}{a^2\,d}}\right)\,{\left(-\frac{1}{a^8\,d^4\,e^2}\right)}^{1/4}}{2}+\mathrm{atan}\left(\frac{e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{256\,a^8\,d^4\,e^2}\right)}^{1/4}\,16{}\mathrm{i}}{\frac{4\,e^8}{a^2\,d}-576\,a^2\,d\,e^9\,\sqrt{-\frac{1}{256\,a^8\,d^4\,e^2}}}-\frac{e^9\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{256\,a^8\,d^4\,e^2}\right)}^{3/4}\,2304{}\mathrm{i}}{\frac{4\,e^8}{a^6\,d^3}-\frac{576\,e^9\,\sqrt{-\frac{1}{256\,a^8\,d^4\,e^2}}}{a^2\,d}}\right)\,{\left(-\frac{1}{256\,a^8\,d^4\,e^2}\right)}^{1/4}\,2{}\mathrm{i}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\left(a^2\,d\,e+a^2\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)}-\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}}{\sqrt{-e}}\right)\,3{}\mathrm{i}}{2\,a^2\,d\,\sqrt{-e}}","Not used",1,"(atan((4*e^8*(e*cot(c + d*x))^(1/2)*(-1/(a^8*d^4*e^2))^(1/4))/((4*e^8)/(a^2*d) + 36*a^2*d*e^9*(-1/(a^8*d^4*e^2))^(1/2)) + (36*e^9*(e*cot(c + d*x))^(1/2)*(-1/(a^8*d^4*e^2))^(3/4))/((4*e^8)/(a^6*d^3) + (36*e^9*(-1/(a^8*d^4*e^2))^(1/2))/(a^2*d)))*(-1/(a^8*d^4*e^2))^(1/4))/2 + atan((e^8*(e*cot(c + d*x))^(1/2)*(-1/(256*a^8*d^4*e^2))^(1/4)*16i)/((4*e^8)/(a^2*d) - 576*a^2*d*e^9*(-1/(256*a^8*d^4*e^2))^(1/2)) - (e^9*(e*cot(c + d*x))^(1/2)*(-1/(256*a^8*d^4*e^2))^(3/4)*2304i)/((4*e^8)/(a^6*d^3) - (576*e^9*(-1/(256*a^8*d^4*e^2))^(1/2))/(a^2*d)))*(-1/(256*a^8*d^4*e^2))^(1/4)*2i - (e*cot(c + d*x))^(1/2)/(2*(a^2*d*e + a^2*d*e*cot(c + d*x))) - (atan(((e*cot(c + d*x))^(1/2)*1i)/(-e)^(1/2))*3i)/(2*a^2*d*(-e)^(1/2))","B"
33,1,414,306,0.922779,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + a*cot(c + d*x))^2),x)","\frac{\frac{5\,\mathrm{cot}\left(c+d\,x\right)}{2}+2}{a^2\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}+a^2\,d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}-\frac{\mathrm{atan}\left(\frac{2048\,a^{10}\,d^5\,e^{13}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{a^8\,d^4\,e^6}\right)}^{1/4}}{51200\,a^8\,d^4\,e^{12}-2048\,a^{12}\,d^6\,e^{15}\,\sqrt{-\frac{1}{a^8\,d^4\,e^6}}}+\frac{51200\,a^{14}\,d^7\,e^{16}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{a^8\,d^4\,e^6}\right)}^{3/4}}{51200\,a^8\,d^4\,e^{12}-2048\,a^{12}\,d^6\,e^{15}\,\sqrt{-\frac{1}{a^8\,d^4\,e^6}}}\right)\,{\left(-\frac{1}{a^8\,d^4\,e^6}\right)}^{1/4}}{2}-\mathrm{atan}\left(\frac{a^{10}\,d^5\,e^{13}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{256\,a^8\,d^4\,e^6}\right)}^{1/4}\,8192{}\mathrm{i}}{51200\,a^8\,d^4\,e^{12}+32768\,a^{12}\,d^6\,e^{15}\,\sqrt{-\frac{1}{256\,a^8\,d^4\,e^6}}}-\frac{a^{14}\,d^7\,e^{16}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{256\,a^8\,d^4\,e^6}\right)}^{3/4}\,3276800{}\mathrm{i}}{51200\,a^8\,d^4\,e^{12}+32768\,a^{12}\,d^6\,e^{15}\,\sqrt{-\frac{1}{256\,a^8\,d^4\,e^6}}}\right)\,{\left(-\frac{1}{256\,a^8\,d^4\,e^6}\right)}^{1/4}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-e^3}\,1{}\mathrm{i}}{e^2}\right)\,\sqrt{-e^3}\,5{}\mathrm{i}}{2\,a^2\,d\,e^3}","Not used",1,"((5*cot(c + d*x))/2 + 2)/(a^2*d*(e*cot(c + d*x))^(3/2) + a^2*d*e*(e*cot(c + d*x))^(1/2)) - (atan((2048*a^10*d^5*e^13*(e*cot(c + d*x))^(1/2)*(-1/(a^8*d^4*e^6))^(1/4))/(51200*a^8*d^4*e^12 - 2048*a^12*d^6*e^15*(-1/(a^8*d^4*e^6))^(1/2)) + (51200*a^14*d^7*e^16*(e*cot(c + d*x))^(1/2)*(-1/(a^8*d^4*e^6))^(3/4))/(51200*a^8*d^4*e^12 - 2048*a^12*d^6*e^15*(-1/(a^8*d^4*e^6))^(1/2)))*(-1/(a^8*d^4*e^6))^(1/4))/2 - atan((a^10*d^5*e^13*(e*cot(c + d*x))^(1/2)*(-1/(256*a^8*d^4*e^6))^(1/4)*8192i)/(51200*a^8*d^4*e^12 + 32768*a^12*d^6*e^15*(-1/(256*a^8*d^4*e^6))^(1/2)) - (a^14*d^7*e^16*(e*cot(c + d*x))^(1/2)*(-1/(256*a^8*d^4*e^6))^(3/4)*3276800i)/(51200*a^8*d^4*e^12 + 32768*a^12*d^6*e^15*(-1/(256*a^8*d^4*e^6))^(1/2)))*(-1/(256*a^8*d^4*e^6))^(1/4)*2i + (atan(((e*cot(c + d*x))^(1/2)*(-e^3)^(1/2)*1i)/e^2)*(-e^3)^(1/2)*5i)/(2*a^2*d*e^3)","B"
34,1,425,331,1.226302,"\text{Not used}","int(1/((e*cot(c + d*x))^(5/2)*(a + a*cot(c + d*x))^2),x)","-\frac{\mathrm{atan}\left(\frac{2048\,a^{10}\,d^5\,e^{18}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{a^8\,d^4\,e^{10}}\right)}^{1/4}}{2048\,a^8\,d^4\,e^{16}+100352\,a^{12}\,d^6\,e^{21}\,\sqrt{-\frac{1}{a^8\,d^4\,e^{10}}}}+\frac{100352\,a^{14}\,d^7\,e^{23}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{a^8\,d^4\,e^{10}}\right)}^{3/4}}{2048\,a^8\,d^4\,e^{16}+100352\,a^{12}\,d^6\,e^{21}\,\sqrt{-\frac{1}{a^8\,d^4\,e^{10}}}}\right)\,{\left(-\frac{1}{a^8\,d^4\,e^{10}}\right)}^{1/4}}{2}-\mathrm{atan}\left(\frac{a^{10}\,d^5\,e^{18}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{256\,a^8\,d^4\,e^{10}}\right)}^{1/4}\,8192{}\mathrm{i}}{2048\,a^8\,d^4\,e^{16}-1605632\,a^{12}\,d^6\,e^{21}\,\sqrt{-\frac{1}{256\,a^8\,d^4\,e^{10}}}}-\frac{a^{14}\,d^7\,e^{23}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(-\frac{1}{256\,a^8\,d^4\,e^{10}}\right)}^{3/4}\,6422528{}\mathrm{i}}{2048\,a^8\,d^4\,e^{16}-1605632\,a^{12}\,d^6\,e^{21}\,\sqrt{-\frac{1}{256\,a^8\,d^4\,e^{10}}}}\right)\,{\left(-\frac{1}{256\,a^8\,d^4\,e^{10}}\right)}^{1/4}\,2{}\mathrm{i}-\frac{\frac{9\,{\mathrm{cot}\left(c+d\,x\right)}^2}{2}+\frac{10\,\mathrm{cot}\left(c+d\,x\right)}{3}-\frac{2}{3}}{a^2\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}+a^2\,d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-\frac{\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-e^5}\,1{}\mathrm{i}}{e^3}\right)\,\sqrt{-e^5}\,7{}\mathrm{i}}{2\,a^2\,d\,e^5}","Not used",1,"- (atan((2048*a^10*d^5*e^18*(e*cot(c + d*x))^(1/2)*(-1/(a^8*d^4*e^10))^(1/4))/(2048*a^8*d^4*e^16 + 100352*a^12*d^6*e^21*(-1/(a^8*d^4*e^10))^(1/2)) + (100352*a^14*d^7*e^23*(e*cot(c + d*x))^(1/2)*(-1/(a^8*d^4*e^10))^(3/4))/(2048*a^8*d^4*e^16 + 100352*a^12*d^6*e^21*(-1/(a^8*d^4*e^10))^(1/2)))*(-1/(a^8*d^4*e^10))^(1/4))/2 - atan((a^10*d^5*e^18*(e*cot(c + d*x))^(1/2)*(-1/(256*a^8*d^4*e^10))^(1/4)*8192i)/(2048*a^8*d^4*e^16 - 1605632*a^12*d^6*e^21*(-1/(256*a^8*d^4*e^10))^(1/2)) - (a^14*d^7*e^23*(e*cot(c + d*x))^(1/2)*(-1/(256*a^8*d^4*e^10))^(3/4)*6422528i)/(2048*a^8*d^4*e^16 - 1605632*a^12*d^6*e^21*(-1/(256*a^8*d^4*e^10))^(1/2)))*(-1/(256*a^8*d^4*e^10))^(1/4)*2i - ((10*cot(c + d*x))/3 + (9*cot(c + d*x)^2)/2 - 2/3)/(a^2*d*(e*cot(c + d*x))^(5/2) + a^2*d*e*(e*cot(c + d*x))^(3/2)) - (atan(((e*cot(c + d*x))^(1/2)*(-e^5)^(1/2)*1i)/e^3)*(-e^5)^(1/2)*7i)/(2*a^2*d*e^5)","B"
35,1,154,164,1.036968,"\text{Not used}","int((e*cot(c + d*x))^(5/2)/(a + a*cot(c + d*x))^3,x)","\frac{\sqrt{2}\,e^{5/2}\,\mathrm{atanh}\left(\frac{9\,\sqrt{2}\,e^{33/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{32\,\left(\frac{9\,e^{17}\,\mathrm{cot}\left(c+d\,x\right)}{32}+\frac{9\,e^{17}}{32}\right)}\right)}{4\,a^3\,d}-\frac{e^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{8\,a^3\,d}-\frac{\frac{3\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{8}+\frac{5\,e^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{8}}{d\,a^3\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2+2\,d\,a^3\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,a^3\,e^2}","Not used",1,"(2^(1/2)*e^(5/2)*atanh((9*2^(1/2)*e^(33/2)*(e*cot(c + d*x))^(1/2))/(32*((9*e^17*cot(c + d*x))/32 + (9*e^17)/32))))/(4*a^3*d) - (e^(5/2)*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(8*a^3*d) - ((3*e^4*(e*cot(c + d*x))^(1/2))/8 + (5*e^3*(e*cot(c + d*x))^(3/2))/8)/(a^3*d*e^2 + a^3*d*e^2*cot(c + d*x)^2 + 2*a^3*d*e^2*cot(c + d*x))","B"
36,1,178,164,0.937804,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + a*cot(c + d*x))^3,x)","\frac{5\,e^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{8\,a^3\,d}-\frac{\frac{e^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{8}-\frac{e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{8}}{d\,a^3\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2+2\,d\,a^3\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,a^3\,e^2}-\frac{\sqrt{2}\,e^{3/2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{8\,a^3\,d}","Not used",1,"(5*e^(3/2)*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(8*a^3*d) - ((e^3*(e*cot(c + d*x))^(1/2))/8 - (e^2*(e*cot(c + d*x))^(3/2))/8)/(a^3*d*e^2 + a^3*d*e^2*cot(c + d*x)^2 + 2*a^3*d*e^2*cot(c + d*x)) - (2^(1/2)*e^(3/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(8*a^3*d)","B"
37,1,151,161,0.897532,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + a*cot(c + d*x))^3,x)","\frac{\frac{3\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{8}+\frac{5\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{8}}{d\,a^3\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2+2\,d\,a^3\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,a^3\,e^2}-\frac{\sqrt{e}\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{8\,a^3\,d}-\frac{\sqrt{2}\,\sqrt{e}\,\mathrm{atanh}\left(\frac{9\,\sqrt{2}\,e^{17/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{32\,\left(\frac{9\,e^9\,\mathrm{cot}\left(c+d\,x\right)}{32}+\frac{9\,e^9}{32}\right)}\right)}{4\,a^3\,d}","Not used",1,"((3*e*(e*cot(c + d*x))^(3/2))/8 + (5*e^2*(e*cot(c + d*x))^(1/2))/8)/(a^3*d*e^2 + a^3*d*e^2*cot(c + d*x)^2 + 2*a^3*d*e^2*cot(c + d*x)) - (e^(1/2)*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(8*a^3*d) - (2^(1/2)*e^(1/2)*atanh((9*2^(1/2)*e^(17/2)*(e*cot(c + d*x))^(1/2))/(32*((9*e^9*cot(c + d*x))/32 + (9*e^9)/32))))/(4*a^3*d)","B"
38,1,173,165,0.944196,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + a*cot(c + d*x))^3),x)","\frac{\sqrt{2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{8\,a^3\,d\,\sqrt{e}}-\frac{11\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{8\,a^3\,d\,\sqrt{e}}-\frac{\frac{9\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{8}+\frac{7\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{8}}{d\,a^3\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2+2\,d\,a^3\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,a^3\,e^2}","Not used",1,"(2^(1/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(8*a^3*d*e^(1/2)) - (11*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(8*a^3*d*e^(1/2)) - ((9*e*(e*cot(c + d*x))^(1/2))/8 + (7*(e*cot(c + d*x))^(3/2))/8)/(a^3*d*e^2 + a^3*d*e^2*cot(c + d*x)^2 + 2*a^3*d*e^2*cot(c + d*x))","B"
39,1,175,189,1.141488,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + a*cot(c + d*x))^3),x)","\frac{\frac{27\,e\,{\mathrm{cot}\left(c+d\,x\right)}^2}{8}+\frac{45\,e\,\mathrm{cot}\left(c+d\,x\right)}{8}+2\,e}{a^3\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}+2\,a^3\,d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}+a^3\,d\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{31\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{8\,a^3\,d\,e^{3/2}}+\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{63504384\,\sqrt{2}\,a^9\,d^3\,e^{15/2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{63504384\,a^9\,d^3\,e^8+63504384\,a^9\,d^3\,e^8\,\mathrm{cot}\left(c+d\,x\right)}\right)}{4\,a^3\,d\,e^{3/2}}","Not used",1,"(2*e + (45*e*cot(c + d*x))/8 + (27*e*cot(c + d*x)^2)/8)/(a^3*d*(e*cot(c + d*x))^(5/2) + 2*a^3*d*e*(e*cot(c + d*x))^(3/2) + a^3*d*e^2*(e*cot(c + d*x))^(1/2)) + (31*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(8*a^3*d*e^(3/2)) + (2^(1/2)*atanh((63504384*2^(1/2)*a^9*d^3*e^(15/2)*(e*cot(c + d*x))^(1/2))/(63504384*a^9*d^3*e^8 + 63504384*a^9*d^3*e^8*cot(c + d*x))))/(4*a^3*d*e^(3/2))","B"
40,1,193,215,1.384788,"\text{Not used}","int(1/((e*cot(c + d*x))^(5/2)*(a + a*cot(c + d*x))^3),x)","-\frac{\frac{63\,e\,{\mathrm{cot}\left(c+d\,x\right)}^3}{8}+\frac{323\,e\,{\mathrm{cot}\left(c+d\,x\right)}^2}{24}+\frac{14\,e\,\mathrm{cot}\left(c+d\,x\right)}{3}-\frac{2\,e}{3}}{a^3\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}+2\,a^3\,d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}+a^3\,d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-\frac{59\,\mathrm{atan}\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{8\,a^3\,d\,e^{5/2}}-\frac{\sqrt{2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{2\,\sqrt{e}}+\frac{\sqrt{2}\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{2\,e^{3/2}}\right)\right)}{8\,a^3\,d\,e^{5/2}}","Not used",1,"- ((14*e*cot(c + d*x))/3 - (2*e)/3 + (323*e*cot(c + d*x)^2)/24 + (63*e*cot(c + d*x)^3)/8)/(a^3*d*(e*cot(c + d*x))^(7/2) + 2*a^3*d*e*(e*cot(c + d*x))^(5/2) + a^3*d*e^2*(e*cot(c + d*x))^(3/2)) - (59*atan((e*cot(c + d*x))^(1/2)/e^(1/2)))/(8*a^3*d*e^(5/2)) - (2^(1/2)*(2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2))) + 2*atan((2^(1/2)*(e*cot(c + d*x))^(1/2))/(2*e^(1/2)) + (2^(1/2)*(e*cot(c + d*x))^(3/2))/(2*e^(3/2)))))/(8*a^3*d*e^(5/2))","B"
41,1,119,223,0.631309,"\text{Not used}","int(cot(x)^2*(cot(x) + 1)^(1/2),x)","\mathrm{atanh}\left(4\,\sqrt{\mathrm{cot}\left(x\right)+1}\,{\left(\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}+\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)}^3\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}+2\,\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)-\frac{2\,{\left(\mathrm{cot}\left(x\right)+1\right)}^{3/2}}{3}+\mathrm{atanh}\left(4\,\sqrt{\mathrm{cot}\left(x\right)+1}\,{\left(\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}-\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)}^3\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{8}-\frac{1}{8}}-2\,\sqrt{\frac{\sqrt{2}}{8}-\frac{1}{8}}\right)","Not used",1,"atanh(4*(cot(x) + 1)^(1/2)*((- 2^(1/2)/8 - 1/8)^(1/2) + (2^(1/2)/8 - 1/8)^(1/2))^3)*(2*(- 2^(1/2)/8 - 1/8)^(1/2) + 2*(2^(1/2)/8 - 1/8)^(1/2)) - (2*(cot(x) + 1)^(3/2))/3 + atanh(4*(cot(x) + 1)^(1/2)*((- 2^(1/2)/8 - 1/8)^(1/2) - (2^(1/2)/8 - 1/8)^(1/2))^3)*(2*(- 2^(1/2)/8 - 1/8)^(1/2) - 2*(2^(1/2)/8 - 1/8)^(1/2))","B"
42,1,210,135,0.483264,"\text{Not used}","int(cot(x)*(cot(x) + 1)^(1/2),x)","\mathrm{atanh}\left(\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{4\,\sqrt{\frac{1}{8}-\frac{\sqrt{2}}{8}}}+\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{4\,\sqrt{\frac{\sqrt{2}}{8}+\frac{1}{8}}}-\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{1}{8}-\frac{\sqrt{2}}{8}}}+\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{\sqrt{2}}{8}+\frac{1}{8}}}\right)\,\left(2\,\sqrt{\frac{1}{8}-\frac{\sqrt{2}}{8}}+2\,\sqrt{\frac{\sqrt{2}}{8}+\frac{1}{8}}\right)-\mathrm{atanh}\left(\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{4\,\sqrt{\frac{\sqrt{2}}{8}+\frac{1}{8}}}-\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{4\,\sqrt{\frac{1}{8}-\frac{\sqrt{2}}{8}}}+\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{1}{8}-\frac{\sqrt{2}}{8}}}+\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{\sqrt{2}}{8}+\frac{1}{8}}}\right)\,\left(2\,\sqrt{\frac{1}{8}-\frac{\sqrt{2}}{8}}-2\,\sqrt{\frac{\sqrt{2}}{8}+\frac{1}{8}}\right)-2\,\sqrt{\mathrm{cot}\left(x\right)+1}","Not used",1,"atanh((cot(x) + 1)^(1/2)/(4*(1/8 - 2^(1/2)/8)^(1/2)) + (cot(x) + 1)^(1/2)/(4*(2^(1/2)/8 + 1/8)^(1/2)) - (2^(1/2)*(cot(x) + 1)^(1/2))/(8*(1/8 - 2^(1/2)/8)^(1/2)) + (2^(1/2)*(cot(x) + 1)^(1/2))/(8*(2^(1/2)/8 + 1/8)^(1/2)))*(2*(1/8 - 2^(1/2)/8)^(1/2) + 2*(2^(1/2)/8 + 1/8)^(1/2)) - atanh((cot(x) + 1)^(1/2)/(4*(2^(1/2)/8 + 1/8)^(1/2)) - (cot(x) + 1)^(1/2)/(4*(1/8 - 2^(1/2)/8)^(1/2)) + (2^(1/2)*(cot(x) + 1)^(1/2))/(8*(1/8 - 2^(1/2)/8)^(1/2)) + (2^(1/2)*(cot(x) + 1)^(1/2))/(8*(2^(1/2)/8 + 1/8)^(1/2)))*(2*(1/8 - 2^(1/2)/8)^(1/2) - 2*(2^(1/2)/8 + 1/8)^(1/2)) - 2*(cot(x) + 1)^(1/2)","B"
43,1,254,139,0.995827,"\text{Not used}","int(cot(x)^2*(cot(x) + 1)^(3/2),x)","\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}-64}-\frac{\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}-64}\right)\,\left(\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,2{}\mathrm{i}+\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}\,2{}\mathrm{i}\right)-\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}+64}+\frac{\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}+64}\right)\,\left(\sqrt{\frac{1}{4}-\frac{\sqrt{2}}{4}}\,2{}\mathrm{i}-\sqrt{\frac{\sqrt{2}}{4}+\frac{1}{4}}\,2{}\mathrm{i}\right)+2\,\sqrt{\mathrm{cot}\left(x\right)+1}-\frac{2\,{\left(\mathrm{cot}\left(x\right)+1\right)}^{5/2}}{5}","Not used",1,"atan((2^(1/2)*(1/4 - 2^(1/2)/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(1/4 - 2^(1/2)/4)^(1/2)*(2^(1/2)/4 + 1/4)^(1/2) - 64) - (2^(1/2)*(2^(1/2)/4 + 1/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(1/4 - 2^(1/2)/4)^(1/2)*(2^(1/2)/4 + 1/4)^(1/2) - 64))*((1/4 - 2^(1/2)/4)^(1/2)*2i + (2^(1/2)/4 + 1/4)^(1/2)*2i) - atan((2^(1/2)*(1/4 - 2^(1/2)/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(1/4 - 2^(1/2)/4)^(1/2)*(2^(1/2)/4 + 1/4)^(1/2) + 64) + (2^(1/2)*(2^(1/2)/4 + 1/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(1/4 - 2^(1/2)/4)^(1/2)*(2^(1/2)/4 + 1/4)^(1/2) + 64))*((1/4 - 2^(1/2)/4)^(1/2)*2i - (2^(1/2)/4 + 1/4)^(1/2)*2i) + 2*(cot(x) + 1)^(1/2) - (2*(cot(x) + 1)^(5/2))/5","B"
44,1,254,221,0.673566,"\text{Not used}","int(cot(x)*(cot(x) + 1)^(3/2),x)","-\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}-64}-\frac{\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}-64}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}+\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}\right)+\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}+64}+\frac{\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{\mathrm{cot}\left(x\right)+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}+64}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}-\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}\right)-2\,\sqrt{\mathrm{cot}\left(x\right)+1}-\frac{2\,{\left(\mathrm{cot}\left(x\right)+1\right)}^{3/2}}{3}","Not used",1,"atan((2^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) + 64) + (2^(1/2)*(2^(1/2)/4 - 1/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) + 64))*((- 2^(1/2)/4 - 1/4)^(1/2)*2i - (2^(1/2)/4 - 1/4)^(1/2)*2i) - atan((2^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) - 64) - (2^(1/2)*(2^(1/2)/4 - 1/4)^(1/2)*(cot(x) + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) - 64))*((- 2^(1/2)/4 - 1/4)^(1/2)*2i + (2^(1/2)/4 - 1/4)^(1/2)*2i) - 2*(cot(x) + 1)^(1/2) - (2*(cot(x) + 1)^(3/2))/3","B"
45,1,238,214,0.438320,"\text{Not used}","int(cot(x)^2/(cot(x) + 1)^(1/2),x)","\mathrm{atanh}\left(\frac{16\,\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}-8}-\frac{16\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}-8}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}+2\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\right)-\mathrm{atanh}\left(\frac{16\,\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}+8}+\frac{16\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}+8}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{16}-\frac{1}{16}}-2\,\sqrt{\frac{\sqrt{2}}{16}-\frac{1}{16}}\right)-2\,\sqrt{\mathrm{cot}\left(x\right)+1}","Not used",1,"atanh((16*2^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) - 8) - (16*2^(1/2)*(2^(1/2)/16 - 1/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) - 8))*(2*(- 2^(1/2)/16 - 1/16)^(1/2) + 2*(2^(1/2)/16 - 1/16)^(1/2)) - atanh((16*2^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) + 8) + (16*2^(1/2)*(2^(1/2)/16 - 1/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(2^(1/2)/16 - 1/16)^(1/2)*(- 2^(1/2)/16 - 1/16)^(1/2) + 8))*(2*(- 2^(1/2)/16 - 1/16)^(1/2) - 2*(2^(1/2)/16 - 1/16)^(1/2)) - 2*(cot(x) + 1)^(1/2)","B"
46,1,230,121,0.409551,"\text{Not used}","int(cot(x)/(cot(x) + 1)^(1/2),x)","\mathrm{atanh}\left(\frac{16\,\sqrt{2}\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}-8}-\frac{16\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}-8}\right)\,\left(2\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}+2\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}\right)-\mathrm{atanh}\left(\frac{16\,\sqrt{2}\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}+8}+\frac{16\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{128\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}+8}\right)\,\left(2\,\sqrt{\frac{1}{16}-\frac{\sqrt{2}}{16}}-2\,\sqrt{\frac{\sqrt{2}}{16}+\frac{1}{16}}\right)","Not used",1,"atanh((16*2^(1/2)*(1/16 - 2^(1/2)/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(1/16 - 2^(1/2)/16)^(1/2)*(2^(1/2)/16 + 1/16)^(1/2) - 8) - (16*2^(1/2)*(2^(1/2)/16 + 1/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(1/16 - 2^(1/2)/16)^(1/2)*(2^(1/2)/16 + 1/16)^(1/2) - 8))*(2*(1/16 - 2^(1/2)/16)^(1/2) + 2*(2^(1/2)/16 + 1/16)^(1/2)) - atanh((16*2^(1/2)*(1/16 - 2^(1/2)/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(1/16 - 2^(1/2)/16)^(1/2)*(2^(1/2)/16 + 1/16)^(1/2) + 8) + (16*2^(1/2)*(2^(1/2)/16 + 1/16)^(1/2)*(cot(x) + 1)^(1/2))/(128*(1/16 - 2^(1/2)/16)^(1/2)*(2^(1/2)/16 + 1/16)^(1/2) + 8))*(2*(1/16 - 2^(1/2)/16)^(1/2) - 2*(2^(1/2)/16 + 1/16)^(1/2))","B"
47,1,208,139,0.501496,"\text{Not used}","int(cot(x)^2/(cot(x) + 1)^(3/2),x)","\frac{1}{\sqrt{\mathrm{cot}\left(x\right)+1}}-\mathrm{atanh}\left(\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{\sqrt{2}}{32}+\frac{1}{32}}}-\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{1}{32}-\frac{\sqrt{2}}{32}}}+\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{16\,\sqrt{\frac{1}{32}-\frac{\sqrt{2}}{32}}}+\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{16\,\sqrt{\frac{\sqrt{2}}{32}+\frac{1}{32}}}\right)\,\left(2\,\sqrt{\frac{1}{32}-\frac{\sqrt{2}}{32}}-2\,\sqrt{\frac{\sqrt{2}}{32}+\frac{1}{32}}\right)+\mathrm{atanh}\left(\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{1}{32}-\frac{\sqrt{2}}{32}}}+\frac{\sqrt{\mathrm{cot}\left(x\right)+1}}{8\,\sqrt{\frac{\sqrt{2}}{32}+\frac{1}{32}}}-\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{16\,\sqrt{\frac{1}{32}-\frac{\sqrt{2}}{32}}}+\frac{\sqrt{2}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{16\,\sqrt{\frac{\sqrt{2}}{32}+\frac{1}{32}}}\right)\,\left(2\,\sqrt{\frac{1}{32}-\frac{\sqrt{2}}{32}}+2\,\sqrt{\frac{\sqrt{2}}{32}+\frac{1}{32}}\right)","Not used",1,"1/(cot(x) + 1)^(1/2) - atanh((cot(x) + 1)^(1/2)/(8*(2^(1/2)/32 + 1/32)^(1/2)) - (cot(x) + 1)^(1/2)/(8*(1/32 - 2^(1/2)/32)^(1/2)) + (2^(1/2)*(cot(x) + 1)^(1/2))/(16*(1/32 - 2^(1/2)/32)^(1/2)) + (2^(1/2)*(cot(x) + 1)^(1/2))/(16*(2^(1/2)/32 + 1/32)^(1/2)))*(2*(1/32 - 2^(1/2)/32)^(1/2) - 2*(2^(1/2)/32 + 1/32)^(1/2)) + atanh((cot(x) + 1)^(1/2)/(8*(1/32 - 2^(1/2)/32)^(1/2)) + (cot(x) + 1)^(1/2)/(8*(2^(1/2)/32 + 1/32)^(1/2)) - (2^(1/2)*(cot(x) + 1)^(1/2))/(16*(1/32 - 2^(1/2)/32)^(1/2)) + (2^(1/2)*(cot(x) + 1)^(1/2))/(16*(2^(1/2)/32 + 1/32)^(1/2)))*(2*(1/32 - 2^(1/2)/32)^(1/2) + 2*(2^(1/2)/32 + 1/32)^(1/2))","B"
48,1,121,226,0.400214,"\text{Not used}","int(cot(x)/(cot(x) + 1)^(3/2),x)","-\mathrm{atanh}\left(32\,\sqrt{\mathrm{cot}\left(x\right)+1}\,{\left(\sqrt{-\frac{\sqrt{2}}{32}-\frac{1}{32}}+\sqrt{\frac{\sqrt{2}}{32}-\frac{1}{32}}\right)}^3\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{32}-\frac{1}{32}}+2\,\sqrt{\frac{\sqrt{2}}{32}-\frac{1}{32}}\right)-\frac{1}{\sqrt{\mathrm{cot}\left(x\right)+1}}-\mathrm{atanh}\left(32\,\sqrt{\mathrm{cot}\left(x\right)+1}\,{\left(\sqrt{-\frac{\sqrt{2}}{32}-\frac{1}{32}}-\sqrt{\frac{\sqrt{2}}{32}-\frac{1}{32}}\right)}^3\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{32}-\frac{1}{32}}-2\,\sqrt{\frac{\sqrt{2}}{32}-\frac{1}{32}}\right)","Not used",1,"- atanh(32*(cot(x) + 1)^(1/2)*((- 2^(1/2)/32 - 1/32)^(1/2) + (2^(1/2)/32 - 1/32)^(1/2))^3)*(2*(- 2^(1/2)/32 - 1/32)^(1/2) + 2*(2^(1/2)/32 - 1/32)^(1/2)) - 1/(cot(x) + 1)^(1/2) - atanh(32*(cot(x) + 1)^(1/2)*((- 2^(1/2)/32 - 1/32)^(1/2) - (2^(1/2)/32 - 1/32)^(1/2))^3)*(2*(- 2^(1/2)/32 - 1/32)^(1/2) - 2*(2^(1/2)/32 - 1/32)^(1/2))","B"
49,1,242,143,0.800232,"\text{Not used}","int(cot(x)^2/(cot(x) + 1)^(5/2),x)","\mathrm{atanh}\left(\frac{4\,\sqrt{2}\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}-1}-\frac{4\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}-1}\right)\,\left(2\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}+2\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}\right)-\mathrm{atanh}\left(\frac{4\,\sqrt{2}\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}+1}+\frac{4\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}+1}\right)\,\left(2\,\sqrt{\frac{1}{64}-\frac{\sqrt{2}}{64}}-2\,\sqrt{\frac{\sqrt{2}}{64}+\frac{1}{64}}\right)-\frac{\mathrm{cot}\left(x\right)+\frac{2}{3}}{{\left(\mathrm{cot}\left(x\right)+1\right)}^{3/2}}","Not used",1,"atanh((4*2^(1/2)*(1/64 - 2^(1/2)/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(1/64 - 2^(1/2)/64)^(1/2)*(2^(1/2)/64 + 1/64)^(1/2) - 1) - (4*2^(1/2)*(2^(1/2)/64 + 1/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(1/64 - 2^(1/2)/64)^(1/2)*(2^(1/2)/64 + 1/64)^(1/2) - 1))*(2*(1/64 - 2^(1/2)/64)^(1/2) + 2*(2^(1/2)/64 + 1/64)^(1/2)) - atanh((4*2^(1/2)*(1/64 - 2^(1/2)/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(1/64 - 2^(1/2)/64)^(1/2)*(2^(1/2)/64 + 1/64)^(1/2) + 1) + (4*2^(1/2)*(2^(1/2)/64 + 1/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(1/64 - 2^(1/2)/64)^(1/2)*(2^(1/2)/64 + 1/64)^(1/2) + 1))*(2*(1/64 - 2^(1/2)/64)^(1/2) - 2*(2^(1/2)/64 + 1/64)^(1/2)) - (cot(x) + 2/3)/(cot(x) + 1)^(3/2)","B"
50,1,238,216,0.708796,"\text{Not used}","int(cot(x)/(cot(x) + 1)^(5/2),x)","\mathrm{atanh}\left(\frac{4\,\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+1}+\frac{4\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+1}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)-\mathrm{atanh}\left(\frac{4\,\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-1}-\frac{4\,\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{\mathrm{cot}\left(x\right)+1}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-1}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)-\frac{1}{3\,{\left(\mathrm{cot}\left(x\right)+1\right)}^{3/2}}","Not used",1,"atanh((4*2^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) + 1) + (4*2^(1/2)*(2^(1/2)/64 - 1/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) + 1))*(2*(- 2^(1/2)/64 - 1/64)^(1/2) - 2*(2^(1/2)/64 - 1/64)^(1/2)) - atanh((4*2^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) - 1) - (4*2^(1/2)*(2^(1/2)/64 - 1/64)^(1/2)*(cot(x) + 1)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) - 1))*(2*(- 2^(1/2)/64 - 1/64)^(1/2) + 2*(2^(1/2)/64 - 1/64)^(1/2)) - 1/(3*(cot(x) + 1)^(3/2))","B"
51,1,153,247,1.397358,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + b*cot(c + d*x)),x)","\frac{{\left(-1\right)}^{1/4}\,b\,e^{3/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d}-\frac{2\,a\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{2\,b\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{{\left(-1\right)}^{1/4}\,b\,e^{3/2}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,e^{3/2}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,e^{3/2}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d}","Not used",1,"((-1)^(1/4)*b*e^(3/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/d - (2*a*e*(e*cot(c + d*x))^(1/2))/d - ((-1)^(1/4)*a*e^(3/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/d - ((-1)^(1/4)*a*e^(3/2)*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/d - (2*b*(e*cot(c + d*x))^(3/2))/(3*d) - ((-1)^(1/4)*b*e^(3/2)*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/d","B"
52,1,128,226,0.725866,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + b*cot(c + d*x)),x)","-\frac{2\,b\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{{\left(-1\right)}^{1/4}\,a\,\sqrt{e}\,\left(\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)-\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\right)}{d}-\frac{{\left(-1\right)}^{1/4}\,b\,\sqrt{e}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d}-\frac{{\left(-1\right)}^{1/4}\,b\,\sqrt{e}\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d}","Not used",1,"- (2*b*(e*cot(c + d*x))^(1/2))/d - ((-1)^(1/4)*b*e^(1/2)*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/d - ((-1)^(1/4)*b*e^(1/2)*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/d - ((-1)^(1/4)*a*e^(1/2)*(atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)) - atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))))/d","B"
53,1,118,208,0.646880,"\text{Not used}","int((a + b*cot(c + d*x))/(e*cot(c + d*x))^(1/2),x)","\frac{{\left(-1\right)}^{1/4}\,b\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,\sqrt{e}}-\frac{{\left(-1\right)}^{1/4}\,b\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,\sqrt{e}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d\,\sqrt{e}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d\,\sqrt{e}}","Not used",1,"((-1)^(1/4)*a*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/(d*e^(1/2)) + ((-1)^(1/4)*a*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/(d*e^(1/2)) - ((-1)^(1/4)*b*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(1/2)) + ((-1)^(1/4)*b*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(1/2))","B"
54,1,137,229,0.804774,"\text{Not used}","int((a + b*cot(c + d*x))/(e*cot(c + d*x))^(3/2),x)","\frac{2\,a}{d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,e^{3/2}}-\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,e^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,b\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d\,e^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,b\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d\,e^{3/2}}","Not used",1,"(2*a)/(d*e*(e*cot(c + d*x))^(1/2)) + ((-1)^(1/4)*a*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(3/2)) - ((-1)^(1/4)*a*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(3/2)) + ((-1)^(1/4)*b*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/(d*e^(3/2)) + ((-1)^(1/4)*b*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/(d*e^(3/2))","B"
55,1,158,252,1.244554,"\text{Not used}","int((a + b*cot(c + d*x))/(e*cot(c + d*x))^(5/2),x)","\frac{2\,a}{3\,d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}+\frac{2\,b}{d\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+\frac{{\left(-1\right)}^{1/4}\,b\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,e^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,b\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)}{d\,e^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d\,e^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,a\,\mathrm{atanh}\left(\frac{{\left(-1\right)}^{1/4}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\sqrt{e}}\right)\,1{}\mathrm{i}}{d\,e^{5/2}}","Not used",1,"(2*a)/(3*d*e*(e*cot(c + d*x))^(3/2)) + (2*b)/(d*e^2*(e*cot(c + d*x))^(1/2)) - ((-1)^(1/4)*a*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/(d*e^(5/2)) - ((-1)^(1/4)*a*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2))*1i)/(d*e^(5/2)) + ((-1)^(1/4)*b*atan(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(5/2)) - ((-1)^(1/4)*b*atanh(((-1)^(1/4)*(e*cot(c + d*x))^(1/2))/e^(1/2)))/(d*e^(5/2))","B"
56,1,1274,317,2.470591,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + b*cot(c + d*x))^2,x)","-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(\frac{2\,a^2\,e}{d}-\frac{2\,b^2\,e}{d}\right)-\frac{2\,b^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d\,e}-\frac{4\,a\,b\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}+\mathrm{atan}\left(\frac{a^4\,e^6\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3\,e^3}{d^2}-\frac{b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}-\frac{a^4\,e^3\,1{}\mathrm{i}}{4\,d^2}-\frac{a^3\,b\,e^3}{d^2}+\frac{a^2\,b^2\,e^3\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{a^6\,e^8\,16{}\mathrm{i}}{d}-\frac{b^6\,e^8\,16{}\mathrm{i}}{d}+\frac{32\,a\,b^5\,e^8}{d}+\frac{32\,a^5\,b\,e^8}{d}+\frac{a^2\,b^4\,e^8\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^8}{d}-\frac{a^4\,b^2\,e^8\,112{}\mathrm{i}}{d}}+\frac{b^4\,e^6\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3\,e^3}{d^2}-\frac{b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}-\frac{a^4\,e^3\,1{}\mathrm{i}}{4\,d^2}-\frac{a^3\,b\,e^3}{d^2}+\frac{a^2\,b^2\,e^3\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{a^6\,e^8\,16{}\mathrm{i}}{d}-\frac{b^6\,e^8\,16{}\mathrm{i}}{d}+\frac{32\,a\,b^5\,e^8}{d}+\frac{32\,a^5\,b\,e^8}{d}+\frac{a^2\,b^4\,e^8\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^8}{d}-\frac{a^4\,b^2\,e^8\,112{}\mathrm{i}}{d}}-\frac{a^2\,b^2\,e^6\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3\,e^3}{d^2}-\frac{b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}-\frac{a^4\,e^3\,1{}\mathrm{i}}{4\,d^2}-\frac{a^3\,b\,e^3}{d^2}+\frac{a^2\,b^2\,e^3\,3{}\mathrm{i}}{2\,d^2}}\,192{}\mathrm{i}}{\frac{a^6\,e^8\,16{}\mathrm{i}}{d}-\frac{b^6\,e^8\,16{}\mathrm{i}}{d}+\frac{32\,a\,b^5\,e^8}{d}+\frac{32\,a^5\,b\,e^8}{d}+\frac{a^2\,b^4\,e^8\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^8}{d}-\frac{a^4\,b^2\,e^8\,112{}\mathrm{i}}{d}}\right)\,\sqrt{-\frac{a^4\,e^3\,1{}\mathrm{i}+4\,a^3\,b\,e^3-a^2\,b^2\,e^3\,6{}\mathrm{i}-4\,a\,b^3\,e^3+b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{a^4\,e^6\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,e^3\,1{}\mathrm{i}}{4\,d^2}+\frac{b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}+\frac{a\,b^3\,e^3}{d^2}-\frac{a^3\,b\,e^3}{d^2}-\frac{a^2\,b^2\,e^3\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{32\,a\,b^5\,e^8}{d}+\frac{b^6\,e^8\,16{}\mathrm{i}}{d}-\frac{a^6\,e^8\,16{}\mathrm{i}}{d}+\frac{32\,a^5\,b\,e^8}{d}-\frac{a^2\,b^4\,e^8\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^8}{d}+\frac{a^4\,b^2\,e^8\,112{}\mathrm{i}}{d}}+\frac{b^4\,e^6\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,e^3\,1{}\mathrm{i}}{4\,d^2}+\frac{b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}+\frac{a\,b^3\,e^3}{d^2}-\frac{a^3\,b\,e^3}{d^2}-\frac{a^2\,b^2\,e^3\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{32\,a\,b^5\,e^8}{d}+\frac{b^6\,e^8\,16{}\mathrm{i}}{d}-\frac{a^6\,e^8\,16{}\mathrm{i}}{d}+\frac{32\,a^5\,b\,e^8}{d}-\frac{a^2\,b^4\,e^8\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^8}{d}+\frac{a^4\,b^2\,e^8\,112{}\mathrm{i}}{d}}-\frac{a^2\,b^2\,e^6\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,e^3\,1{}\mathrm{i}}{4\,d^2}+\frac{b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}+\frac{a\,b^3\,e^3}{d^2}-\frac{a^3\,b\,e^3}{d^2}-\frac{a^2\,b^2\,e^3\,3{}\mathrm{i}}{2\,d^2}}\,192{}\mathrm{i}}{\frac{32\,a\,b^5\,e^8}{d}+\frac{b^6\,e^8\,16{}\mathrm{i}}{d}-\frac{a^6\,e^8\,16{}\mathrm{i}}{d}+\frac{32\,a^5\,b\,e^8}{d}-\frac{a^2\,b^4\,e^8\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^8}{d}+\frac{a^4\,b^2\,e^8\,112{}\mathrm{i}}{d}}\right)\,\sqrt{\frac{a^4\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,e^3-a^2\,b^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,e^3+b^4\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,2{}\mathrm{i}","Not used",1,"atan((a^4*e^6*(e*cot(c + d*x))^(1/2)*((a*b^3*e^3)/d^2 - (b^4*e^3*1i)/(4*d^2) - (a^4*e^3*1i)/(4*d^2) - (a^3*b*e^3)/d^2 + (a^2*b^2*e^3*3i)/(2*d^2))^(1/2)*32i)/((a^6*e^8*16i)/d - (b^6*e^8*16i)/d + (32*a*b^5*e^8)/d + (32*a^5*b*e^8)/d + (a^2*b^4*e^8*112i)/d - (192*a^3*b^3*e^8)/d - (a^4*b^2*e^8*112i)/d) + (b^4*e^6*(e*cot(c + d*x))^(1/2)*((a*b^3*e^3)/d^2 - (b^4*e^3*1i)/(4*d^2) - (a^4*e^3*1i)/(4*d^2) - (a^3*b*e^3)/d^2 + (a^2*b^2*e^3*3i)/(2*d^2))^(1/2)*32i)/((a^6*e^8*16i)/d - (b^6*e^8*16i)/d + (32*a*b^5*e^8)/d + (32*a^5*b*e^8)/d + (a^2*b^4*e^8*112i)/d - (192*a^3*b^3*e^8)/d - (a^4*b^2*e^8*112i)/d) - (a^2*b^2*e^6*(e*cot(c + d*x))^(1/2)*((a*b^3*e^3)/d^2 - (b^4*e^3*1i)/(4*d^2) - (a^4*e^3*1i)/(4*d^2) - (a^3*b*e^3)/d^2 + (a^2*b^2*e^3*3i)/(2*d^2))^(1/2)*192i)/((a^6*e^8*16i)/d - (b^6*e^8*16i)/d + (32*a*b^5*e^8)/d + (32*a^5*b*e^8)/d + (a^2*b^4*e^8*112i)/d - (192*a^3*b^3*e^8)/d - (a^4*b^2*e^8*112i)/d))*(-(a^4*e^3*1i + b^4*e^3*1i - 4*a*b^3*e^3 + 4*a^3*b*e^3 - a^2*b^2*e^3*6i)/(4*d^2))^(1/2)*2i + atan((a^4*e^6*(e*cot(c + d*x))^(1/2)*((a^4*e^3*1i)/(4*d^2) + (b^4*e^3*1i)/(4*d^2) + (a*b^3*e^3)/d^2 - (a^3*b*e^3)/d^2 - (a^2*b^2*e^3*3i)/(2*d^2))^(1/2)*32i)/((b^6*e^8*16i)/d - (a^6*e^8*16i)/d + (32*a*b^5*e^8)/d + (32*a^5*b*e^8)/d - (a^2*b^4*e^8*112i)/d - (192*a^3*b^3*e^8)/d + (a^4*b^2*e^8*112i)/d) + (b^4*e^6*(e*cot(c + d*x))^(1/2)*((a^4*e^3*1i)/(4*d^2) + (b^4*e^3*1i)/(4*d^2) + (a*b^3*e^3)/d^2 - (a^3*b*e^3)/d^2 - (a^2*b^2*e^3*3i)/(2*d^2))^(1/2)*32i)/((b^6*e^8*16i)/d - (a^6*e^8*16i)/d + (32*a*b^5*e^8)/d + (32*a^5*b*e^8)/d - (a^2*b^4*e^8*112i)/d - (192*a^3*b^3*e^8)/d + (a^4*b^2*e^8*112i)/d) - (a^2*b^2*e^6*(e*cot(c + d*x))^(1/2)*((a^4*e^3*1i)/(4*d^2) + (b^4*e^3*1i)/(4*d^2) + (a*b^3*e^3)/d^2 - (a^3*b*e^3)/d^2 - (a^2*b^2*e^3*3i)/(2*d^2))^(1/2)*192i)/((b^6*e^8*16i)/d - (a^6*e^8*16i)/d + (32*a*b^5*e^8)/d + (32*a^5*b*e^8)/d - (a^2*b^4*e^8*112i)/d - (192*a^3*b^3*e^8)/d + (a^4*b^2*e^8*112i)/d))*((a^4*e^3*1i + b^4*e^3*1i + 4*a*b^3*e^3 - 4*a^3*b*e^3 - a^2*b^2*e^3*6i)/(4*d^2))^(1/2)*2i - (e*cot(c + d*x))^(1/2)*((2*a^2*e)/d - (2*b^2*e)/d) - (2*b^2*(e*cot(c + d*x))^(5/2))/(5*d*e) - (4*a*b*(e*cot(c + d*x))^(3/2))/(3*d)","B"
57,1,1157,288,1.212496,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + b*cot(c + d*x))^2,x)","-\frac{2\,b^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d\,e}-\frac{4\,a\,b\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\mathrm{atan}\left(\frac{a^4\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b\,e}{d^2}-\frac{a\,b^3\,e}{d^2}-\frac{a^4\,e\,1{}\mathrm{i}}{4\,d^2}-\frac{b^4\,e\,1{}\mathrm{i}}{4\,d^2}+\frac{a^2\,b^2\,e\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{16\,a^6\,e^5}{d}-\frac{16\,b^6\,e^5}{d}+\frac{112\,a^2\,b^4\,e^5}{d}-\frac{112\,a^4\,b^2\,e^5}{d}+\frac{a\,b^5\,e^5\,32{}\mathrm{i}}{d}+\frac{a^5\,b\,e^5\,32{}\mathrm{i}}{d}-\frac{a^3\,b^3\,e^5\,192{}\mathrm{i}}{d}}+\frac{b^4\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b\,e}{d^2}-\frac{a\,b^3\,e}{d^2}-\frac{a^4\,e\,1{}\mathrm{i}}{4\,d^2}-\frac{b^4\,e\,1{}\mathrm{i}}{4\,d^2}+\frac{a^2\,b^2\,e\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{16\,a^6\,e^5}{d}-\frac{16\,b^6\,e^5}{d}+\frac{112\,a^2\,b^4\,e^5}{d}-\frac{112\,a^4\,b^2\,e^5}{d}+\frac{a\,b^5\,e^5\,32{}\mathrm{i}}{d}+\frac{a^5\,b\,e^5\,32{}\mathrm{i}}{d}-\frac{a^3\,b^3\,e^5\,192{}\mathrm{i}}{d}}-\frac{a^2\,b^2\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b\,e}{d^2}-\frac{a\,b^3\,e}{d^2}-\frac{a^4\,e\,1{}\mathrm{i}}{4\,d^2}-\frac{b^4\,e\,1{}\mathrm{i}}{4\,d^2}+\frac{a^2\,b^2\,e\,3{}\mathrm{i}}{2\,d^2}}\,192{}\mathrm{i}}{\frac{16\,a^6\,e^5}{d}-\frac{16\,b^6\,e^5}{d}+\frac{112\,a^2\,b^4\,e^5}{d}-\frac{112\,a^4\,b^2\,e^5}{d}+\frac{a\,b^5\,e^5\,32{}\mathrm{i}}{d}+\frac{a^5\,b\,e^5\,32{}\mathrm{i}}{d}-\frac{a^3\,b^3\,e^5\,192{}\mathrm{i}}{d}}\right)\,\sqrt{-\frac{1{}\mathrm{i}\,e\,a^4-4\,e\,a^3\,b-6{}\mathrm{i}\,e\,a^2\,b^2+4\,e\,a\,b^3+1{}\mathrm{i}\,e\,b^4}{4\,d^2}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{a^4\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b\,e}{d^2}-\frac{a\,b^3\,e}{d^2}+\frac{a^4\,e\,1{}\mathrm{i}}{4\,d^2}+\frac{b^4\,e\,1{}\mathrm{i}}{4\,d^2}-\frac{a^2\,b^2\,e\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{16\,b^6\,e^5}{d}-\frac{16\,a^6\,e^5}{d}-\frac{112\,a^2\,b^4\,e^5}{d}+\frac{112\,a^4\,b^2\,e^5}{d}+\frac{a\,b^5\,e^5\,32{}\mathrm{i}}{d}+\frac{a^5\,b\,e^5\,32{}\mathrm{i}}{d}-\frac{a^3\,b^3\,e^5\,192{}\mathrm{i}}{d}}+\frac{b^4\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b\,e}{d^2}-\frac{a\,b^3\,e}{d^2}+\frac{a^4\,e\,1{}\mathrm{i}}{4\,d^2}+\frac{b^4\,e\,1{}\mathrm{i}}{4\,d^2}-\frac{a^2\,b^2\,e\,3{}\mathrm{i}}{2\,d^2}}\,32{}\mathrm{i}}{\frac{16\,b^6\,e^5}{d}-\frac{16\,a^6\,e^5}{d}-\frac{112\,a^2\,b^4\,e^5}{d}+\frac{112\,a^4\,b^2\,e^5}{d}+\frac{a\,b^5\,e^5\,32{}\mathrm{i}}{d}+\frac{a^5\,b\,e^5\,32{}\mathrm{i}}{d}-\frac{a^3\,b^3\,e^5\,192{}\mathrm{i}}{d}}-\frac{a^2\,b^2\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b\,e}{d^2}-\frac{a\,b^3\,e}{d^2}+\frac{a^4\,e\,1{}\mathrm{i}}{4\,d^2}+\frac{b^4\,e\,1{}\mathrm{i}}{4\,d^2}-\frac{a^2\,b^2\,e\,3{}\mathrm{i}}{2\,d^2}}\,192{}\mathrm{i}}{\frac{16\,b^6\,e^5}{d}-\frac{16\,a^6\,e^5}{d}-\frac{112\,a^2\,b^4\,e^5}{d}+\frac{112\,a^4\,b^2\,e^5}{d}+\frac{a\,b^5\,e^5\,32{}\mathrm{i}}{d}+\frac{a^5\,b\,e^5\,32{}\mathrm{i}}{d}-\frac{a^3\,b^3\,e^5\,192{}\mathrm{i}}{d}}\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^4+4\,e\,a^3\,b-6{}\mathrm{i}\,e\,a^2\,b^2-4\,e\,a\,b^3+1{}\mathrm{i}\,e\,b^4}{4\,d^2}}\,2{}\mathrm{i}","Not used",1,"atan((a^4*e^4*(e*cot(c + d*x))^(1/2)*((a^4*e*1i)/(4*d^2) + (b^4*e*1i)/(4*d^2) - (a^2*b^2*e*3i)/(2*d^2) - (a*b^3*e)/d^2 + (a^3*b*e)/d^2)^(1/2)*32i)/((16*b^6*e^5)/d - (16*a^6*e^5)/d + (a*b^5*e^5*32i)/d + (a^5*b*e^5*32i)/d - (112*a^2*b^4*e^5)/d - (a^3*b^3*e^5*192i)/d + (112*a^4*b^2*e^5)/d) + (b^4*e^4*(e*cot(c + d*x))^(1/2)*((a^4*e*1i)/(4*d^2) + (b^4*e*1i)/(4*d^2) - (a^2*b^2*e*3i)/(2*d^2) - (a*b^3*e)/d^2 + (a^3*b*e)/d^2)^(1/2)*32i)/((16*b^6*e^5)/d - (16*a^6*e^5)/d + (a*b^5*e^5*32i)/d + (a^5*b*e^5*32i)/d - (112*a^2*b^4*e^5)/d - (a^3*b^3*e^5*192i)/d + (112*a^4*b^2*e^5)/d) - (a^2*b^2*e^4*(e*cot(c + d*x))^(1/2)*((a^4*e*1i)/(4*d^2) + (b^4*e*1i)/(4*d^2) - (a^2*b^2*e*3i)/(2*d^2) - (a*b^3*e)/d^2 + (a^3*b*e)/d^2)^(1/2)*192i)/((16*b^6*e^5)/d - (16*a^6*e^5)/d + (a*b^5*e^5*32i)/d + (a^5*b*e^5*32i)/d - (112*a^2*b^4*e^5)/d - (a^3*b^3*e^5*192i)/d + (112*a^4*b^2*e^5)/d))*((a^4*e*1i + b^4*e*1i - a^2*b^2*e*6i - 4*a*b^3*e + 4*a^3*b*e)/(4*d^2))^(1/2)*2i - atan((a^4*e^4*(e*cot(c + d*x))^(1/2)*((a^2*b^2*e*3i)/(2*d^2) - (b^4*e*1i)/(4*d^2) - (a^4*e*1i)/(4*d^2) - (a*b^3*e)/d^2 + (a^3*b*e)/d^2)^(1/2)*32i)/((16*a^6*e^5)/d - (16*b^6*e^5)/d + (a*b^5*e^5*32i)/d + (a^5*b*e^5*32i)/d + (112*a^2*b^4*e^5)/d - (a^3*b^3*e^5*192i)/d - (112*a^4*b^2*e^5)/d) + (b^4*e^4*(e*cot(c + d*x))^(1/2)*((a^2*b^2*e*3i)/(2*d^2) - (b^4*e*1i)/(4*d^2) - (a^4*e*1i)/(4*d^2) - (a*b^3*e)/d^2 + (a^3*b*e)/d^2)^(1/2)*32i)/((16*a^6*e^5)/d - (16*b^6*e^5)/d + (a*b^5*e^5*32i)/d + (a^5*b*e^5*32i)/d + (112*a^2*b^4*e^5)/d - (a^3*b^3*e^5*192i)/d - (112*a^4*b^2*e^5)/d) - (a^2*b^2*e^4*(e*cot(c + d*x))^(1/2)*((a^2*b^2*e*3i)/(2*d^2) - (b^4*e*1i)/(4*d^2) - (a^4*e*1i)/(4*d^2) - (a*b^3*e)/d^2 + (a^3*b*e)/d^2)^(1/2)*192i)/((16*a^6*e^5)/d - (16*b^6*e^5)/d + (a*b^5*e^5*32i)/d + (a^5*b*e^5*32i)/d + (112*a^2*b^4*e^5)/d - (a^3*b^3*e^5*192i)/d - (112*a^4*b^2*e^5)/d))*(-(a^4*e*1i + b^4*e*1i - a^2*b^2*e*6i + 4*a*b^3*e - 4*a^3*b*e)/(4*d^2))^(1/2)*2i - (2*b^2*(e*cot(c + d*x))^(3/2))/(3*d*e) - (4*a*b*(e*cot(c + d*x))^(1/2))/d","B"
58,1,1234,267,1.012674,"\text{Not used}","int((a + b*cot(c + d*x))^2/(e*cot(c + d*x))^(1/2),x)","2\,\mathrm{atanh}\left(\frac{32\,a^4\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3}{d^2\,e}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^3\,b}{d^2\,e}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}}{\frac{a^6\,e^2\,16{}\mathrm{i}}{d}-\frac{b^6\,e^2\,16{}\mathrm{i}}{d}+\frac{32\,a\,b^5\,e^2}{d}+\frac{32\,a^5\,b\,e^2}{d}+\frac{a^2\,b^4\,e^2\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^2}{d}-\frac{a^4\,b^2\,e^2\,112{}\mathrm{i}}{d}}+\frac{32\,b^4\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3}{d^2\,e}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^3\,b}{d^2\,e}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}}{\frac{a^6\,e^2\,16{}\mathrm{i}}{d}-\frac{b^6\,e^2\,16{}\mathrm{i}}{d}+\frac{32\,a\,b^5\,e^2}{d}+\frac{32\,a^5\,b\,e^2}{d}+\frac{a^2\,b^4\,e^2\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^2}{d}-\frac{a^4\,b^2\,e^2\,112{}\mathrm{i}}{d}}-\frac{192\,a^2\,b^2\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3}{d^2\,e}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^3\,b}{d^2\,e}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}}{\frac{a^6\,e^2\,16{}\mathrm{i}}{d}-\frac{b^6\,e^2\,16{}\mathrm{i}}{d}+\frac{32\,a\,b^5\,e^2}{d}+\frac{32\,a^5\,b\,e^2}{d}+\frac{a^2\,b^4\,e^2\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^2}{d}-\frac{a^4\,b^2\,e^2\,112{}\mathrm{i}}{d}}\right)\,\sqrt{\frac{a\,b^3}{d^2\,e}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}-\frac{a^3\,b}{d^2\,e}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}+2\,\mathrm{atanh}\left(\frac{32\,a^4\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{a\,b^3}{d^2\,e}-\frac{a^3\,b}{d^2\,e}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}}{\frac{32\,a\,b^5\,e^2}{d}+\frac{b^6\,e^2\,16{}\mathrm{i}}{d}-\frac{a^6\,e^2\,16{}\mathrm{i}}{d}+\frac{32\,a^5\,b\,e^2}{d}-\frac{a^2\,b^4\,e^2\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^2}{d}+\frac{a^4\,b^2\,e^2\,112{}\mathrm{i}}{d}}+\frac{32\,b^4\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{a\,b^3}{d^2\,e}-\frac{a^3\,b}{d^2\,e}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}}{\frac{32\,a\,b^5\,e^2}{d}+\frac{b^6\,e^2\,16{}\mathrm{i}}{d}-\frac{a^6\,e^2\,16{}\mathrm{i}}{d}+\frac{32\,a^5\,b\,e^2}{d}-\frac{a^2\,b^4\,e^2\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^2}{d}+\frac{a^4\,b^2\,e^2\,112{}\mathrm{i}}{d}}-\frac{192\,a^2\,b^2\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{a\,b^3}{d^2\,e}-\frac{a^3\,b}{d^2\,e}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}}{\frac{32\,a\,b^5\,e^2}{d}+\frac{b^6\,e^2\,16{}\mathrm{i}}{d}-\frac{a^6\,e^2\,16{}\mathrm{i}}{d}+\frac{32\,a^5\,b\,e^2}{d}-\frac{a^2\,b^4\,e^2\,112{}\mathrm{i}}{d}-\frac{192\,a^3\,b^3\,e^2}{d}+\frac{a^4\,b^2\,e^2\,112{}\mathrm{i}}{d}}\right)\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e}+\frac{a\,b^3}{d^2\,e}-\frac{a^3\,b}{d^2\,e}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e}}-\frac{2\,b^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d\,e}","Not used",1,"2*atanh((32*a^4*e^2*(e*cot(c + d*x))^(1/2)*((a*b^3)/(d^2*e) - (b^4*1i)/(4*d^2*e) - (a^4*1i)/(4*d^2*e) - (a^3*b)/(d^2*e) + (a^2*b^2*3i)/(2*d^2*e))^(1/2))/((a^6*e^2*16i)/d - (b^6*e^2*16i)/d + (32*a*b^5*e^2)/d + (32*a^5*b*e^2)/d + (a^2*b^4*e^2*112i)/d - (192*a^3*b^3*e^2)/d - (a^4*b^2*e^2*112i)/d) + (32*b^4*e^2*(e*cot(c + d*x))^(1/2)*((a*b^3)/(d^2*e) - (b^4*1i)/(4*d^2*e) - (a^4*1i)/(4*d^2*e) - (a^3*b)/(d^2*e) + (a^2*b^2*3i)/(2*d^2*e))^(1/2))/((a^6*e^2*16i)/d - (b^6*e^2*16i)/d + (32*a*b^5*e^2)/d + (32*a^5*b*e^2)/d + (a^2*b^4*e^2*112i)/d - (192*a^3*b^3*e^2)/d - (a^4*b^2*e^2*112i)/d) - (192*a^2*b^2*e^2*(e*cot(c + d*x))^(1/2)*((a*b^3)/(d^2*e) - (b^4*1i)/(4*d^2*e) - (a^4*1i)/(4*d^2*e) - (a^3*b)/(d^2*e) + (a^2*b^2*3i)/(2*d^2*e))^(1/2))/((a^6*e^2*16i)/d - (b^6*e^2*16i)/d + (32*a*b^5*e^2)/d + (32*a^5*b*e^2)/d + (a^2*b^4*e^2*112i)/d - (192*a^3*b^3*e^2)/d - (a^4*b^2*e^2*112i)/d))*((a*b^3)/(d^2*e) - (b^4*1i)/(4*d^2*e) - (a^4*1i)/(4*d^2*e) - (a^3*b)/(d^2*e) + (a^2*b^2*3i)/(2*d^2*e))^(1/2) + 2*atanh((32*a^4*e^2*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e) + (b^4*1i)/(4*d^2*e) + (a*b^3)/(d^2*e) - (a^3*b)/(d^2*e) - (a^2*b^2*3i)/(2*d^2*e))^(1/2))/((b^6*e^2*16i)/d - (a^6*e^2*16i)/d + (32*a*b^5*e^2)/d + (32*a^5*b*e^2)/d - (a^2*b^4*e^2*112i)/d - (192*a^3*b^3*e^2)/d + (a^4*b^2*e^2*112i)/d) + (32*b^4*e^2*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e) + (b^4*1i)/(4*d^2*e) + (a*b^3)/(d^2*e) - (a^3*b)/(d^2*e) - (a^2*b^2*3i)/(2*d^2*e))^(1/2))/((b^6*e^2*16i)/d - (a^6*e^2*16i)/d + (32*a*b^5*e^2)/d + (32*a^5*b*e^2)/d - (a^2*b^4*e^2*112i)/d - (192*a^3*b^3*e^2)/d + (a^4*b^2*e^2*112i)/d) - (192*a^2*b^2*e^2*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e) + (b^4*1i)/(4*d^2*e) + (a*b^3)/(d^2*e) - (a^3*b)/(d^2*e) - (a^2*b^2*3i)/(2*d^2*e))^(1/2))/((b^6*e^2*16i)/d - (a^6*e^2*16i)/d + (32*a*b^5*e^2)/d + (32*a^5*b*e^2)/d - (a^2*b^4*e^2*112i)/d - (192*a^3*b^3*e^2)/d + (a^4*b^2*e^2*112i)/d))*((a^4*1i)/(4*d^2*e) + (b^4*1i)/(4*d^2*e) + (a*b^3)/(d^2*e) - (a^3*b)/(d^2*e) - (a^2*b^2*3i)/(2*d^2*e))^(1/2) - (2*b^2*(e*cot(c + d*x))^(1/2))/(d*e)","B"
59,1,1196,267,0.935523,"\text{Not used}","int((a + b*cot(c + d*x))^2/(e*cot(c + d*x))^(3/2),x)","\frac{2\,a^2}{d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}+2\,\mathrm{atanh}\left(\frac{32\,a^4\,d^3\,e^5\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^3}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^3}-\frac{a\,b^3}{d^2\,e^3}+\frac{a^3\,b}{d^2\,e^3}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^3}}}{-16\,a^6\,d^2\,e^4+a^5\,b\,d^2\,e^4\,32{}\mathrm{i}+112\,a^4\,b^2\,d^2\,e^4-a^3\,b^3\,d^2\,e^4\,192{}\mathrm{i}-112\,a^2\,b^4\,d^2\,e^4+a\,b^5\,d^2\,e^4\,32{}\mathrm{i}+16\,b^6\,d^2\,e^4}+\frac{32\,b^4\,d^3\,e^5\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^3}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^3}-\frac{a\,b^3}{d^2\,e^3}+\frac{a^3\,b}{d^2\,e^3}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^3}}}{-16\,a^6\,d^2\,e^4+a^5\,b\,d^2\,e^4\,32{}\mathrm{i}+112\,a^4\,b^2\,d^2\,e^4-a^3\,b^3\,d^2\,e^4\,192{}\mathrm{i}-112\,a^2\,b^4\,d^2\,e^4+a\,b^5\,d^2\,e^4\,32{}\mathrm{i}+16\,b^6\,d^2\,e^4}-\frac{192\,a^2\,b^2\,d^3\,e^5\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^3}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^3}-\frac{a\,b^3}{d^2\,e^3}+\frac{a^3\,b}{d^2\,e^3}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^3}}}{-16\,a^6\,d^2\,e^4+a^5\,b\,d^2\,e^4\,32{}\mathrm{i}+112\,a^4\,b^2\,d^2\,e^4-a^3\,b^3\,d^2\,e^4\,192{}\mathrm{i}-112\,a^2\,b^4\,d^2\,e^4+a\,b^5\,d^2\,e^4\,32{}\mathrm{i}+16\,b^6\,d^2\,e^4}\right)\,\sqrt{\frac{\left(a^4-a^3\,b\,4{}\mathrm{i}-6\,a^2\,b^2+a\,b^3\,4{}\mathrm{i}+b^4\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}-2\,\mathrm{atanh}\left(\frac{32\,a^4\,d^3\,e^5\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b}{d^2\,e^3}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^3}-\frac{a\,b^3}{d^2\,e^3}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^3}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^3}}}{16\,a^6\,d^2\,e^4+a^5\,b\,d^2\,e^4\,32{}\mathrm{i}-112\,a^4\,b^2\,d^2\,e^4-a^3\,b^3\,d^2\,e^4\,192{}\mathrm{i}+112\,a^2\,b^4\,d^2\,e^4+a\,b^5\,d^2\,e^4\,32{}\mathrm{i}-16\,b^6\,d^2\,e^4}+\frac{32\,b^4\,d^3\,e^5\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b}{d^2\,e^3}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^3}-\frac{a\,b^3}{d^2\,e^3}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^3}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^3}}}{16\,a^6\,d^2\,e^4+a^5\,b\,d^2\,e^4\,32{}\mathrm{i}-112\,a^4\,b^2\,d^2\,e^4-a^3\,b^3\,d^2\,e^4\,192{}\mathrm{i}+112\,a^2\,b^4\,d^2\,e^4+a\,b^5\,d^2\,e^4\,32{}\mathrm{i}-16\,b^6\,d^2\,e^4}-\frac{192\,a^2\,b^2\,d^3\,e^5\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b}{d^2\,e^3}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^3}-\frac{a\,b^3}{d^2\,e^3}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^3}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^3}}}{16\,a^6\,d^2\,e^4+a^5\,b\,d^2\,e^4\,32{}\mathrm{i}-112\,a^4\,b^2\,d^2\,e^4-a^3\,b^3\,d^2\,e^4\,192{}\mathrm{i}+112\,a^2\,b^4\,d^2\,e^4+a\,b^5\,d^2\,e^4\,32{}\mathrm{i}-16\,b^6\,d^2\,e^4}\right)\,\sqrt{-\frac{\left(a^4+a^3\,b\,4{}\mathrm{i}-6\,a^2\,b^2-a\,b^3\,4{}\mathrm{i}+b^4\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}","Not used",1,"2*atanh((32*a^4*d^3*e^5*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^3) + (b^4*1i)/(4*d^2*e^3) - (a*b^3)/(d^2*e^3) + (a^3*b)/(d^2*e^3) - (a^2*b^2*3i)/(2*d^2*e^3))^(1/2))/(16*b^6*d^2*e^4 - 16*a^6*d^2*e^4 + a*b^5*d^2*e^4*32i + a^5*b*d^2*e^4*32i - 112*a^2*b^4*d^2*e^4 - a^3*b^3*d^2*e^4*192i + 112*a^4*b^2*d^2*e^4) + (32*b^4*d^3*e^5*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^3) + (b^4*1i)/(4*d^2*e^3) - (a*b^3)/(d^2*e^3) + (a^3*b)/(d^2*e^3) - (a^2*b^2*3i)/(2*d^2*e^3))^(1/2))/(16*b^6*d^2*e^4 - 16*a^6*d^2*e^4 + a*b^5*d^2*e^4*32i + a^5*b*d^2*e^4*32i - 112*a^2*b^4*d^2*e^4 - a^3*b^3*d^2*e^4*192i + 112*a^4*b^2*d^2*e^4) - (192*a^2*b^2*d^3*e^5*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^3) + (b^4*1i)/(4*d^2*e^3) - (a*b^3)/(d^2*e^3) + (a^3*b)/(d^2*e^3) - (a^2*b^2*3i)/(2*d^2*e^3))^(1/2))/(16*b^6*d^2*e^4 - 16*a^6*d^2*e^4 + a*b^5*d^2*e^4*32i + a^5*b*d^2*e^4*32i - 112*a^2*b^4*d^2*e^4 - a^3*b^3*d^2*e^4*192i + 112*a^4*b^2*d^2*e^4))*(((a*b^3*4i - a^3*b*4i + a^4 + b^4 - 6*a^2*b^2)*1i)/(4*d^2*e^3))^(1/2) - 2*atanh((32*a^4*d^3*e^5*(e*cot(c + d*x))^(1/2)*((a^3*b)/(d^2*e^3) - (b^4*1i)/(4*d^2*e^3) - (a*b^3)/(d^2*e^3) - (a^4*1i)/(4*d^2*e^3) + (a^2*b^2*3i)/(2*d^2*e^3))^(1/2))/(16*a^6*d^2*e^4 - 16*b^6*d^2*e^4 + a*b^5*d^2*e^4*32i + a^5*b*d^2*e^4*32i + 112*a^2*b^4*d^2*e^4 - a^3*b^3*d^2*e^4*192i - 112*a^4*b^2*d^2*e^4) + (32*b^4*d^3*e^5*(e*cot(c + d*x))^(1/2)*((a^3*b)/(d^2*e^3) - (b^4*1i)/(4*d^2*e^3) - (a*b^3)/(d^2*e^3) - (a^4*1i)/(4*d^2*e^3) + (a^2*b^2*3i)/(2*d^2*e^3))^(1/2))/(16*a^6*d^2*e^4 - 16*b^6*d^2*e^4 + a*b^5*d^2*e^4*32i + a^5*b*d^2*e^4*32i + 112*a^2*b^4*d^2*e^4 - a^3*b^3*d^2*e^4*192i - 112*a^4*b^2*d^2*e^4) - (192*a^2*b^2*d^3*e^5*(e*cot(c + d*x))^(1/2)*((a^3*b)/(d^2*e^3) - (b^4*1i)/(4*d^2*e^3) - (a*b^3)/(d^2*e^3) - (a^4*1i)/(4*d^2*e^3) + (a^2*b^2*3i)/(2*d^2*e^3))^(1/2))/(16*a^6*d^2*e^4 - 16*b^6*d^2*e^4 + a*b^5*d^2*e^4*32i + a^5*b*d^2*e^4*32i + 112*a^2*b^4*d^2*e^4 - a^3*b^3*d^2*e^4*192i - 112*a^4*b^2*d^2*e^4))*(-((a^3*b*4i - a*b^3*4i + a^4 + b^4 - 6*a^2*b^2)*1i)/(4*d^2*e^3))^(1/2) + (2*a^2)/(d*e*(e*cot(c + d*x))^(1/2))","B"
60,1,1214,291,1.511582,"\text{Not used}","int((a + b*cot(c + d*x))^2/(e*cot(c + d*x))^(5/2),x)","\frac{\frac{2\,a^2}{3}+4\,b\,\mathrm{cot}\left(c+d\,x\right)\,a}{d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-2\,\mathrm{atanh}\left(\frac{32\,a^4\,d^3\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^5}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^5}+\frac{a\,b^3}{d^2\,e^5}-\frac{a^3\,b}{d^2\,e^5}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^5}}}{-a^6\,d^2\,e^6\,16{}\mathrm{i}+32\,a^5\,b\,d^2\,e^6+a^4\,b^2\,d^2\,e^6\,112{}\mathrm{i}-192\,a^3\,b^3\,d^2\,e^6-a^2\,b^4\,d^2\,e^6\,112{}\mathrm{i}+32\,a\,b^5\,d^2\,e^6+b^6\,d^2\,e^6\,16{}\mathrm{i}}+\frac{32\,b^4\,d^3\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^5}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^5}+\frac{a\,b^3}{d^2\,e^5}-\frac{a^3\,b}{d^2\,e^5}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^5}}}{-a^6\,d^2\,e^6\,16{}\mathrm{i}+32\,a^5\,b\,d^2\,e^6+a^4\,b^2\,d^2\,e^6\,112{}\mathrm{i}-192\,a^3\,b^3\,d^2\,e^6-a^2\,b^4\,d^2\,e^6\,112{}\mathrm{i}+32\,a\,b^5\,d^2\,e^6+b^6\,d^2\,e^6\,16{}\mathrm{i}}-\frac{192\,a^2\,b^2\,d^3\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^5}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^5}+\frac{a\,b^3}{d^2\,e^5}-\frac{a^3\,b}{d^2\,e^5}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^5}}}{-a^6\,d^2\,e^6\,16{}\mathrm{i}+32\,a^5\,b\,d^2\,e^6+a^4\,b^2\,d^2\,e^6\,112{}\mathrm{i}-192\,a^3\,b^3\,d^2\,e^6-a^2\,b^4\,d^2\,e^6\,112{}\mathrm{i}+32\,a\,b^5\,d^2\,e^6+b^6\,d^2\,e^6\,16{}\mathrm{i}}\right)\,\sqrt{\frac{\left(a^4+a^3\,b\,4{}\mathrm{i}-6\,a^2\,b^2-a\,b^3\,4{}\mathrm{i}+b^4\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}-2\,\mathrm{atanh}\left(\frac{32\,a^4\,d^3\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3}{d^2\,e^5}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^5}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^5}-\frac{a^3\,b}{d^2\,e^5}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^5}}}{a^6\,d^2\,e^6\,16{}\mathrm{i}+32\,a^5\,b\,d^2\,e^6-a^4\,b^2\,d^2\,e^6\,112{}\mathrm{i}-192\,a^3\,b^3\,d^2\,e^6+a^2\,b^4\,d^2\,e^6\,112{}\mathrm{i}+32\,a\,b^5\,d^2\,e^6-b^6\,d^2\,e^6\,16{}\mathrm{i}}+\frac{32\,b^4\,d^3\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3}{d^2\,e^5}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^5}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^5}-\frac{a^3\,b}{d^2\,e^5}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^5}}}{a^6\,d^2\,e^6\,16{}\mathrm{i}+32\,a^5\,b\,d^2\,e^6-a^4\,b^2\,d^2\,e^6\,112{}\mathrm{i}-192\,a^3\,b^3\,d^2\,e^6+a^2\,b^4\,d^2\,e^6\,112{}\mathrm{i}+32\,a\,b^5\,d^2\,e^6-b^6\,d^2\,e^6\,16{}\mathrm{i}}-\frac{192\,a^2\,b^2\,d^3\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a\,b^3}{d^2\,e^5}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^5}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^5}-\frac{a^3\,b}{d^2\,e^5}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^5}}}{a^6\,d^2\,e^6\,16{}\mathrm{i}+32\,a^5\,b\,d^2\,e^6-a^4\,b^2\,d^2\,e^6\,112{}\mathrm{i}-192\,a^3\,b^3\,d^2\,e^6+a^2\,b^4\,d^2\,e^6\,112{}\mathrm{i}+32\,a\,b^5\,d^2\,e^6-b^6\,d^2\,e^6\,16{}\mathrm{i}}\right)\,\sqrt{-\frac{\left(a^4-a^3\,b\,4{}\mathrm{i}-6\,a^2\,b^2+a\,b^3\,4{}\mathrm{i}+b^4\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}","Not used",1,"((2*a^2)/3 + 4*a*b*cot(c + d*x))/(d*e*(e*cot(c + d*x))^(3/2)) - 2*atanh((32*a^4*d^3*e^8*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^5) + (b^4*1i)/(4*d^2*e^5) + (a*b^3)/(d^2*e^5) - (a^3*b)/(d^2*e^5) - (a^2*b^2*3i)/(2*d^2*e^5))^(1/2))/(b^6*d^2*e^6*16i - a^6*d^2*e^6*16i + 32*a*b^5*d^2*e^6 + 32*a^5*b*d^2*e^6 - a^2*b^4*d^2*e^6*112i - 192*a^3*b^3*d^2*e^6 + a^4*b^2*d^2*e^6*112i) + (32*b^4*d^3*e^8*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^5) + (b^4*1i)/(4*d^2*e^5) + (a*b^3)/(d^2*e^5) - (a^3*b)/(d^2*e^5) - (a^2*b^2*3i)/(2*d^2*e^5))^(1/2))/(b^6*d^2*e^6*16i - a^6*d^2*e^6*16i + 32*a*b^5*d^2*e^6 + 32*a^5*b*d^2*e^6 - a^2*b^4*d^2*e^6*112i - 192*a^3*b^3*d^2*e^6 + a^4*b^2*d^2*e^6*112i) - (192*a^2*b^2*d^3*e^8*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^5) + (b^4*1i)/(4*d^2*e^5) + (a*b^3)/(d^2*e^5) - (a^3*b)/(d^2*e^5) - (a^2*b^2*3i)/(2*d^2*e^5))^(1/2))/(b^6*d^2*e^6*16i - a^6*d^2*e^6*16i + 32*a*b^5*d^2*e^6 + 32*a^5*b*d^2*e^6 - a^2*b^4*d^2*e^6*112i - 192*a^3*b^3*d^2*e^6 + a^4*b^2*d^2*e^6*112i))*(((a^3*b*4i - a*b^3*4i + a^4 + b^4 - 6*a^2*b^2)*1i)/(4*d^2*e^5))^(1/2) - 2*atanh((32*a^4*d^3*e^8*(e*cot(c + d*x))^(1/2)*((a*b^3)/(d^2*e^5) - (b^4*1i)/(4*d^2*e^5) - (a^4*1i)/(4*d^2*e^5) - (a^3*b)/(d^2*e^5) + (a^2*b^2*3i)/(2*d^2*e^5))^(1/2))/(a^6*d^2*e^6*16i - b^6*d^2*e^6*16i + 32*a*b^5*d^2*e^6 + 32*a^5*b*d^2*e^6 + a^2*b^4*d^2*e^6*112i - 192*a^3*b^3*d^2*e^6 - a^4*b^2*d^2*e^6*112i) + (32*b^4*d^3*e^8*(e*cot(c + d*x))^(1/2)*((a*b^3)/(d^2*e^5) - (b^4*1i)/(4*d^2*e^5) - (a^4*1i)/(4*d^2*e^5) - (a^3*b)/(d^2*e^5) + (a^2*b^2*3i)/(2*d^2*e^5))^(1/2))/(a^6*d^2*e^6*16i - b^6*d^2*e^6*16i + 32*a*b^5*d^2*e^6 + 32*a^5*b*d^2*e^6 + a^2*b^4*d^2*e^6*112i - 192*a^3*b^3*d^2*e^6 - a^4*b^2*d^2*e^6*112i) - (192*a^2*b^2*d^3*e^8*(e*cot(c + d*x))^(1/2)*((a*b^3)/(d^2*e^5) - (b^4*1i)/(4*d^2*e^5) - (a^4*1i)/(4*d^2*e^5) - (a^3*b)/(d^2*e^5) + (a^2*b^2*3i)/(2*d^2*e^5))^(1/2))/(a^6*d^2*e^6*16i - b^6*d^2*e^6*16i + 32*a*b^5*d^2*e^6 + 32*a^5*b*d^2*e^6 + a^2*b^4*d^2*e^6*112i - 192*a^3*b^3*d^2*e^6 - a^4*b^2*d^2*e^6*112i))*(-((a*b^3*4i - a^3*b*4i + a^4 + b^4 - 6*a^2*b^2)*1i)/(4*d^2*e^5))^(1/2)","B"
61,1,1227,322,2.319549,"\text{Not used}","int((a + b*cot(c + d*x))^2/(e*cot(c + d*x))^(7/2),x)","2\,\mathrm{atanh}\left(\frac{32\,a^4\,d^3\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b}{d^2\,e^7}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^7}-\frac{a\,b^3}{d^2\,e^7}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^7}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^7}}}{16\,a^6\,d^2\,e^8+a^5\,b\,d^2\,e^8\,32{}\mathrm{i}-112\,a^4\,b^2\,d^2\,e^8-a^3\,b^3\,d^2\,e^8\,192{}\mathrm{i}+112\,a^2\,b^4\,d^2\,e^8+a\,b^5\,d^2\,e^8\,32{}\mathrm{i}-16\,b^6\,d^2\,e^8}+\frac{32\,b^4\,d^3\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b}{d^2\,e^7}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^7}-\frac{a\,b^3}{d^2\,e^7}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^7}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^7}}}{16\,a^6\,d^2\,e^8+a^5\,b\,d^2\,e^8\,32{}\mathrm{i}-112\,a^4\,b^2\,d^2\,e^8-a^3\,b^3\,d^2\,e^8\,192{}\mathrm{i}+112\,a^2\,b^4\,d^2\,e^8+a\,b^5\,d^2\,e^8\,32{}\mathrm{i}-16\,b^6\,d^2\,e^8}-\frac{192\,a^2\,b^2\,d^3\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^3\,b}{d^2\,e^7}-\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^7}-\frac{a\,b^3}{d^2\,e^7}-\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^7}+\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^7}}}{16\,a^6\,d^2\,e^8+a^5\,b\,d^2\,e^8\,32{}\mathrm{i}-112\,a^4\,b^2\,d^2\,e^8-a^3\,b^3\,d^2\,e^8\,192{}\mathrm{i}+112\,a^2\,b^4\,d^2\,e^8+a\,b^5\,d^2\,e^8\,32{}\mathrm{i}-16\,b^6\,d^2\,e^8}\right)\,\sqrt{-\frac{\left(a^4+a^3\,b\,4{}\mathrm{i}-6\,a^2\,b^2-a\,b^3\,4{}\mathrm{i}+b^4\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}-2\,\mathrm{atanh}\left(\frac{32\,a^4\,d^3\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^7}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^7}-\frac{a\,b^3}{d^2\,e^7}+\frac{a^3\,b}{d^2\,e^7}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^7}}}{-16\,a^6\,d^2\,e^8+a^5\,b\,d^2\,e^8\,32{}\mathrm{i}+112\,a^4\,b^2\,d^2\,e^8-a^3\,b^3\,d^2\,e^8\,192{}\mathrm{i}-112\,a^2\,b^4\,d^2\,e^8+a\,b^5\,d^2\,e^8\,32{}\mathrm{i}+16\,b^6\,d^2\,e^8}+\frac{32\,b^4\,d^3\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^7}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^7}-\frac{a\,b^3}{d^2\,e^7}+\frac{a^3\,b}{d^2\,e^7}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^7}}}{-16\,a^6\,d^2\,e^8+a^5\,b\,d^2\,e^8\,32{}\mathrm{i}+112\,a^4\,b^2\,d^2\,e^8-a^3\,b^3\,d^2\,e^8\,192{}\mathrm{i}-112\,a^2\,b^4\,d^2\,e^8+a\,b^5\,d^2\,e^8\,32{}\mathrm{i}+16\,b^6\,d^2\,e^8}-\frac{192\,a^2\,b^2\,d^3\,e^{11}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{a^4\,1{}\mathrm{i}}{4\,d^2\,e^7}+\frac{b^4\,1{}\mathrm{i}}{4\,d^2\,e^7}-\frac{a\,b^3}{d^2\,e^7}+\frac{a^3\,b}{d^2\,e^7}-\frac{a^2\,b^2\,3{}\mathrm{i}}{2\,d^2\,e^7}}}{-16\,a^6\,d^2\,e^8+a^5\,b\,d^2\,e^8\,32{}\mathrm{i}+112\,a^4\,b^2\,d^2\,e^8-a^3\,b^3\,d^2\,e^8\,192{}\mathrm{i}-112\,a^2\,b^4\,d^2\,e^8+a\,b^5\,d^2\,e^8\,32{}\mathrm{i}+16\,b^6\,d^2\,e^8}\right)\,\sqrt{\frac{\left(a^4-a^3\,b\,4{}\mathrm{i}-6\,a^2\,b^2+a\,b^3\,4{}\mathrm{i}+b^4\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}+\frac{\frac{2\,a^2}{5}-2\,{\mathrm{cot}\left(c+d\,x\right)}^2\,\left(a^2-b^2\right)+\frac{4\,a\,b\,\mathrm{cot}\left(c+d\,x\right)}{3}}{d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}","Not used",1,"2*atanh((32*a^4*d^3*e^11*(e*cot(c + d*x))^(1/2)*((a^3*b)/(d^2*e^7) - (b^4*1i)/(4*d^2*e^7) - (a*b^3)/(d^2*e^7) - (a^4*1i)/(4*d^2*e^7) + (a^2*b^2*3i)/(2*d^2*e^7))^(1/2))/(16*a^6*d^2*e^8 - 16*b^6*d^2*e^8 + a*b^5*d^2*e^8*32i + a^5*b*d^2*e^8*32i + 112*a^2*b^4*d^2*e^8 - a^3*b^3*d^2*e^8*192i - 112*a^4*b^2*d^2*e^8) + (32*b^4*d^3*e^11*(e*cot(c + d*x))^(1/2)*((a^3*b)/(d^2*e^7) - (b^4*1i)/(4*d^2*e^7) - (a*b^3)/(d^2*e^7) - (a^4*1i)/(4*d^2*e^7) + (a^2*b^2*3i)/(2*d^2*e^7))^(1/2))/(16*a^6*d^2*e^8 - 16*b^6*d^2*e^8 + a*b^5*d^2*e^8*32i + a^5*b*d^2*e^8*32i + 112*a^2*b^4*d^2*e^8 - a^3*b^3*d^2*e^8*192i - 112*a^4*b^2*d^2*e^8) - (192*a^2*b^2*d^3*e^11*(e*cot(c + d*x))^(1/2)*((a^3*b)/(d^2*e^7) - (b^4*1i)/(4*d^2*e^7) - (a*b^3)/(d^2*e^7) - (a^4*1i)/(4*d^2*e^7) + (a^2*b^2*3i)/(2*d^2*e^7))^(1/2))/(16*a^6*d^2*e^8 - 16*b^6*d^2*e^8 + a*b^5*d^2*e^8*32i + a^5*b*d^2*e^8*32i + 112*a^2*b^4*d^2*e^8 - a^3*b^3*d^2*e^8*192i - 112*a^4*b^2*d^2*e^8))*(-((a^3*b*4i - a*b^3*4i + a^4 + b^4 - 6*a^2*b^2)*1i)/(4*d^2*e^7))^(1/2) - 2*atanh((32*a^4*d^3*e^11*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^7) + (b^4*1i)/(4*d^2*e^7) - (a*b^3)/(d^2*e^7) + (a^3*b)/(d^2*e^7) - (a^2*b^2*3i)/(2*d^2*e^7))^(1/2))/(16*b^6*d^2*e^8 - 16*a^6*d^2*e^8 + a*b^5*d^2*e^8*32i + a^5*b*d^2*e^8*32i - 112*a^2*b^4*d^2*e^8 - a^3*b^3*d^2*e^8*192i + 112*a^4*b^2*d^2*e^8) + (32*b^4*d^3*e^11*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^7) + (b^4*1i)/(4*d^2*e^7) - (a*b^3)/(d^2*e^7) + (a^3*b)/(d^2*e^7) - (a^2*b^2*3i)/(2*d^2*e^7))^(1/2))/(16*b^6*d^2*e^8 - 16*a^6*d^2*e^8 + a*b^5*d^2*e^8*32i + a^5*b*d^2*e^8*32i - 112*a^2*b^4*d^2*e^8 - a^3*b^3*d^2*e^8*192i + 112*a^4*b^2*d^2*e^8) - (192*a^2*b^2*d^3*e^11*(e*cot(c + d*x))^(1/2)*((a^4*1i)/(4*d^2*e^7) + (b^4*1i)/(4*d^2*e^7) - (a*b^3)/(d^2*e^7) + (a^3*b)/(d^2*e^7) - (a^2*b^2*3i)/(2*d^2*e^7))^(1/2))/(16*b^6*d^2*e^8 - 16*a^6*d^2*e^8 + a*b^5*d^2*e^8*32i + a^5*b*d^2*e^8*32i - 112*a^2*b^4*d^2*e^8 - a^3*b^3*d^2*e^8*192i + 112*a^4*b^2*d^2*e^8))*(((a*b^3*4i - a^3*b*4i + a^4 + b^4 - 6*a^2*b^2)*1i)/(4*d^2*e^7))^(1/2) + ((2*a^2)/5 - 2*cot(c + d*x)^2*(a^2 - b^2) + (4*a*b*cot(c + d*x))/3)/(d*e*(e*cot(c + d*x))^(5/2))","B"
62,1,2317,372,5.473920,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + b*cot(c + d*x))^3,x)","{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(\frac{2\,b^3}{3\,d}-\frac{2\,a^2\,b}{d}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(\frac{2\,a^3\,e}{d}-\frac{6\,a\,b^2\,e}{d}\right)-\frac{2\,b^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}}{7\,d\,e^2}-\frac{6\,a\,b^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d\,e}-\mathrm{atan}\left(\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,1{}\mathrm{i}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,1{}\mathrm{i}}{\frac{16\,\left(3\,a^8\,b\,e^8+8\,a^6\,b^3\,e^8+6\,a^4\,b^5\,e^8-b^9\,e^8\right)}{d^3}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}-\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}\right)\,\sqrt{-\frac{-a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3+a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3-a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3+b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,1{}\mathrm{i}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,1{}\mathrm{i}}{\frac{16\,\left(3\,a^8\,b\,e^8+8\,a^6\,b^3\,e^8+6\,a^4\,b^5\,e^8-b^9\,e^8\right)}{d^3}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}-\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^6-15\,a^4\,b^2\,e^6+15\,a^2\,b^4\,e^6-b^6\,e^6\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^5-12\,a\,b^2\,d^2\,e^5\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}{d^3}\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}}\right)\,\sqrt{-\frac{a^6\,e^3\,1{}\mathrm{i}+6\,a^5\,b\,e^3-a^4\,b^2\,e^3\,15{}\mathrm{i}-20\,a^3\,b^3\,e^3+a^2\,b^4\,e^3\,15{}\mathrm{i}+6\,a\,b^5\,e^3-b^6\,e^3\,1{}\mathrm{i}}{4\,d^2}}\,2{}\mathrm{i}","Not used",1,"(e*cot(c + d*x))^(3/2)*((2*b^3)/(3*d) - (2*a^2*b)/d) - (e*cot(c + d*x))^(1/2)*((2*a^3*e)/d - (6*a*b^2*e)/d) - atan((((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 - (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2)*1i + ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 + (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2)*1i)/(((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 + (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2) - ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 - (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2) + (16*(3*a^8*b*e^8 - b^9*e^8 + 6*a^4*b^5*e^8 + 8*a^6*b^3*e^8))/d^3))*(-(b^6*e^3*1i - a^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 - a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 + a^4*b^2*e^3*15i)/(4*d^2))^(1/2)*2i - atan((((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 - (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2)*1i + ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 + (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2)*1i)/(((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 + (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2) - ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^6 - b^6*e^6 + 15*a^2*b^4*e^6 - 15*a^4*b^2*e^6))/d^2 - (8*(4*a^3*d^2*e^5 - 12*a*b^2*d^2*e^5)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2))/d^3)*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2) + (16*(3*a^8*b*e^8 - b^9*e^8 + 6*a^4*b^5*e^8 + 8*a^6*b^3*e^8))/d^3))*(-(a^6*e^3*1i - b^6*e^3*1i + 6*a*b^5*e^3 + 6*a^5*b*e^3 + a^2*b^4*e^3*15i - 20*a^3*b^3*e^3 - a^4*b^2*e^3*15i)/(4*d^2))^(1/2)*2i - (2*b^3*(e*cot(c + d*x))^(7/2))/(7*d*e^2) - (6*a*b^2*(e*cot(c + d*x))^(5/2))/(5*d*e)","B"
63,1,2071,342,2.546416,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + b*cot(c + d*x))^3,x)","\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(\frac{2\,b^3}{d}-\frac{6\,a^2\,b}{d}\right)-\frac{2\,b^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d\,e^2}-\frac{2\,a\,b^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{d\,e}+\mathrm{atan}\left(\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}-\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}\,1{}\mathrm{i}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}+\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}\,1{}\mathrm{i}}{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}-\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}-\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}+\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}+\frac{16\,\left(-a^9\,e^5+6\,a^5\,b^4\,e^5+8\,a^3\,b^6\,e^5+3\,a\,b^8\,e^5\right)}{d^3}}\right)\,\sqrt{\frac{-1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b+15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3-15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5+1{}\mathrm{i}\,e\,b^6}{4\,d^2}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}-\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}\,1{}\mathrm{i}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}+\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}\,1{}\mathrm{i}}{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}-\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}-\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^4-15\,a^4\,b^2\,e^4+15\,a^2\,b^4\,e^4-b^6\,e^4\right)}{d^2}+\frac{8\,\left(4\,b^3\,d^2\,e^4-12\,a^2\,b\,d^2\,e^4\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}}{d^3}\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}+\frac{16\,\left(-a^9\,e^5+6\,a^5\,b^4\,e^5+8\,a^3\,b^6\,e^5+3\,a\,b^8\,e^5\right)}{d^3}}\right)\,\sqrt{\frac{1{}\mathrm{i}\,e\,a^6+6\,e\,a^5\,b-15{}\mathrm{i}\,e\,a^4\,b^2-20\,e\,a^3\,b^3+15{}\mathrm{i}\,e\,a^2\,b^4+6\,e\,a\,b^5-1{}\mathrm{i}\,e\,b^6}{4\,d^2}}\,2{}\mathrm{i}","Not used",1,"(e*cot(c + d*x))^(1/2)*((2*b^3)/d - (6*a^2*b)/d) + atan((((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 - (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2)*1i + ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 + (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2)*1i)/(((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 - (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2) - ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 + (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2) + (16*(3*a*b^8*e^5 - a^9*e^5 + 8*a^3*b^6*e^5 + 6*a^5*b^4*e^5))/d^3))*((b^6*e*1i - a^6*e*1i - a^2*b^4*e*15i - 20*a^3*b^3*e + a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2)*2i + atan((((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 - (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2)*1i + ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 + (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2)*1i)/(((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 - (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2) - ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^4 - b^6*e^4 + 15*a^2*b^4*e^4 - 15*a^4*b^2*e^4))/d^2 + (8*(4*b^3*d^2*e^4 - 12*a^2*b*d^2*e^4)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2))/d^3)*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2) + (16*(3*a*b^8*e^5 - a^9*e^5 + 8*a^3*b^6*e^5 + 6*a^5*b^4*e^5))/d^3))*((a^6*e*1i - b^6*e*1i + a^2*b^4*e*15i - 20*a^3*b^3*e - a^4*b^2*e*15i + 6*a*b^5*e + 6*a^5*b*e)/(4*d^2))^(1/2)*2i - (2*b^3*(e*cot(c + d*x))^(5/2))/(5*d*e^2) - (2*a*b^2*(e*cot(c + d*x))^(3/2))/(d*e)","B"
64,1,1896,313,1.412803,"\text{Not used}","int((a + b*cot(c + d*x))^3/(e*cot(c + d*x))^(1/2),x)","-\frac{2\,b^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d\,e^2}-\frac{6\,a\,b^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d\,e}+\mathrm{atan}\left(\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}\,1{}\mathrm{i}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}\,1{}\mathrm{i}}{\frac{16\,\left(3\,a^8\,b\,e^2+8\,a^6\,b^3\,e^2+6\,a^4\,b^5\,e^2-b^9\,e^2\right)}{d^3}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}-\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}\,1{}\mathrm{i}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}\,1{}\mathrm{i}}{\frac{16\,\left(3\,a^8\,b\,e^2+8\,a^6\,b^3\,e^2+6\,a^4\,b^5\,e^2-b^9\,e^2\right)}{d^3}+\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}+\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}-\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6\,e^2-15\,a^4\,b^2\,e^2+15\,a^2\,b^4\,e^2-b^6\,e^2\right)}{d^2}-\frac{8\,\left(4\,a^3\,d^2\,e^3-12\,a\,b^2\,d^2\,e^3\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}{d^3}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e}}\,2{}\mathrm{i}","Not used",1,"atan((((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 - (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2)*1i + ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 + (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2)*1i)/(((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 + (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2) - ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 - (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2) + (16*(3*a^8*b*e^2 - b^9*e^2 + 6*a^4*b^5*e^2 + 8*a^6*b^3*e^2))/d^3))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2)*2i + atan((((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 - (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2)*1i + ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 + (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2)*1i)/(((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 + (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2) - ((16*(e*cot(c + d*x))^(1/2)*(a^6*e^2 - b^6*e^2 + 15*a^2*b^4*e^2 - 15*a^4*b^2*e^2))/d^2 - (8*(4*a^3*d^2*e^3 - 12*a*b^2*d^2*e^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2))/d^3)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2) + (16*(3*a^8*b*e^2 - b^9*e^2 + 6*a^4*b^5*e^2 + 8*a^6*b^3*e^2))/d^3))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e))^(1/2)*2i - (2*b^3*(e*cot(c + d*x))^(3/2))/(3*d*e^2) - (6*a*b^2*(e*cot(c + d*x))^(1/2))/(d*e)","B"
65,1,1951,313,1.203931,"\text{Not used}","int((a + b*cot(c + d*x))^3/(e*cot(c + d*x))^(3/2),x)","\frac{2\,a^3}{d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}-\frac{2\,b^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d\,e^2}-\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)+\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)-\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\,1{}\mathrm{i}}{48\,a\,b^8\,d^2\,e^4+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)-\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}-16\,a^9\,d^2\,e^4-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)+\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}+128\,a^3\,b^6\,d^2\,e^4+96\,a^5\,b^4\,d^2\,e^4}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)+\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)-\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\,1{}\mathrm{i}}{48\,a\,b^8\,d^2\,e^4+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)-\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}-16\,a^9\,d^2\,e^4-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^5-240\,a^4\,b^2\,d^3\,e^5+240\,a^2\,b^4\,d^3\,e^5-16\,b^6\,d^3\,e^5\right)+\left(32\,b^3\,d^4\,e^7-96\,a^2\,b\,d^4\,e^7\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}+128\,a^3\,b^6\,d^2\,e^4+96\,a^5\,b^4\,d^2\,e^4}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^3}}\,2{}\mathrm{i}","Not used",1,"(2*a^3)/(d*e*(e*cot(c + d*x))^(1/2)) - atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) + (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) - (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) - (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) + (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2) - 16*a^9*d^2*e^4 + 48*a*b^8*d^2*e^4 + 128*a^3*b^6*d^2*e^4 + 96*a^5*b^4*d^2*e^4))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2)*2i - atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) + (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) - (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) - (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^5 - 16*b^6*d^3*e^5 + 240*a^2*b^4*d^3*e^5 - 240*a^4*b^2*d^3*e^5) + (32*b^3*d^4*e^7 - 96*a^2*b*d^4*e^7)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2) - 16*a^9*d^2*e^4 + 48*a*b^8*d^2*e^4 + 128*a^3*b^6*d^2*e^4 + 96*a^5*b^4*d^2*e^4))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^3))^(1/2)*2i - (2*b^3*(e*cot(c + d*x))^(1/2))/(d*e^2)","B"
66,1,1946,313,1.670601,"\text{Not used}","int((a + b*cot(c + d*x))^3/(e*cot(c + d*x))^(5/2),x)","\frac{\frac{2\,e\,a^3}{3}+6\,b\,e\,\mathrm{cot}\left(c+d\,x\right)\,a^2}{d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)+\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)-\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\,1{}\mathrm{i}}{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)+\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)-\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}-16\,b^9\,d^2\,e^6+48\,a^8\,b\,d^2\,e^6+96\,a^4\,b^5\,d^2\,e^6+128\,a^6\,b^3\,d^2\,e^6}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)+\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)-\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\,1{}\mathrm{i}}{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)+\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^8-240\,a^4\,b^2\,d^3\,e^8+240\,a^2\,b^4\,d^3\,e^8-16\,b^6\,d^3\,e^8\right)-\left(32\,a^3\,d^4\,e^{11}-96\,a\,b^2\,d^4\,e^{11}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}-16\,b^9\,d^2\,e^6+48\,a^8\,b\,d^2\,e^6+96\,a^4\,b^5\,d^2\,e^6+128\,a^6\,b^3\,d^2\,e^6}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^5}}\,2{}\mathrm{i}","Not used",1,"((2*a^3*e)/3 + 6*a^2*b*e*cot(c + d*x))/(d*e^2*(e*cot(c + d*x))^(3/2)) - atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) + (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) - (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) + (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) - (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2) - 16*b^9*d^2*e^6 + 48*a^8*b*d^2*e^6 + 96*a^4*b^5*d^2*e^6 + 128*a^6*b^3*d^2*e^6))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2)*2i - atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) + (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) - (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) + (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^8 - 16*b^6*d^3*e^8 + 240*a^2*b^4*d^3*e^8 - 240*a^4*b^2*d^3*e^8) - (32*a^3*d^4*e^11 - 96*a*b^2*d^4*e^11)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2) - 16*b^9*d^2*e^6 + 48*a^8*b*d^2*e^6 + 96*a^4*b^5*d^2*e^6 + 128*a^6*b^3*d^2*e^6))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^5))^(1/2)*2i","B"
67,1,1969,343,3.062910,"\text{Not used}","int((a + b*cot(c + d*x))^3/(e*cot(c + d*x))^(7/2),x)","\frac{\frac{2\,a^3\,e}{5}+2\,e\,{\mathrm{cot}\left(c+d\,x\right)}^2\,\left(3\,a\,b^2-a^3\right)+2\,a^2\,b\,e\,\mathrm{cot}\left(c+d\,x\right)}{d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)+\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)-\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\,1{}\mathrm{i}}{48\,a\,b^8\,d^2\,e^8+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)-\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}-16\,a^9\,d^2\,e^8-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)+\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}+128\,a^3\,b^6\,d^2\,e^8+96\,a^5\,b^4\,d^2\,e^8}\right)\,\sqrt{-\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)+\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)-\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\,1{}\mathrm{i}}{48\,a\,b^8\,d^2\,e^8+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)-\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}-16\,a^9\,d^2\,e^8-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{11}-240\,a^4\,b^2\,d^3\,e^{11}+240\,a^2\,b^4\,d^3\,e^{11}-16\,b^6\,d^3\,e^{11}\right)+\left(32\,b^3\,d^4\,e^{15}-96\,a^2\,b\,d^4\,e^{15}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}+128\,a^3\,b^6\,d^2\,e^8+96\,a^5\,b^4\,d^2\,e^8}\right)\,\sqrt{-\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^7}}\,2{}\mathrm{i}","Not used",1,"atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) + (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) - (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) - (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) + (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2) - 16*a^9*d^2*e^8 + 48*a*b^8*d^2*e^8 + 128*a^3*b^6*d^2*e^8 + 96*a^5*b^4*d^2*e^8))*(-((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2)*2i + atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) + (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) - (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) - (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^11 - 16*b^6*d^3*e^11 + 240*a^2*b^4*d^3*e^11 - 240*a^4*b^2*d^3*e^11) + (32*b^3*d^4*e^15 - 96*a^2*b*d^4*e^15)*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2) - 16*a^9*d^2*e^8 + 48*a*b^8*d^2*e^8 + 128*a^3*b^6*d^2*e^8 + 96*a^5*b^4*d^2*e^8))*(-((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^7))^(1/2)*2i + ((2*a^3*e)/5 + 2*e*cot(c + d*x)^2*(3*a*b^2 - a^3) + 2*a^2*b*e*cot(c + d*x))/(d*e^2*(e*cot(c + d*x))^(5/2))","B"
68,1,1992,377,5.256868,"\text{Not used}","int((a + b*cot(c + d*x))^3/(e*cot(c + d*x))^(9/2),x)","\frac{\frac{2\,a^3\,e}{7}+\frac{2\,e\,{\mathrm{cot}\left(c+d\,x\right)}^2\,\left(3\,a\,b^2-a^3\right)}{3}-2\,e\,{\mathrm{cot}\left(c+d\,x\right)}^3\,\left(3\,a^2\,b-b^3\right)+\frac{6\,a^2\,b\,e\,\mathrm{cot}\left(c+d\,x\right)}{5}}{d\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)+\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)-\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\,1{}\mathrm{i}}{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)+\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)-\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}-16\,b^9\,d^2\,e^{10}+48\,a^8\,b\,d^2\,e^{10}+96\,a^4\,b^5\,d^2\,e^{10}+128\,a^6\,b^3\,d^2\,e^{10}}\right)\,\sqrt{\frac{\left(-a^6+a^5\,b\,6{}\mathrm{i}+15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}-15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}+b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)+\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)-\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\,1{}\mathrm{i}}{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)+\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^6\,d^3\,e^{14}-240\,a^4\,b^2\,d^3\,e^{14}+240\,a^2\,b^4\,d^3\,e^{14}-16\,b^6\,d^3\,e^{14}\right)-\left(32\,a^3\,d^4\,e^{19}-96\,a\,b^2\,d^4\,e^{19}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}-16\,b^9\,d^2\,e^{10}+48\,a^8\,b\,d^2\,e^{10}+96\,a^4\,b^5\,d^2\,e^{10}+128\,a^6\,b^3\,d^2\,e^{10}}\right)\,\sqrt{\frac{\left(a^6+a^5\,b\,6{}\mathrm{i}-15\,a^4\,b^2-a^3\,b^3\,20{}\mathrm{i}+15\,a^2\,b^4+a\,b^5\,6{}\mathrm{i}-b^6\right)\,1{}\mathrm{i}}{4\,d^2\,e^9}}\,2{}\mathrm{i}","Not used",1,"atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) + (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) - (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) + (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) - (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2) - 16*b^9*d^2*e^10 + 48*a^8*b*d^2*e^10 + 96*a^4*b^5*d^2*e^10 + 128*a^6*b^3*d^2*e^10))*(((a*b^5*6i + a^5*b*6i - a^6 + b^6 - 15*a^2*b^4 - a^3*b^3*20i + 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2)*2i + atan((((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) + (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) - (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) + (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2) - ((e*cot(c + d*x))^(1/2)*(16*a^6*d^3*e^14 - 16*b^6*d^3*e^14 + 240*a^2*b^4*d^3*e^14 - 240*a^4*b^2*d^3*e^14) - (32*a^3*d^4*e^19 - 96*a*b^2*d^4*e^19)*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2) - 16*b^9*d^2*e^10 + 48*a^8*b*d^2*e^10 + 96*a^4*b^5*d^2*e^10 + 128*a^6*b^3*d^2*e^10))*(((a*b^5*6i + a^5*b*6i + a^6 - b^6 + 15*a^2*b^4 - a^3*b^3*20i - 15*a^4*b^2)*1i)/(4*d^2*e^9))^(1/2)*2i + ((2*a^3*e)/7 + (2*e*cot(c + d*x)^2*(3*a*b^2 - a^3))/3 - 2*e*cot(c + d*x)^3*(3*a^2*b - b^3) + (6*a^2*b*e*cot(c + d*x))/5)/(d*e^2*(e*cot(c + d*x))^(7/2))","B"
69,1,5579,325,1.973474,"\text{Not used}","int((e*cot(c + d*x))^(5/2)/(a + b*cot(c + d*x)),x)","-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{64\,\left(a^5\,e^{23}-a^3\,b^2\,e^{23}\right)}{b\,d^5}}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{64\,\left(a^5\,e^{23}-a^3\,b^2\,e^{23}\right)}{b\,d^5}}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\frac{2\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{b\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}+\frac{\left(\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}-\frac{\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e^5}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b^4\,d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}\,1{}\mathrm{i}}{b^3\,d\,\left(a^2+b^2\right)}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}-\frac{\left(\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}-\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}+\frac{\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e^5}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b^4\,d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}\,1{}\mathrm{i}}{b^3\,d\,\left(a^2+b^2\right)}}{\frac{64\,\left(a^5\,e^{23}-a^3\,b^2\,e^{23}\right)}{b\,d^5}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}+\frac{\left(\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}-\frac{\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e^5}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b^4\,d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}-\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^6\,e^{20}-b^6\,e^{20}\right)}{b\,d^4}-\frac{\left(\frac{32\,\left(12\,a^6\,b\,d^2\,e^{18}-15\,a^4\,b^3\,d^2\,e^{18}+a^2\,b^5\,d^2\,e^{18}\right)}{b\,d^5}-\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16\,a^7\,b\,d^2\,e^{15}+2\,a^5\,b^3\,d^2\,e^{15}+4\,a^3\,b^5\,d^2\,e^{15}-14\,a\,b^7\,d^2\,e^{15}\right)}{b\,d^4}+\frac{\left(\frac{32\,\left(4\,a^5\,b^4\,d^4\,e^{13}+8\,a^3\,b^6\,d^4\,e^{13}+4\,a\,b^8\,d^4\,e^{13}\right)}{b\,d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e^5}\,\left(-16\,a^6\,b^4\,d^4\,e^{10}-16\,a^4\,b^6\,d^4\,e^{10}+16\,a^2\,b^8\,d^4\,e^{10}+16\,b^{10}\,d^4\,e^{10}\right)}{b^4\,d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^3\,e^5}}{b^3\,d\,\left(a^2+b^2\right)}}\right)\,\sqrt{-a^5\,b^3\,e^5}\,2{}\mathrm{i}}{b^3\,d\,\left(a^2+b^2\right)}","Not used",1,"(atan(((((32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4) + (((32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5) + (((32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4) - (((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) + (32*(e*cot(c + d*x))^(1/2)*(-a^5*b^3*e^5)^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b^4*d^5*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2)*1i)/(b^3*d*(a^2 + b^2)) + (((32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4) - (((32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5) - (((32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4) + (((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) - (32*(e*cot(c + d*x))^(1/2)*(-a^5*b^3*e^5)^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b^4*d^5*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2)*1i)/(b^3*d*(a^2 + b^2)))/((64*(a^5*e^23 - a^3*b^2*e^23))/(b*d^5) + (((32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4) + (((32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5) + (((32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4) - (((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) + (32*(e*cot(c + d*x))^(1/2)*(-a^5*b^3*e^5)^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b^4*d^5*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)) - (((32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4) - (((32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5) - (((32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4) + (((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) - (32*(e*cot(c + d*x))^(1/2)*(-a^5*b^3*e^5)^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b^4*d^5*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2)))*(-a^5*b^3*e^5)^(1/2))/(b^3*d*(a^2 + b^2))))*(-a^5*b^3*e^5)^(1/2)*2i)/(b^3*d*(a^2 + b^2)) - atan(((((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) - (32*(e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*1i - (((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) + (32*(e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*1i)/((((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) - (32*(e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) + (32*(e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (64*(a^5*e^23 - a^3*b^2*e^23))/(b*d^5)))*(-e^5/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*2i - (2*e^2*(e*cot(c + d*x))^(1/2))/(b*d) - atan(((((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) - (32*(e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*1i - (((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) + (32*(e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*1i)/((((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) - (32*(e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (((((32*(4*a*b^8*d^4*e^13 + 8*a^3*b^6*d^4*e^13 + 4*a^5*b^4*d^4*e^13))/(b*d^5) + (32*(e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^10*d^4*e^10 + 16*a^2*b^8*d^4*e^10 - 16*a^4*b^6*d^4*e^10 - 16*a^6*b^4*d^4*e^10))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(16*a^7*b*d^2*e^15 - 14*a*b^7*d^2*e^15 + 4*a^3*b^5*d^2*e^15 + 2*a^5*b^3*d^2*e^15))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(12*a^6*b*d^2*e^18 + a^2*b^5*d^2*e^18 - 15*a^4*b^3*d^2*e^18))/(b*d^5))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(2*a^6*e^20 - b^6*e^20))/(b*d^4))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (64*(a^5*e^23 - a^3*b^2*e^23))/(b*d^5)))*(-(e^5*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*2i","B"
70,1,5129,302,1.627304,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + b*cot(c + d*x)),x)","\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{64\,a^2\,b^2\,e^{18}}{d^5}}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{64\,a^2\,b^2\,e^{18}}{d^5}}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\left(\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}+\frac{\left(\frac{\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b\,e^3}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,a^2\,b+d\,b^3\right)}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}\,1{}\mathrm{i}}{d\,a^2\,b+d\,b^3}-\frac{\left(\frac{\left(\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}+\frac{\left(\frac{\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b\,e^3}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,a^2\,b+d\,b^3\right)}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}\,1{}\mathrm{i}}{d\,a^2\,b+d\,b^3}}{\frac{\left(\frac{\left(\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}+\frac{\left(\frac{\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b\,e^3}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,a^2\,b+d\,b^3\right)}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}+\frac{\left(\frac{\left(\frac{32\,\left(4\,a^5\,b\,d^2\,e^{15}-15\,a^3\,b^3\,d^2\,e^{15}+a\,b^5\,d^2\,e^{15}\right)}{d^5}+\frac{\left(\frac{\left(\frac{32\,\left(4\,a^6\,b^2\,d^4\,e^{12}+8\,a^4\,b^4\,d^4\,e^{12}+4\,a^2\,b^6\,d^4\,e^{12}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b\,e^3}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,a^2\,b+d\,b^3\right)}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(14\,a^5\,b^2\,d^2\,e^{13}-4\,a^3\,b^4\,d^2\,e^{13}+14\,a\,b^6\,d^2\,e^{13}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^4\,b\,e^{16}+b^5\,e^{16}\right)}{d^4}\right)\,\sqrt{-a^3\,b\,e^3}}{d\,a^2\,b+d\,b^3}+\frac{64\,a^2\,b^2\,e^{18}}{d^5}}\right)\,\sqrt{-a^3\,b\,e^3}\,2{}\mathrm{i}}{d\,a^2\,b+d\,b^3}","Not used",1,"atan(((((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 - (32*(e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*1i - (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 + (32*(e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*1i)/((((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 - (32*(e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 + (32*(e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (64*a^2*b^2*e^18)/d^5))*((e^3*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*2i + atan(((((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*1i - (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*1i)/((((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (64*a^2*b^2*e^18)/d^5))*(e^3/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*2i - (atan(-((((((32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5 + (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-a^3*b*e^3)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(b^3*d + a^2*b*d)))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) + (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(-a^3*b*e^3)^(1/2)*1i)/(b^3*d + a^2*b*d) - (((((32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5 + (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-a^3*b*e^3)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(b^3*d + a^2*b*d)))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) - (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(-a^3*b*e^3)^(1/2)*1i)/(b^3*d + a^2*b*d))/((((((32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5 + (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-a^3*b*e^3)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(b^3*d + a^2*b*d)))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) + (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) + (((((32*(a*b^5*d^2*e^15 + 4*a^5*b*d^2*e^15 - 15*a^3*b^3*d^2*e^15))/d^5 + (((((32*(4*a^2*b^6*d^4*e^12 + 8*a^4*b^4*d^4*e^12 + 4*a^6*b^2*d^4*e^12))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-a^3*b*e^3)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(b^3*d + a^2*b*d)))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) - (32*(e*cot(c + d*x))^(1/2)*(14*a*b^6*d^2*e^13 - 4*a^3*b^4*d^2*e^13 + 14*a^5*b^2*d^2*e^13))/d^4)*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d))*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^16 + 2*a^4*b*e^16))/d^4)*(-a^3*b*e^3)^(1/2))/(b^3*d + a^2*b*d) + (64*a^2*b^2*e^18)/d^5))*(-a^3*b*e^3)^(1/2)*2i)/(b^3*d + a^2*b*d)","B"
71,1,4808,302,1.386309,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + b*cot(c + d*x)),x)","-\mathrm{atan}\left(\frac{\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}+\frac{64\,a\,b^3\,e^{13}}{d^5}}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^2\,d^2+a\,b\,d^2\,2{}\mathrm{i}+b^2\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\left(\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}+\frac{64\,a\,b^3\,e^{13}}{d^5}}\right)\,\sqrt{-\frac{e}{4\,\left(-a^2\,d^2\,1{}\mathrm{i}+2\,a\,b\,d^2+b^2\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}-\frac{\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}+\frac{\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}\,1{}\mathrm{i}}{d\,\left(a^2+b^2\right)}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}+\frac{\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}-\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}-\frac{\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}\,1{}\mathrm{i}}{d\,\left(a^2+b^2\right)}}{\frac{64\,a\,b^3\,e^{13}}{d^5}-\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}-\frac{\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}+\frac{\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}+\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(b^5\,e^{12}-2\,a^2\,b^3\,e^{12}\right)}{d^4}+\frac{\left(\frac{32\,\left(a^4\,b^2\,d^2\,e^{12}+13\,a^2\,b^4\,d^2\,e^{12}\right)}{d^5}-\frac{\left(\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^{11}+20\,a^3\,b^4\,d^2\,e^{11}-14\,a\,b^6\,d^2\,e^{11}\right)}{d^4}-\frac{\left(\frac{32\,\left(12\,a^5\,b^3\,d^4\,e^{11}+24\,a^3\,b^5\,d^4\,e^{11}+12\,a\,b^7\,d^4\,e^{11}\right)}{d^5}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}\right)\,\sqrt{-a\,b\,e}}{d\,\left(a^2+b^2\right)}}\right)\,\sqrt{-a\,b\,e}\,2{}\mathrm{i}}{d\,\left(a^2+b^2\right)}","Not used",1,"(atan(((((32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4 - (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-a*b*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^5*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2)*1i)/(d*(a^2 + b^2)) + (((32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4 + (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 - (((32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4 - (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-a*b*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^5*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2)*1i)/(d*(a^2 + b^2)))/((64*a*b^3*e^13)/d^5 - (((32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4 - (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-a*b*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^5*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)) + (((32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4 + (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 - (((32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4 - (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-a*b*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^5*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2)))*(-a*b*e)^(1/2))/(d*(a^2 + b^2))))*(-a*b*e)^(1/2)*2i)/(d*(a^2 + b^2)) - atan(((((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2))*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*1i - (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2))*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*1i)/((((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2))*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2))*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2) + (64*a*b^3*e^13)/d^5))*(-e/(4*(b^2*d^2*1i - a^2*d^2*1i + 2*a*b*d^2)))^(1/2)*2i - atan(((((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2))*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*1i - (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2))*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*1i)/((((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 - (32*(e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2))*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (((32*(13*a^2*b^4*d^2*e^12 + a^4*b^2*d^2*e^12))/d^5 + (((32*(12*a*b^7*d^4*e^11 + 24*a^3*b^5*d^4*e^11 + 12*a^5*b^3*d^4*e^11))/d^5 + (32*(e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(20*a^3*b^4*d^2*e^11 - 14*a*b^6*d^2*e^11 + 2*a^5*b^2*d^2*e^11))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2))*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(b^5*e^12 - 2*a^2*b^3*e^12))/d^4)*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2) + (64*a*b^3*e^13)/d^5))*(-(e*1i)/(4*(b^2*d^2 - a^2*d^2 + a*b*d^2*2i)))^(1/2)*2i","B"
72,1,4871,302,1.768418,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + b*cot(c + d*x))),x)","\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)}{2}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}+\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,1{}\mathrm{i}}{2}-\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)}{2}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}-\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,1{}\mathrm{i}}{2}}{\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)}{2}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}+\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}+\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)}{2}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}-\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}}{2}}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^2\,d^2+2\,e\,a\,b\,d^2+1{}\mathrm{i}\,e\,b^2\,d^2}}\,1{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\left(\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}+\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\left(\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}-\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\left(\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}+\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}+\left(\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\left(\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}-\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^2\,d^2+2{}\mathrm{i}\,e\,a\,b\,d^2+e\,b^2\,d^2\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b^3\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,e\,a^3+d\,e\,a\,b^2\right)}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}+\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{-a\,b^3\,e}\,1{}\mathrm{i}}{d\,e\,a^3+d\,e\,a\,b^2}-\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b^3\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,e\,a^3+d\,e\,a\,b^2\right)}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}-\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{-a\,b^3\,e}\,1{}\mathrm{i}}{d\,e\,a^3+d\,e\,a\,b^2}}{\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b^3\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,e\,a^3+d\,e\,a\,b^2\right)}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}-\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}+\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}+\frac{\left(\frac{\left(\frac{32\,\left(a^3\,b^3\,e^9+5\,a\,b^5\,e^9\right)}{d^3}-\frac{\left(\frac{\left(\frac{32\,\left(-4\,a^6\,b^2\,d^2\,e^{10}+8\,a^4\,b^4\,d^2\,e^{10}+28\,a^2\,b^6\,d^2\,e^{10}+16\,b^8\,d^2\,e^{10}\right)}{d^3}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a\,b^3\,e}\,\left(-16\,a^6\,b^3\,d^4\,e^{10}-16\,a^4\,b^5\,d^4\,e^{10}+16\,a^2\,b^7\,d^4\,e^{10}+16\,b^9\,d^4\,e^{10}\right)}{d^4\,\left(d\,e\,a^3+d\,e\,a\,b^2\right)}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}+\frac{32\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(2\,a^5\,b^2\,d^2\,e^9+4\,a^3\,b^4\,d^2\,e^9-30\,a\,b^6\,d^2\,e^9\right)}{d^4}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}-\frac{96\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{-a\,b^3\,e}}{d\,e\,a^3+d\,e\,a\,b^2}}\right)\,\sqrt{-a\,b^3\,e}\,2{}\mathrm{i}}{d\,e\,a^3+d\,e\,a\,b^2}","Not used",1,"atan(((((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - ((((1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 - (16*(e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4))/2 - (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2 + (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*1i)/2 - (((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - ((((1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 + (16*(e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4))/2 + (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2 - (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*1i)/2)/((((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - ((((1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 - (16*(e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4))/2 - (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2 + (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2 + (((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - ((((1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 + (16*(e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4))/2 + (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2 - (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2))/2))*(1/(b^2*d^2*e*1i - a^2*d^2*e*1i + 2*a*b*d^2*e))^(1/2)*1i + atan(((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 - (32*(e*cot(c + d*x))^(1/2)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2))*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) + (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*1i - (((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 + (32*(e*cot(c + d*x))^(1/2)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2))*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) - (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*1i)/((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 - (32*(e*cot(c + d*x))^(1/2)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) - (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2))*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) + (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) + (((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 + (32*(e*cot(c + d*x))^(1/2)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) + (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2))*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2) - (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)))*(1i/(4*(b^2*d^2*e - a^2*d^2*e + a*b*d^2*e*2i)))^(1/2)*2i + (atan(((((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 - (32*(e*cot(c + d*x))^(1/2)*(-a*b^3*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(a^3*d*e + a*b^2*d*e)))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) - (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) + (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(-a*b^3*e)^(1/2)*1i)/(a^3*d*e + a*b^2*d*e) - (((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 + (32*(e*cot(c + d*x))^(1/2)*(-a*b^3*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(a^3*d*e + a*b^2*d*e)))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) + (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) - (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(-a*b^3*e)^(1/2)*1i)/(a^3*d*e + a*b^2*d*e))/((((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 - (32*(e*cot(c + d*x))^(1/2)*(-a*b^3*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(a^3*d*e + a*b^2*d*e)))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) - (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) + (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) + (((((32*(5*a*b^5*e^9 + a^3*b^3*e^9))/d^3 - (((((32*(16*b^8*d^2*e^10 + 28*a^2*b^6*d^2*e^10 + 8*a^4*b^4*d^2*e^10 - 4*a^6*b^2*d^2*e^10))/d^3 + (32*(e*cot(c + d*x))^(1/2)*(-a*b^3*e)^(1/2)*(16*b^9*d^4*e^10 + 16*a^2*b^7*d^4*e^10 - 16*a^4*b^5*d^4*e^10 - 16*a^6*b^3*d^4*e^10))/(d^4*(a^3*d*e + a*b^2*d*e)))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) + (32*(e*cot(c + d*x))^(1/2)*(4*a^3*b^4*d^2*e^9 - 30*a*b^6*d^2*e^9 + 2*a^5*b^2*d^2*e^9))/d^4)*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e))*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e) - (96*b^5*e^8*(e*cot(c + d*x))^(1/2))/d^4)*(-a*b^3*e)^(1/2))/(a^3*d*e + a*b^2*d*e)))*(-a*b^3*e)^(1/2)*2i)/(a^3*d*e + a*b^2*d*e)","B"
73,1,4899,325,1.860465,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + b*cot(c + d*x))),x)","\frac{\ln\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)-\frac{\sqrt{-\frac{1}{-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\left(\frac{\sqrt{-\frac{1}{-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{1}{-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)}{2}-512\,a^8\,b^9\,d^8\,e^{18}-640\,a^{10}\,b^7\,d^8\,e^{18}+256\,a^{12}\,b^5\,d^8\,e^{18}+384\,a^{14}\,b^3\,d^8\,e^{18}\right)}{2}-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)\right)\,\sqrt{-\frac{1}{-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}}}}{2}-128\,a^7\,b^8\,d^6\,e^{15}+32\,a^{11}\,b^4\,d^6\,e^{15}+32\,a^{13}\,b^2\,d^6\,e^{15}\right)}{2}\right)\,\sqrt{-\frac{1}{-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}}}}{2}-\ln\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)-\sqrt{-\frac{1}{4\,\left(-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}\right)}}\,\left(\sqrt{-\frac{1}{4\,\left(-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}\right)}}\,\left(\sqrt{-\frac{1}{4\,\left(-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}\right)}}\,\left(\sqrt{-\frac{1}{4\,\left(-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)+512\,a^8\,b^9\,d^8\,e^{18}+640\,a^{10}\,b^7\,d^8\,e^{18}-256\,a^{12}\,b^5\,d^8\,e^{18}-384\,a^{14}\,b^3\,d^8\,e^{18}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)\right)+128\,a^7\,b^8\,d^6\,e^{15}-32\,a^{11}\,b^4\,d^6\,e^{15}-32\,a^{13}\,b^2\,d^6\,e^{15}\right)\right)\,\sqrt{-\frac{1}{4\,\left(-a^2\,d^2\,e^3\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^3+b^2\,d^2\,e^3\,1{}\mathrm{i}\right)}}+\frac{2}{a\,d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}-\mathrm{atan}\left(\frac{\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)-512\,a^8\,b^9\,d^8\,e^{18}-640\,a^{10}\,b^7\,d^8\,e^{18}+256\,a^{12}\,b^5\,d^8\,e^{18}+384\,a^{14}\,b^3\,d^8\,e^{18}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)\right)-128\,a^7\,b^8\,d^6\,e^{15}+32\,a^{11}\,b^4\,d^6\,e^{15}+32\,a^{13}\,b^2\,d^6\,e^{15}\right)\right)\,1{}\mathrm{i}+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)+512\,a^8\,b^9\,d^8\,e^{18}+640\,a^{10}\,b^7\,d^8\,e^{18}-256\,a^{12}\,b^5\,d^8\,e^{18}-384\,a^{14}\,b^3\,d^8\,e^{18}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)\right)+128\,a^7\,b^8\,d^6\,e^{15}-32\,a^{11}\,b^4\,d^6\,e^{15}-32\,a^{13}\,b^2\,d^6\,e^{15}\right)\right)\,1{}\mathrm{i}}{\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)-512\,a^8\,b^9\,d^8\,e^{18}-640\,a^{10}\,b^7\,d^8\,e^{18}+256\,a^{12}\,b^5\,d^8\,e^{18}+384\,a^{14}\,b^3\,d^8\,e^{18}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)\right)-128\,a^7\,b^8\,d^6\,e^{15}+32\,a^{11}\,b^4\,d^6\,e^{15}+32\,a^{13}\,b^2\,d^6\,e^{15}\right)\right)-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)+512\,a^8\,b^9\,d^8\,e^{18}+640\,a^{10}\,b^7\,d^8\,e^{18}-256\,a^{12}\,b^5\,d^8\,e^{18}-384\,a^{14}\,b^3\,d^8\,e^{18}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)\right)+128\,a^7\,b^8\,d^6\,e^{15}-32\,a^{11}\,b^4\,d^6\,e^{15}-32\,a^{13}\,b^2\,d^6\,e^{15}\right)\right)}\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^3+a\,b\,d^2\,e^3\,2{}\mathrm{i}+b^2\,d^2\,e^3\right)}}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)+\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)-\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(256\,a^{12}\,b^5\,d^8\,e^{18}-640\,a^{10}\,b^7\,d^8\,e^{18}-512\,a^8\,b^9\,d^8\,e^{18}+384\,a^{14}\,b^3\,d^8\,e^{18}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b^5\,e^3}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}+128\,a^7\,b^8\,d^6\,e^{15}-32\,a^{11}\,b^4\,d^6\,e^{15}-32\,a^{13}\,b^2\,d^6\,e^{15}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}\,1{}\mathrm{i}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)+\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)-\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(512\,a^8\,b^9\,d^8\,e^{18}+640\,a^{10}\,b^7\,d^8\,e^{18}-256\,a^{12}\,b^5\,d^8\,e^{18}-384\,a^{14}\,b^3\,d^8\,e^{18}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b^5\,e^3}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}-128\,a^7\,b^8\,d^6\,e^{15}+32\,a^{11}\,b^4\,d^6\,e^{15}+32\,a^{13}\,b^2\,d^6\,e^{15}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}\,1{}\mathrm{i}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}}{\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)+\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)-\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(256\,a^{12}\,b^5\,d^8\,e^{18}-640\,a^{10}\,b^7\,d^8\,e^{18}-512\,a^8\,b^9\,d^8\,e^{18}+384\,a^{14}\,b^3\,d^8\,e^{18}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b^5\,e^3}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}+128\,a^7\,b^8\,d^6\,e^{15}-32\,a^{11}\,b^4\,d^6\,e^{15}-32\,a^{13}\,b^2\,d^6\,e^{15}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}-\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^7\,b^7\,d^5\,e^{13}-32\,a^9\,b^5\,d^5\,e^{13}\right)+\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{14}\,b^2\,d^7\,e^{16}+128\,a^{12}\,b^4\,d^7\,e^{16}-448\,a^{10}\,b^6\,d^7\,e^{16}+512\,a^8\,b^8\,d^7\,e^{16}\right)-\frac{\sqrt{-a^3\,b^5\,e^3}\,\left(512\,a^8\,b^9\,d^8\,e^{18}+640\,a^{10}\,b^7\,d^8\,e^{18}-256\,a^{12}\,b^5\,d^8\,e^{18}-384\,a^{14}\,b^3\,d^8\,e^{18}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^3\,b^5\,e^3}\,\left(-512\,a^{15}\,b^3\,d^9\,e^{19}-512\,a^{13}\,b^5\,d^9\,e^{19}+512\,a^{11}\,b^7\,d^9\,e^{19}+512\,a^9\,b^9\,d^9\,e^{19}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}-128\,a^7\,b^8\,d^6\,e^{15}+32\,a^{11}\,b^4\,d^6\,e^{15}+32\,a^{13}\,b^2\,d^6\,e^{15}\right)}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}\right)\,\sqrt{-a^3\,b^5\,e^3}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}}\right)\,\sqrt{-a^3\,b^5\,e^3}\,2{}\mathrm{i}}{d\,a^5\,e^3+d\,a^3\,b^2\,e^3}","Not used",1,"(log((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) - ((-1/(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3))^(1/2)*(((((-1/(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3))^(1/2)*(((e*cot(c + d*x))^(1/2)*(-1/(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3))^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19))/2 - 512*a^8*b^9*d^8*e^18 - 640*a^10*b^7*d^8*e^18 + 256*a^12*b^5*d^8*e^18 + 384*a^14*b^3*d^8*e^18))/2 - (e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16))*(-1/(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3))^(1/2))/2 - 128*a^7*b^8*d^6*e^15 + 32*a^11*b^4*d^6*e^15 + 32*a^13*b^2*d^6*e^15))/2)*(-1/(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3))^(1/2))/2 - atan(((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) - (-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19) - 512*a^8*b^9*d^8*e^18 - 640*a^10*b^7*d^8*e^18 + 256*a^12*b^5*d^8*e^18 + 384*a^14*b^3*d^8*e^18) - (e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16)) - 128*a^7*b^8*d^6*e^15 + 32*a^11*b^4*d^6*e^15 + 32*a^13*b^2*d^6*e^15))*1i + (-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) - (-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19) + 512*a^8*b^9*d^8*e^18 + 640*a^10*b^7*d^8*e^18 - 256*a^12*b^5*d^8*e^18 - 384*a^14*b^3*d^8*e^18) - (e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16)) + 128*a^7*b^8*d^6*e^15 - 32*a^11*b^4*d^6*e^15 - 32*a^13*b^2*d^6*e^15))*1i)/((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) - (-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19) - 512*a^8*b^9*d^8*e^18 - 640*a^10*b^7*d^8*e^18 + 256*a^12*b^5*d^8*e^18 + 384*a^14*b^3*d^8*e^18) - (e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16)) - 128*a^7*b^8*d^6*e^15 + 32*a^11*b^4*d^6*e^15 + 32*a^13*b^2*d^6*e^15)) - (-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) - (-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*((-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19) + 512*a^8*b^9*d^8*e^18 + 640*a^10*b^7*d^8*e^18 - 256*a^12*b^5*d^8*e^18 - 384*a^14*b^3*d^8*e^18) - (e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16)) + 128*a^7*b^8*d^6*e^15 - 32*a^11*b^4*d^6*e^15 - 32*a^13*b^2*d^6*e^15))))*(-1i/(4*(b^2*d^2*e^3 - a^2*d^2*e^3 + a*b*d^2*e^3*2i)))^(1/2)*2i - log((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) - (-1/(4*(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3)))^(1/2)*((-1/(4*(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3)))^(1/2)*((-1/(4*(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3)))^(1/2)*((-1/(4*(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19) + 512*a^8*b^9*d^8*e^18 + 640*a^10*b^7*d^8*e^18 - 256*a^12*b^5*d^8*e^18 - 384*a^14*b^3*d^8*e^18) - (e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16)) + 128*a^7*b^8*d^6*e^15 - 32*a^11*b^4*d^6*e^15 - 32*a^13*b^2*d^6*e^15))*(-1/(4*(b^2*d^2*e^3*1i - a^2*d^2*e^3*1i + 2*a*b*d^2*e^3)))^(1/2) - (atan(((((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) + ((-a^3*b^5*e^3)^(1/2)*((((e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16) - ((-a^3*b^5*e^3)^(1/2)*(256*a^12*b^5*d^8*e^18 - 640*a^10*b^7*d^8*e^18 - 512*a^8*b^9*d^8*e^18 + 384*a^14*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(-a^3*b^5*e^3)^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19))/(a^5*d*e^3 + a^3*b^2*d*e^3)))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2))/(a^5*d*e^3 + a^3*b^2*d*e^3) + 128*a^7*b^8*d^6*e^15 - 32*a^11*b^4*d^6*e^15 - 32*a^13*b^2*d^6*e^15))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2)*1i)/(a^5*d*e^3 + a^3*b^2*d*e^3) + (((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) + ((-a^3*b^5*e^3)^(1/2)*((((e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16) - ((-a^3*b^5*e^3)^(1/2)*(512*a^8*b^9*d^8*e^18 + 640*a^10*b^7*d^8*e^18 - 256*a^12*b^5*d^8*e^18 - 384*a^14*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(-a^3*b^5*e^3)^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19))/(a^5*d*e^3 + a^3*b^2*d*e^3)))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2))/(a^5*d*e^3 + a^3*b^2*d*e^3) - 128*a^7*b^8*d^6*e^15 + 32*a^11*b^4*d^6*e^15 + 32*a^13*b^2*d^6*e^15))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2)*1i)/(a^5*d*e^3 + a^3*b^2*d*e^3))/((((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) + ((-a^3*b^5*e^3)^(1/2)*((((e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16) - ((-a^3*b^5*e^3)^(1/2)*(256*a^12*b^5*d^8*e^18 - 640*a^10*b^7*d^8*e^18 - 512*a^8*b^9*d^8*e^18 + 384*a^14*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(-a^3*b^5*e^3)^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19))/(a^5*d*e^3 + a^3*b^2*d*e^3)))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2))/(a^5*d*e^3 + a^3*b^2*d*e^3) + 128*a^7*b^8*d^6*e^15 - 32*a^11*b^4*d^6*e^15 - 32*a^13*b^2*d^6*e^15))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2))/(a^5*d*e^3 + a^3*b^2*d*e^3) - (((e*cot(c + d*x))^(1/2)*(64*a^7*b^7*d^5*e^13 - 32*a^9*b^5*d^5*e^13) + ((-a^3*b^5*e^3)^(1/2)*((((e*cot(c + d*x))^(1/2)*(512*a^8*b^8*d^7*e^16 - 448*a^10*b^6*d^7*e^16 + 128*a^12*b^4*d^7*e^16 + 64*a^14*b^2*d^7*e^16) - ((-a^3*b^5*e^3)^(1/2)*(512*a^8*b^9*d^8*e^18 + 640*a^10*b^7*d^8*e^18 - 256*a^12*b^5*d^8*e^18 - 384*a^14*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(-a^3*b^5*e^3)^(1/2)*(512*a^9*b^9*d^9*e^19 + 512*a^11*b^7*d^9*e^19 - 512*a^13*b^5*d^9*e^19 - 512*a^15*b^3*d^9*e^19))/(a^5*d*e^3 + a^3*b^2*d*e^3)))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2))/(a^5*d*e^3 + a^3*b^2*d*e^3) - 128*a^7*b^8*d^6*e^15 + 32*a^11*b^4*d^6*e^15 + 32*a^13*b^2*d^6*e^15))/(a^5*d*e^3 + a^3*b^2*d*e^3))*(-a^3*b^5*e^3)^(1/2))/(a^5*d*e^3 + a^3*b^2*d*e^3)))*(-a^3*b^5*e^3)^(1/2)*2i)/(a^5*d*e^3 + a^3*b^2*d*e^3) + 2/(a*d*e*(e*cot(c + d*x))^(1/2))","B"
74,1,6042,351,2.807053,"\text{Not used}","int(1/((e*cot(c + d*x))^(5/2)*(a + b*cot(c + d*x))),x)","\frac{\frac{2}{3\,a\,e}-\frac{2\,b\,\mathrm{cot}\left(c+d\,x\right)}{a^2\,e}}{d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-\mathrm{atan}\left(\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)}{2}+\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\left(\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{4}-256\,a^{16}\,b^{10}\,d^8\,e^{26}-256\,a^{18}\,b^8\,d^8\,e^{26}+192\,a^{20}\,b^6\,d^8\,e^{26}+128\,a^{22}\,b^4\,d^8\,e^{26}-64\,a^{24}\,b^2\,d^8\,e^{26}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}}{2}+192\,a^{15}\,b^9\,d^6\,e^{21}-16\,a^{19}\,b^5\,d^6\,e^{21}-16\,a^{21}\,b^3\,d^6\,e^{21}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,1{}\mathrm{i}+\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)}{2}+\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\left(\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{4}+256\,a^{16}\,b^{10}\,d^8\,e^{26}+256\,a^{18}\,b^8\,d^8\,e^{26}-192\,a^{20}\,b^6\,d^8\,e^{26}-128\,a^{22}\,b^4\,d^8\,e^{26}+64\,a^{24}\,b^2\,d^8\,e^{26}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}}{2}-192\,a^{15}\,b^9\,d^6\,e^{21}+16\,a^{19}\,b^5\,d^6\,e^{21}+16\,a^{21}\,b^3\,d^6\,e^{21}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,1{}\mathrm{i}}{64\,a^{14}\,b^8\,d^4\,e^{16}+\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)}{2}+\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\left(\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{4}+256\,a^{16}\,b^{10}\,d^8\,e^{26}+256\,a^{18}\,b^8\,d^8\,e^{26}-192\,a^{20}\,b^6\,d^8\,e^{26}-128\,a^{22}\,b^4\,d^8\,e^{26}+64\,a^{24}\,b^2\,d^8\,e^{26}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}}{2}-192\,a^{15}\,b^9\,d^6\,e^{21}+16\,a^{19}\,b^5\,d^6\,e^{21}+16\,a^{21}\,b^3\,d^6\,e^{21}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}-\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)}{2}+\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\left(\frac{\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{4}-256\,a^{16}\,b^{10}\,d^8\,e^{26}-256\,a^{18}\,b^8\,d^8\,e^{26}+192\,a^{20}\,b^6\,d^8\,e^{26}+128\,a^{22}\,b^4\,d^8\,e^{26}-64\,a^{24}\,b^2\,d^8\,e^{26}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}}{2}+192\,a^{15}\,b^9\,d^6\,e^{21}-16\,a^{19}\,b^5\,d^6\,e^{21}-16\,a^{21}\,b^3\,d^6\,e^{21}\right)}{2}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}}\right)\,\sqrt{\frac{1}{-a^2\,d^2\,e^5\,1{}\mathrm{i}+2\,a\,b\,d^2\,e^5+b^2\,d^2\,e^5\,1{}\mathrm{i}}}\,1{}\mathrm{i}-\mathrm{atan}\left(\frac{\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)-512\,a^{16}\,b^{10}\,d^8\,e^{26}-512\,a^{18}\,b^8\,d^8\,e^{26}+384\,a^{20}\,b^6\,d^8\,e^{26}+256\,a^{22}\,b^4\,d^8\,e^{26}-128\,a^{24}\,b^2\,d^8\,e^{26}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)\right)+384\,a^{15}\,b^9\,d^6\,e^{21}-32\,a^{19}\,b^5\,d^6\,e^{21}-32\,a^{21}\,b^3\,d^6\,e^{21}\right)\right)\,1{}\mathrm{i}+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)+512\,a^{16}\,b^{10}\,d^8\,e^{26}+512\,a^{18}\,b^8\,d^8\,e^{26}-384\,a^{20}\,b^6\,d^8\,e^{26}-256\,a^{22}\,b^4\,d^8\,e^{26}+128\,a^{24}\,b^2\,d^8\,e^{26}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)\right)-384\,a^{15}\,b^9\,d^6\,e^{21}+32\,a^{19}\,b^5\,d^6\,e^{21}+32\,a^{21}\,b^3\,d^6\,e^{21}\right)\right)\,1{}\mathrm{i}}{64\,a^{14}\,b^8\,d^4\,e^{16}+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)+512\,a^{16}\,b^{10}\,d^8\,e^{26}+512\,a^{18}\,b^8\,d^8\,e^{26}-384\,a^{20}\,b^6\,d^8\,e^{26}-256\,a^{22}\,b^4\,d^8\,e^{26}+128\,a^{24}\,b^2\,d^8\,e^{26}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)\right)-384\,a^{15}\,b^9\,d^6\,e^{21}+32\,a^{19}\,b^5\,d^6\,e^{21}+32\,a^{21}\,b^3\,d^6\,e^{21}\right)\right)-\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)-512\,a^{16}\,b^{10}\,d^8\,e^{26}-512\,a^{18}\,b^8\,d^8\,e^{26}+384\,a^{20}\,b^6\,d^8\,e^{26}+256\,a^{22}\,b^4\,d^8\,e^{26}-128\,a^{24}\,b^2\,d^8\,e^{26}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)\right)+384\,a^{15}\,b^9\,d^6\,e^{21}-32\,a^{19}\,b^5\,d^6\,e^{21}-32\,a^{21}\,b^3\,d^6\,e^{21}\right)\right)}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-a^2\,d^2\,e^5+a\,b\,d^2\,e^5\,2{}\mathrm{i}+b^2\,d^2\,e^5\right)}}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)-\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(32\,a^{19}\,b^5\,d^6\,e^{21}-384\,a^{15}\,b^9\,d^6\,e^{21}+32\,a^{21}\,b^3\,d^6\,e^{21}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)+\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(512\,a^{16}\,b^{10}\,d^8\,e^{26}+512\,a^{18}\,b^8\,d^8\,e^{26}-384\,a^{20}\,b^6\,d^8\,e^{26}-256\,a^{22}\,b^4\,d^8\,e^{26}+128\,a^{24}\,b^2\,d^8\,e^{26}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^7\,e^5}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}\,1{}\mathrm{i}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)-\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(384\,a^{15}\,b^9\,d^6\,e^{21}-32\,a^{19}\,b^5\,d^6\,e^{21}-32\,a^{21}\,b^3\,d^6\,e^{21}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)-\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(512\,a^{16}\,b^{10}\,d^8\,e^{26}+512\,a^{18}\,b^8\,d^8\,e^{26}-384\,a^{20}\,b^6\,d^8\,e^{26}-256\,a^{22}\,b^4\,d^8\,e^{26}+128\,a^{24}\,b^2\,d^8\,e^{26}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^7\,e^5}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}\,1{}\mathrm{i}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}}{64\,a^{14}\,b^8\,d^4\,e^{16}-\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)-\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(32\,a^{19}\,b^5\,d^6\,e^{21}-384\,a^{15}\,b^9\,d^6\,e^{21}+32\,a^{21}\,b^3\,d^6\,e^{21}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)+\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(512\,a^{16}\,b^{10}\,d^8\,e^{26}+512\,a^{18}\,b^8\,d^8\,e^{26}-384\,a^{20}\,b^6\,d^8\,e^{26}-256\,a^{22}\,b^4\,d^8\,e^{26}+128\,a^{24}\,b^2\,d^8\,e^{26}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^7\,e^5}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{18}\,b^5\,d^5\,e^{18}+64\,a^{14}\,b^9\,d^5\,e^{18}\right)-\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(384\,a^{15}\,b^9\,d^6\,e^{21}-32\,a^{19}\,b^5\,d^6\,e^{21}-32\,a^{21}\,b^3\,d^6\,e^{21}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{23}\,b^2\,d^7\,e^{23}-128\,a^{21}\,b^4\,d^7\,e^{23}+448\,a^{19}\,b^6\,d^7\,e^{23}+512\,a^{15}\,b^{10}\,d^7\,e^{23}\right)-\frac{\sqrt{-a^5\,b^7\,e^5}\,\left(512\,a^{16}\,b^{10}\,d^8\,e^{26}+512\,a^{18}\,b^8\,d^8\,e^{26}-384\,a^{20}\,b^6\,d^8\,e^{26}-256\,a^{22}\,b^4\,d^8\,e^{26}+128\,a^{24}\,b^2\,d^8\,e^{26}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^7\,e^5}\,\left(-512\,a^{24}\,b^3\,d^9\,e^{28}-512\,a^{22}\,b^5\,d^9\,e^{28}+512\,a^{20}\,b^7\,d^9\,e^{28}+512\,a^{18}\,b^9\,d^9\,e^{28}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)}{a^5\,d\,e^5\,\left(a^2+b^2\right)}\right)\,\sqrt{-a^5\,b^7\,e^5}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}}\right)\,\sqrt{-a^5\,b^7\,e^5}\,2{}\mathrm{i}}{a^5\,d\,e^5\,\left(a^2+b^2\right)}","Not used",1,"(2/(3*a*e) - (2*b*cot(c + d*x))/(a^2*e))/(d*(e*cot(c + d*x))^(3/2)) - atan(((((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18))/2 + ((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/4 - 256*a^16*b^10*d^8*e^26 - 256*a^18*b^8*d^8*e^26 + 192*a^20*b^6*d^8*e^26 + 128*a^22*b^4*d^8*e^26 - 64*a^24*b^2*d^8*e^26))/2 - ((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2))/2 + 192*a^15*b^9*d^6*e^21 - 16*a^19*b^5*d^6*e^21 - 16*a^21*b^3*d^6*e^21))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*1i + (((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18))/2 + ((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/4 + 256*a^16*b^10*d^8*e^26 + 256*a^18*b^8*d^8*e^26 - 192*a^20*b^6*d^8*e^26 - 128*a^22*b^4*d^8*e^26 + 64*a^24*b^2*d^8*e^26))/2 - ((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2))/2 - 192*a^15*b^9*d^6*e^21 + 16*a^19*b^5*d^6*e^21 + 16*a^21*b^3*d^6*e^21))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*1i)/((((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18))/2 + ((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/4 + 256*a^16*b^10*d^8*e^26 + 256*a^18*b^8*d^8*e^26 - 192*a^20*b^6*d^8*e^26 - 128*a^22*b^4*d^8*e^26 + 64*a^24*b^2*d^8*e^26))/2 - ((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2))/2 - 192*a^15*b^9*d^6*e^21 + 16*a^19*b^5*d^6*e^21 + 16*a^21*b^3*d^6*e^21))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2) - (((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18))/2 + ((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((((1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/4 - 256*a^16*b^10*d^8*e^26 - 256*a^18*b^8*d^8*e^26 + 192*a^20*b^6*d^8*e^26 + 128*a^22*b^4*d^8*e^26 - 64*a^24*b^2*d^8*e^26))/2 - ((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2))/2 + 192*a^15*b^9*d^6*e^21 - 16*a^19*b^5*d^6*e^21 - 16*a^21*b^3*d^6*e^21))/2)*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2) + 64*a^14*b^8*d^4*e^16))*(1/(b^2*d^2*e^5*1i - a^2*d^2*e^5*1i + 2*a*b*d^2*e^5))^(1/2)*1i - atan(((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) + (1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28) - 512*a^16*b^10*d^8*e^26 - 512*a^18*b^8*d^8*e^26 + 384*a^20*b^6*d^8*e^26 + 256*a^22*b^4*d^8*e^26 - 128*a^24*b^2*d^8*e^26) - (e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23)) + 384*a^15*b^9*d^6*e^21 - 32*a^19*b^5*d^6*e^21 - 32*a^21*b^3*d^6*e^21))*1i + (1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) + (1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28) + 512*a^16*b^10*d^8*e^26 + 512*a^18*b^8*d^8*e^26 - 384*a^20*b^6*d^8*e^26 - 256*a^22*b^4*d^8*e^26 + 128*a^24*b^2*d^8*e^26) - (e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23)) - 384*a^15*b^9*d^6*e^21 + 32*a^19*b^5*d^6*e^21 + 32*a^21*b^3*d^6*e^21))*1i)/((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) + (1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28) + 512*a^16*b^10*d^8*e^26 + 512*a^18*b^8*d^8*e^26 - 384*a^20*b^6*d^8*e^26 - 256*a^22*b^4*d^8*e^26 + 128*a^24*b^2*d^8*e^26) - (e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23)) - 384*a^15*b^9*d^6*e^21 + 32*a^19*b^5*d^6*e^21 + 32*a^21*b^3*d^6*e^21)) - (1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) + (1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*((1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28) - 512*a^16*b^10*d^8*e^26 - 512*a^18*b^8*d^8*e^26 + 384*a^20*b^6*d^8*e^26 + 256*a^22*b^4*d^8*e^26 - 128*a^24*b^2*d^8*e^26) - (e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23)) + 384*a^15*b^9*d^6*e^21 - 32*a^19*b^5*d^6*e^21 - 32*a^21*b^3*d^6*e^21)) + 64*a^14*b^8*d^4*e^16))*(1i/(4*(b^2*d^2*e^5 - a^2*d^2*e^5 + a*b*d^2*e^5*2i)))^(1/2)*2i - (atan(((((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) - ((-a^5*b^7*e^5)^(1/2)*(32*a^19*b^5*d^6*e^21 - 384*a^15*b^9*d^6*e^21 + 32*a^21*b^3*d^6*e^21 + (((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23) + ((-a^5*b^7*e^5)^(1/2)*(512*a^16*b^10*d^8*e^26 + 512*a^18*b^8*d^8*e^26 - 384*a^20*b^6*d^8*e^26 - 256*a^22*b^4*d^8*e^26 + 128*a^24*b^2*d^8*e^26 - ((e*cot(c + d*x))^(1/2)*(-a^5*b^7*e^5)^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2)*1i)/(a^5*d*e^5*(a^2 + b^2)) + (((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) - ((-a^5*b^7*e^5)^(1/2)*(384*a^15*b^9*d^6*e^21 - 32*a^19*b^5*d^6*e^21 - 32*a^21*b^3*d^6*e^21 + (((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23) - ((-a^5*b^7*e^5)^(1/2)*(512*a^16*b^10*d^8*e^26 + 512*a^18*b^8*d^8*e^26 - 384*a^20*b^6*d^8*e^26 - 256*a^22*b^4*d^8*e^26 + 128*a^24*b^2*d^8*e^26 + ((e*cot(c + d*x))^(1/2)*(-a^5*b^7*e^5)^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2)*1i)/(a^5*d*e^5*(a^2 + b^2)))/(64*a^14*b^8*d^4*e^16 - (((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) - ((-a^5*b^7*e^5)^(1/2)*(32*a^19*b^5*d^6*e^21 - 384*a^15*b^9*d^6*e^21 + 32*a^21*b^3*d^6*e^21 + (((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23) + ((-a^5*b^7*e^5)^(1/2)*(512*a^16*b^10*d^8*e^26 + 512*a^18*b^8*d^8*e^26 - 384*a^20*b^6*d^8*e^26 - 256*a^22*b^4*d^8*e^26 + 128*a^24*b^2*d^8*e^26 - ((e*cot(c + d*x))^(1/2)*(-a^5*b^7*e^5)^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2))/(a^5*d*e^5*(a^2 + b^2)) + (((e*cot(c + d*x))^(1/2)*(64*a^14*b^9*d^5*e^18 + 32*a^18*b^5*d^5*e^18) - ((-a^5*b^7*e^5)^(1/2)*(384*a^15*b^9*d^6*e^21 - 32*a^19*b^5*d^6*e^21 - 32*a^21*b^3*d^6*e^21 + (((e*cot(c + d*x))^(1/2)*(512*a^15*b^10*d^7*e^23 + 448*a^19*b^6*d^7*e^23 - 128*a^21*b^4*d^7*e^23 - 64*a^23*b^2*d^7*e^23) - ((-a^5*b^7*e^5)^(1/2)*(512*a^16*b^10*d^8*e^26 + 512*a^18*b^8*d^8*e^26 - 384*a^20*b^6*d^8*e^26 - 256*a^22*b^4*d^8*e^26 + 128*a^24*b^2*d^8*e^26 + ((e*cot(c + d*x))^(1/2)*(-a^5*b^7*e^5)^(1/2)*(512*a^18*b^9*d^9*e^28 + 512*a^20*b^7*d^9*e^28 - 512*a^22*b^5*d^9*e^28 - 512*a^24*b^3*d^9*e^28))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2))/(a^5*d*e^5*(a^2 + b^2))))/(a^5*d*e^5*(a^2 + b^2)))*(-a^5*b^7*e^5)^(1/2))/(a^5*d*e^5*(a^2 + b^2))))*(-a^5*b^7*e^5)^(1/2)*2i)/(a^5*d*e^5*(a^2 + b^2))","B"
75,1,13244,437,3.969992,"\text{Not used}","int((e*cot(c + d*x))^(7/2)/(a + b*cot(c + d*x))^2,x)","-\frac{2\,e^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{b^2\,d}-\frac{a^3\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\left(a^2+b^2\right)\,\left(d\,e\,\mathrm{cot}\left(c+d\,x\right)\,b^3+a\,d\,e\,b^2\right)}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}}{\frac{32\,\left(3\,a^5\,b^5\,e^{28}+7\,a^3\,b^7\,e^{28}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}}\right)\,\sqrt{-\frac{e^7\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\frac{32\,\left(3\,a^5\,b^5\,e^{28}+7\,a^3\,b^7\,e^{28}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}}\right)\,\sqrt{-\frac{e^7}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}+\frac{\left(\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}+\frac{\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,1{}\mathrm{i}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}-\frac{\left(\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}-\frac{\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,1{}\mathrm{i}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}}{\frac{32\,\left(3\,a^5\,b^5\,e^{28}+7\,a^3\,b^7\,e^{28}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}+\frac{\left(\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}+\frac{\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,e^{24}+33\,a^{10}\,b^2\,e^{24}+7\,a^8\,b^4\,e^{24}-49\,a^6\,b^6\,e^{24}+2\,a^4\,b^8\,e^{24}+4\,a^2\,b^{10}\,e^{24}+2\,b^{12}\,e^{24}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}-\frac{\left(\frac{16\,\left(-18\,a^{14}\,d^2\,e^{21}+24\,a^{12}\,b^2\,d^2\,e^{21}+388\,a^{10}\,b^4\,d^2\,e^{21}+600\,a^8\,b^6\,d^2\,e^{21}+30\,a^6\,b^8\,d^2\,e^{21}-224\,a^4\,b^{10}\,d^2\,e^{21}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{15}\,b\,d^2\,e^{17}+480\,a^{13}\,b^3\,d^2\,e^{17}+1132\,a^{11}\,b^5\,d^2\,e^{17}+1108\,a^9\,b^7\,d^2\,e^{17}+448\,a^7\,b^9\,d^2\,e^{17}+72\,a^5\,b^{11}\,d^2\,e^{17}-52\,a^3\,b^{13}\,d^2\,e^{17}-60\,a\,b^{15}\,d^2\,e^{17}\right)}{a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4}-\frac{\left(\frac{16\,\left(56\,a^{13}\,b^5\,d^4\,e^{14}+288\,a^{11}\,b^7\,d^4\,e^{14}+600\,a^9\,b^9\,d^4\,e^{14}+640\,a^7\,b^{11}\,d^4\,e^{14}+360\,a^5\,b^{13}\,d^4\,e^{14}+96\,a^3\,b^{15}\,d^4\,e^{14}+8\,a\,b^{17}\,d^4\,e^{14}\right)}{a^8\,b^3\,d^5+4\,a^6\,b^5\,d^5+6\,a^4\,b^7\,d^5+4\,a^2\,b^9\,d^5+b^{11}\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,\left(-32\,a^{14}\,b^6\,d^4\,e^{10}-160\,a^{12}\,b^8\,d^4\,e^{10}-288\,a^{10}\,b^{10}\,d^4\,e^{10}-160\,a^8\,b^{12}\,d^4\,e^{10}+160\,a^6\,b^{14}\,d^4\,e^{10}+288\,a^4\,b^{16}\,d^4\,e^{10}+160\,a^2\,b^{18}\,d^4\,e^{10}+32\,b^{20}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^8\,b^3\,d^4+4\,a^6\,b^5\,d^4+6\,a^4\,b^7\,d^4+4\,a^2\,b^9\,d^4+b^{11}\,d^4\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}}{2\,\left(d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9\right)}}\right)\,\left(3\,a^2+7\,b^2\right)\,\sqrt{-a^5\,b^5\,e^7}\,1{}\mathrm{i}}{d\,a^4\,b^5+2\,d\,a^2\,b^7+d\,b^9}","Not used",1,"(atan(((((16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) + (((16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) + (((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (8*(e*cot(c + d*x))^(1/2)*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/((b^9*d + 2*a^2*b^7*d + a^4*b^5*d)*(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*1i)/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)) + (((16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) - (((16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (((16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) - (((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (8*(e*cot(c + d*x))^(1/2)*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/((b^9*d + 2*a^2*b^7*d + a^4*b^5*d)*(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*1i)/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))/((32*(7*a^3*b^7*e^28 + 3*a^5*b^5*e^28))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) + (((16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) + (((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (8*(e*cot(c + d*x))^(1/2)*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/((b^9*d + 2*a^2*b^7*d + a^4*b^5*d)*(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)) + (((16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) - (((16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (((16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4) - (((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (8*(e*cot(c + d*x))^(1/2)*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/((b^9*d + 2*a^2*b^7*d + a^4*b^5*d)*(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d)))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2))/(2*(b^9*d + 2*a^2*b^7*d + a^4*b^5*d))))*(3*a^2 + 7*b^2)*(-a^5*b^5*e^7)^(1/2)*1i)/(b^9*d + 2*a^2*b^7*d + a^4*b^5*d) - atan(((((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i - (((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i)/((32*(7*a^3*b^7*e^28 + 3*a^5*b^5*e^28))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)))*(-e^7/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*2i - (2*e^3*(e*cot(c + d*x))^(1/2))/(b^2*d) - atan(((((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i - (((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i)/((32*(7*a^3*b^7*e^28 + 3*a^5*b^5*e^28))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (((((16*(8*a*b^17*d^4*e^14 + 96*a^3*b^15*d^4*e^14 + 360*a^5*b^13*d^4*e^14 + 640*a^7*b^11*d^4*e^14 + 600*a^9*b^9*d^4*e^14 + 288*a^11*b^7*d^4*e^14 + 56*a^13*b^5*d^4*e^14))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^20*d^4*e^10 + 160*a^2*b^18*d^4*e^10 + 288*a^4*b^16*d^4*e^10 + 160*a^6*b^14*d^4*e^10 - 160*a^8*b^12*d^4*e^10 - 288*a^10*b^10*d^4*e^10 - 160*a^12*b^8*d^4*e^10 - 32*a^14*b^6*d^4*e^10))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(72*a^15*b*d^2*e^17 - 60*a*b^15*d^2*e^17 - 52*a^3*b^13*d^2*e^17 + 72*a^5*b^11*d^2*e^17 + 448*a^7*b^9*d^2*e^17 + 1108*a^9*b^7*d^2*e^17 + 1132*a^11*b^5*d^2*e^17 + 480*a^13*b^3*d^2*e^17))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(30*a^6*b^8*d^2*e^21 - 224*a^4*b^10*d^2*e^21 - 18*a^14*d^2*e^21 + 600*a^8*b^6*d^2*e^21 + 388*a^10*b^4*d^2*e^21 + 24*a^12*b^2*d^2*e^21))/(b^11*d^5 + 4*a^2*b^9*d^5 + 6*a^4*b^7*d^5 + 4*a^6*b^5*d^5 + a^8*b^3*d^5))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(9*a^12*e^24 + 2*b^12*e^24 + 4*a^2*b^10*e^24 + 2*a^4*b^8*e^24 - 49*a^6*b^6*e^24 + 7*a^8*b^4*e^24 + 33*a^10*b^2*e^24))/(b^11*d^4 + 4*a^2*b^9*d^4 + 6*a^4*b^7*d^4 + 4*a^6*b^5*d^4 + a^8*b^3*d^4))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)))*(-(e^7*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*2i - (a^3*e^4*(e*cot(c + d*x))^(1/2))/((a^2 + b^2)*(a*b^2*d*e + b^3*d*e*cot(c + d*x)))","B"
76,1,12617,393,3.120902,"\text{Not used}","int((e*cot(c + d*x))^(5/2)/(a + b*cot(c + d*x))^2,x)","\frac{a^2\,e^3\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{b\,\left(a\,d\,e+b\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}+\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}}{\frac{16\,\left(a^8\,e^{23}+10\,a^6\,b^2\,e^{23}+27\,a^4\,b^4\,e^{23}+10\,a^2\,b^6\,e^{23}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}}\right)\,\sqrt{\frac{e^5\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\frac{16\,\left(a^8\,e^{23}+10\,a^6\,b^2\,e^{23}+27\,a^4\,b^4\,e^{23}+10\,a^2\,b^6\,e^{23}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}}\right)\,\sqrt{\frac{e^5}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2+5\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}+\frac{\left(a^2+5\,b^2\right)\,\left(\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}+\frac{\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)\,\left(a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}\,1{}\mathrm{i}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}+\frac{\left(a^2+5\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}-\frac{\left(a^2+5\,b^2\right)\,\left(\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}-\frac{\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)\,\left(a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}\,1{}\mathrm{i}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}}{\frac{16\,\left(a^8\,e^{23}+10\,a^6\,b^2\,e^{23}+27\,a^4\,b^4\,e^{23}+10\,a^2\,b^6\,e^{23}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{\left(a^2+5\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}+\frac{\left(a^2+5\,b^2\right)\,\left(\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}+\frac{\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)\,\left(a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}-\frac{\left(a^2+5\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{10}\,e^{20}+9\,a^8\,b^2\,e^{20}+15\,a^6\,b^4\,e^{20}-27\,a^4\,b^6\,e^{20}-4\,a^2\,b^8\,e^{20}-2\,b^{10}\,e^{20}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}-\frac{\left(a^2+5\,b^2\right)\,\left(\frac{8\,\left(16\,a^{11}\,b\,d^2\,e^{18}+148\,a^9\,b^3\,d^2\,e^{18}+320\,a^7\,b^5\,d^2\,e^{18}-120\,a^5\,b^7\,d^2\,e^{18}-304\,a^3\,b^9\,d^2\,e^{18}+4\,a\,b^{11}\,d^2\,e^{18}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{13}\,b\,d^2\,e^{15}+100\,a^{11}\,b^3\,d^2\,e^{15}+380\,a^9\,b^5\,d^2\,e^{15}+424\,a^7\,b^7\,d^2\,e^{15}+128\,a^5\,b^9\,d^2\,e^{15}+52\,a^3\,b^{11}\,d^2\,e^{15}+60\,a\,b^{13}\,d^2\,e^{15}\right)}{a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4}-\frac{\left(\frac{8\,\left(96\,a^{12}\,b^4\,d^4\,e^{13}+480\,a^{10}\,b^6\,d^4\,e^{13}+960\,a^8\,b^8\,d^4\,e^{13}+960\,a^6\,b^{10}\,d^4\,e^{13}+480\,a^4\,b^{12}\,d^4\,e^{13}+96\,a^2\,b^{14}\,d^4\,e^{13}\right)}{a^8\,b\,d^5+4\,a^6\,b^3\,d^5+6\,a^4\,b^5\,d^5+4\,a^2\,b^7\,d^5+b^9\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}\,\left(-32\,a^{14}\,b^4\,d^4\,e^{10}-160\,a^{12}\,b^6\,d^4\,e^{10}-288\,a^{10}\,b^8\,d^4\,e^{10}-160\,a^8\,b^{10}\,d^4\,e^{10}+160\,a^6\,b^{12}\,d^4\,e^{10}+288\,a^4\,b^{14}\,d^4\,e^{10}+160\,a^2\,b^{16}\,d^4\,e^{10}+32\,b^{18}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)\,\left(a^8\,b\,d^4+4\,a^6\,b^3\,d^4+6\,a^4\,b^5\,d^4+4\,a^2\,b^7\,d^4+b^9\,d^4\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}\right)\,\sqrt{-a^3\,b^3\,e^5}}{2\,\left(d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7\right)}}\right)\,\left(a^2+5\,b^2\right)\,\sqrt{-a^3\,b^3\,e^5}\,1{}\mathrm{i}}{d\,a^4\,b^3+2\,d\,a^2\,b^5+d\,b^7}","Not used",1,"atan(((((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i - (((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i)/((16*(a^8*e^23 + 10*a^2*b^6*e^23 + 27*a^4*b^4*e^23 + 10*a^6*b^2*e^23))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)))*((e^5*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*2i + atan(((((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i - (((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i)/((16*(a^8*e^23 + 10*a^2*b^6*e^23 + 27*a^4*b^4*e^23 + 10*a^6*b^2*e^23))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (16*(e*cot(c + d*x))^(1/2)*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (((((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (16*(e*cot(c + d*x))^(1/2)*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)))*(e^5/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*2i + (atan((((a^2 + 5*b^2)*((16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) + ((a^2 + 5*b^2)*((8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (((16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) + (((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (8*(e*cot(c + d*x))^(1/2)*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/((b^7*d + 2*a^2*b^5*d + a^4*b^3*d)*(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2)*1i)/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)) + ((a^2 + 5*b^2)*((16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) - ((a^2 + 5*b^2)*((8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) - (((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (8*(e*cot(c + d*x))^(1/2)*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/((b^7*d + 2*a^2*b^5*d + a^4*b^3*d)*(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2)*1i)/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))/((16*(a^8*e^23 + 10*a^2*b^6*e^23 + 27*a^4*b^4*e^23 + 10*a^6*b^2*e^23))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + ((a^2 + 5*b^2)*((16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) + ((a^2 + 5*b^2)*((8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (((16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) + (((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (8*(e*cot(c + d*x))^(1/2)*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/((b^7*d + 2*a^2*b^5*d + a^4*b^3*d)*(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)) - ((a^2 + 5*b^2)*((16*(e*cot(c + d*x))^(1/2)*(a^10*e^20 - 2*b^10*e^20 - 4*a^2*b^8*e^20 - 27*a^4*b^6*e^20 + 15*a^6*b^4*e^20 + 9*a^8*b^2*e^20))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) - ((a^2 + 5*b^2)*((8*(4*a*b^11*d^2*e^18 + 16*a^11*b*d^2*e^18 - 304*a^3*b^9*d^2*e^18 - 120*a^5*b^7*d^2*e^18 + 320*a^7*b^5*d^2*e^18 + 148*a^9*b^3*d^2*e^18))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(60*a*b^13*d^2*e^15 + 8*a^13*b*d^2*e^15 + 52*a^3*b^11*d^2*e^15 + 128*a^5*b^9*d^2*e^15 + 424*a^7*b^7*d^2*e^15 + 380*a^9*b^5*d^2*e^15 + 100*a^11*b^3*d^2*e^15))/(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4) - (((8*(96*a^2*b^14*d^4*e^13 + 480*a^4*b^12*d^4*e^13 + 960*a^6*b^10*d^4*e^13 + 960*a^8*b^8*d^4*e^13 + 480*a^10*b^6*d^4*e^13 + 96*a^12*b^4*d^4*e^13))/(b^9*d^5 + a^8*b*d^5 + 4*a^2*b^7*d^5 + 6*a^4*b^5*d^5 + 4*a^6*b^3*d^5) + (8*(e*cot(c + d*x))^(1/2)*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2)*(32*b^18*d^4*e^10 + 160*a^2*b^16*d^4*e^10 + 288*a^4*b^14*d^4*e^10 + 160*a^6*b^12*d^4*e^10 - 160*a^8*b^10*d^4*e^10 - 288*a^10*b^8*d^4*e^10 - 160*a^12*b^6*d^4*e^10 - 32*a^14*b^4*d^4*e^10))/((b^7*d + 2*a^2*b^5*d + a^4*b^3*d)*(b^9*d^4 + a^8*b*d^4 + 4*a^2*b^7*d^4 + 6*a^4*b^5*d^4 + 4*a^6*b^3*d^4)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d)))*(-a^3*b^3*e^5)^(1/2))/(2*(b^7*d + 2*a^2*b^5*d + a^4*b^3*d))))*(a^2 + 5*b^2)*(-a^3*b^3*e^5)^(1/2)*1i)/(b^7*d + 2*a^2*b^5*d + a^4*b^3*d) + (a^2*e^3*(e*cot(c + d*x))^(1/2))/(b*(a*d*e + b*d*e*cot(c + d*x))*(a^2 + b^2))","B"
77,1,11953,387,3.365915,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + b*cot(c + d*x))^2,x)","-\frac{a\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\left(a\,d\,e+b\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}}{\frac{32\,\left(3\,a\,b^6\,e^{18}-a^3\,b^4\,e^{18}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}}\right)\,\sqrt{-\frac{e^3\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\frac{32\,\left(3\,a\,b^6\,e^{18}-a^3\,b^4\,e^{18}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}}\right)\,\sqrt{-\frac{e^3}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2-3\,b^2\right)\,\sqrt{-a\,b\,e^3}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}\,1{}\mathrm{i}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2-3\,b^2\right)\,\sqrt{-a\,b\,e^3}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}\,1{}\mathrm{i}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}}{\frac{32\,\left(3\,a\,b^6\,e^{18}-a^3\,b^4\,e^{18}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2-3\,b^2\right)\,\sqrt{-a\,b\,e^3}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^8\,b\,e^{16}-7\,a^6\,b^3\,e^{16}+17\,a^4\,b^5\,e^{16}-5\,a^2\,b^7\,e^{16}+2\,b^9\,e^{16}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(2\,a^{10}\,b\,d^2\,e^{15}-24\,a^8\,b^3\,d^2\,e^{15}+60\,a^6\,b^5\,d^2\,e^{15}+8\,a^4\,b^7\,d^2\,e^{15}-78\,a^2\,b^9\,d^2\,e^{15}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{13}-44\,a^9\,b^4\,d^2\,e^{13}+40\,a^7\,b^6\,d^2\,e^{13}+168\,a^5\,b^8\,d^2\,e^{13}+20\,a^3\,b^{10}\,d^2\,e^{13}-60\,a\,b^{12}\,d^2\,e^{13}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(a^2-3\,b^2\right)\,\left(\frac{16\,\left(-8\,a^{13}\,b^2\,d^4\,e^{12}+120\,a^9\,b^6\,d^4\,e^{12}+320\,a^7\,b^8\,d^4\,e^{12}+360\,a^5\,b^{10}\,d^4\,e^{12}+192\,a^3\,b^{12}\,d^4\,e^{12}+40\,a\,b^{14}\,d^4\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2-3\,b^2\right)\,\sqrt{-a\,b\,e^3}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}\right)\,\sqrt{-a\,b\,e^3}}{2\,\left(d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5\right)}}\right)\,\left(a^2-3\,b^2\right)\,\sqrt{-a\,b\,e^3}\,1{}\mathrm{i}}{d\,a^4\,b+2\,d\,a^2\,b^3+d\,b^5}","Not used",1,"(atan((((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + ((a^2 - 3*b^2)*((16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + ((a^2 - 3*b^2)*((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (8*(e*cot(c + d*x))^(1/2)*(a^2 - 3*b^2)*(-a*b*e^3)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((b^5*d + 2*a^2*b^3*d + a^4*b*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2)*1i)/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)) + ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - ((a^2 - 3*b^2)*((16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - ((a^2 - 3*b^2)*((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (8*(e*cot(c + d*x))^(1/2)*(a^2 - 3*b^2)*(-a*b*e^3)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((b^5*d + 2*a^2*b^3*d + a^4*b*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2)*1i)/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))/((32*(3*a*b^6*e^18 - a^3*b^4*e^18))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + ((a^2 - 3*b^2)*((16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + ((a^2 - 3*b^2)*((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (8*(e*cot(c + d*x))^(1/2)*(a^2 - 3*b^2)*(-a*b*e^3)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((b^5*d + 2*a^2*b^3*d + a^4*b*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)) + ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - ((a^2 - 3*b^2)*((16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + ((a^2 - 3*b^2)*((16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - ((a^2 - 3*b^2)*((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (8*(e*cot(c + d*x))^(1/2)*(a^2 - 3*b^2)*(-a*b*e^3)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((b^5*d + 2*a^2*b^3*d + a^4*b*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d)))*(-a*b*e^3)^(1/2))/(2*(b^5*d + 2*a^2*b^3*d + a^4*b*d))))*(a^2 - 3*b^2)*(-a*b*e^3)^(1/2)*1i)/(b^5*d + 2*a^2*b^3*d + a^4*b*d) - atan(((((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i - (((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i)/((32*(3*a*b^6*e^18 - a^3*b^4*e^18))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)))*(-e^3/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*2i - atan(((((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i - (((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i)/((32*(3*a*b^6*e^18 - a^3*b^4*e^18))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (((((16*(40*a*b^14*d^4*e^12 + 192*a^3*b^12*d^4*e^12 + 360*a^5*b^10*d^4*e^12 + 320*a^7*b^8*d^4*e^12 + 120*a^9*b^6*d^4*e^12 - 8*a^13*b^2*d^4*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(20*a^3*b^10*d^2*e^13 - 60*a*b^12*d^2*e^13 + 168*a^5*b^8*d^2*e^13 + 40*a^7*b^6*d^2*e^13 - 44*a^9*b^4*d^2*e^13 + 4*a^11*b^2*d^2*e^13))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(2*a^10*b*d^2*e^15 - 78*a^2*b^9*d^2*e^15 + 8*a^4*b^7*d^2*e^15 + 60*a^6*b^5*d^2*e^15 - 24*a^8*b^3*d^2*e^15))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(2*b^9*e^16 + a^8*b*e^16 - 5*a^2*b^7*e^16 + 17*a^4*b^5*e^16 - 7*a^6*b^3*e^16))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)))*(-(e^3*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*2i - (a*e^2*(e*cot(c + d*x))^(1/2))/((a*d*e + b*d*e*cot(c + d*x))*(a^2 + b^2))","B"
78,1,11731,386,3.083976,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + b*cot(c + d*x))^2,x)","\frac{b\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{\left(a\,d\,e+b\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}-\frac{16\,\left(b^7\,e^{13}-9\,a^4\,b^3\,e^{13}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}}\right)\,\sqrt{\frac{e\,1{}\mathrm{i}}{4\,\left(a^4\,d^2-a^3\,b\,d^2\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2+a\,b^3\,d^2\,4{}\mathrm{i}+b^4\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}-\frac{16\,\left(b^7\,e^{13}-9\,a^4\,b^3\,e^{13}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}}\right)\,\sqrt{\frac{e}{4\,\left(a^4\,d^2\,1{}\mathrm{i}-4\,a^3\,b\,d^2-a^2\,b^2\,d^2\,6{}\mathrm{i}+4\,a\,b^3\,d^2+b^4\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,a^2-b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\sqrt{-a\,b\,e}\,1{}\mathrm{i}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}+\frac{\left(3\,a^2-b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\sqrt{-a\,b\,e}\,1{}\mathrm{i}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}}{\frac{16\,\left(b^7\,e^{13}-9\,a^4\,b^3\,e^{13}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{\left(3\,a^2-b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}-\frac{\left(3\,a^2-b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-9\,a^6\,b^3\,e^{12}+17\,a^4\,b^5\,e^{12}-3\,a^2\,b^7\,e^{12}+3\,b^9\,e^{12}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}+\frac{\left(\frac{8\,\left(4\,a^9\,b^2\,d^2\,e^{12}+160\,a^7\,b^4\,d^2\,e^{12}-24\,a^5\,b^6\,d^2\,e^{12}-128\,a^3\,b^8\,d^2\,e^{12}+52\,a\,b^{10}\,d^2\,e^{12}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}-\frac{\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(4\,a^{11}\,b^2\,d^2\,e^{11}+84\,a^9\,b^4\,d^2\,e^{11}+40\,a^7\,b^6\,d^2\,e^{11}-88\,a^5\,b^8\,d^2\,e^{11}+20\,a^3\,b^{10}\,d^2\,e^{11}+68\,a\,b^{12}\,d^2\,e^{11}\right)}{a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4}-\frac{\left(\frac{8\,\left(64\,a^{12}\,b^3\,d^4\,e^{11}+288\,a^{10}\,b^5\,d^4\,e^{11}+480\,a^8\,b^7\,d^4\,e^{11}+320\,a^6\,b^9\,d^4\,e^{11}-96\,a^2\,b^{13}\,d^4\,e^{11}-32\,b^{15}\,d^4\,e^{11}\right)}{a^8\,d^5+4\,a^6\,b^2\,d^5+6\,a^4\,b^4\,d^5+4\,a^2\,b^6\,d^5+b^8\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}\,\left(-32\,a^{14}\,b^3\,d^4\,e^{10}-160\,a^{12}\,b^5\,d^4\,e^{10}-288\,a^{10}\,b^7\,d^4\,e^{10}-160\,a^8\,b^9\,d^4\,e^{10}+160\,a^6\,b^{11}\,d^4\,e^{10}+288\,a^4\,b^{13}\,d^4\,e^{10}+160\,a^2\,b^{15}\,d^4\,e^{10}+32\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)\,\left(a^8\,d^4+4\,a^6\,b^2\,d^4+6\,a^4\,b^4\,d^4+4\,a^2\,b^6\,d^4+b^8\,d^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}\right)\,\sqrt{-a\,b\,e}}{2\,\left(d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4\right)}}\right)\,\left(3\,a^2-b^2\right)\,\sqrt{-a\,b\,e}\,1{}\mathrm{i}}{d\,a^5+2\,d\,a^3\,b^2+d\,a\,b^4}","Not used",1,"(b*e*(e*cot(c + d*x))^(1/2))/((a*d*e + b*d*e*cot(c + d*x))*(a^2 + b^2)) - atan(((((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i - (((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*1i)/((((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2) - (16*(b^7*e^13 - 9*a^4*b^3*e^13))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5)))*(e/(4*(a^4*d^2*1i + b^4*d^2*1i + 4*a*b^3*d^2 - 4*a^3*b*d^2 - a^2*b^2*d^2*6i)))^(1/2)*2i - (atan((((3*a^2 - b^2)*((16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - (((8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (((16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + (((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (8*(e*cot(c + d*x))^(1/2)*(3*a^2 - b^2)*(-a*b*e)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((a^5*d + 2*a^3*b^2*d + a*b^4*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(-a*b*e)^(1/2)*1i)/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)) + ((3*a^2 - b^2)*((16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + (((8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - (((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (8*(e*cot(c + d*x))^(1/2)*(3*a^2 - b^2)*(-a*b*e)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((a^5*d + 2*a^3*b^2*d + a*b^4*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(-a*b*e)^(1/2)*1i)/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))/((16*(b^7*e^13 - 9*a^4*b^3*e^13))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + ((3*a^2 - b^2)*((16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - (((8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (((16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + (((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (8*(e*cot(c + d*x))^(1/2)*(3*a^2 - b^2)*(-a*b*e)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((a^5*d + 2*a^3*b^2*d + a*b^4*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)) - ((3*a^2 - b^2)*((16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) + (((8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (((16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4) - (((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (8*(e*cot(c + d*x))^(1/2)*(3*a^2 - b^2)*(-a*b*e)^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/((a^5*d + 2*a^3*b^2*d + a*b^4*d)*(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(3*a^2 - b^2)*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d)))*(-a*b*e)^(1/2))/(2*(a^5*d + 2*a^3*b^2*d + a*b^4*d))))*(3*a^2 - b^2)*(-a*b*e)^(1/2)*1i)/(a^5*d + 2*a^3*b^2*d + a*b^4*d) - atan(((((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i - (((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*1i)/((((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) - (16*(e*cot(c + d*x))^(1/2)*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (((((8*(320*a^6*b^9*d^4*e^11 - 96*a^2*b^13*d^4*e^11 - 32*b^15*d^4*e^11 + 480*a^8*b^7*d^4*e^11 + 288*a^10*b^5*d^4*e^11 + 64*a^12*b^3*d^4*e^11))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5) + (16*(e*cot(c + d*x))^(1/2)*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*(32*b^17*d^4*e^10 + 160*a^2*b^15*d^4*e^10 + 288*a^4*b^13*d^4*e^10 + 160*a^6*b^11*d^4*e^10 - 160*a^8*b^9*d^4*e^10 - 288*a^10*b^7*d^4*e^10 - 160*a^12*b^5*d^4*e^10 - 32*a^14*b^3*d^4*e^10))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(68*a*b^12*d^2*e^11 + 20*a^3*b^10*d^2*e^11 - 88*a^5*b^8*d^2*e^11 + 40*a^7*b^6*d^2*e^11 + 84*a^9*b^4*d^2*e^11 + 4*a^11*b^2*d^2*e^11))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (8*(52*a*b^10*d^2*e^12 - 128*a^3*b^8*d^2*e^12 - 24*a^5*b^6*d^2*e^12 + 160*a^7*b^4*d^2*e^12 + 4*a^9*b^2*d^2*e^12))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(3*b^9*e^12 - 3*a^2*b^7*e^12 + 17*a^4*b^5*e^12 - 9*a^6*b^3*e^12))/(a^8*d^4 + b^8*d^4 + 4*a^2*b^6*d^4 + 6*a^4*b^4*d^4 + 4*a^6*b^2*d^4))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2) - (16*(b^7*e^13 - 9*a^4*b^3*e^13))/(a^8*d^5 + b^8*d^5 + 4*a^2*b^6*d^5 + 6*a^4*b^4*d^5 + 4*a^6*b^2*d^5)))*((e*1i)/(4*(a^4*d^2 + b^4*d^2 + a*b^3*d^2*4i - a^3*b*d^2*4i - 6*a^2*b^2*d^2)))^(1/2)*2i","B"
79,1,9400,394,8.163231,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + b*cot(c + d*x))^2),x)","\frac{\ln\left(-\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{128\,b^2\,e^{10}\,\left(-a^6+6\,a^4\,b^2+9\,a^2\,b^4+2\,b^6\right)}{a\,d}-256\,b^3\,e^{10}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}-\frac{64\,b^2\,e^9\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-a^8-a^6\,b^2+67\,a^4\,b^4+5\,a^2\,b^6+2\,b^8\right)}{a\,d^2\,{\left(a^2+b^2\right)}^2}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}-\frac{32\,b^5\,e^9\,\left(25\,a^6-85\,a^4\,b^2-13\,a^2\,b^4+b^6\right)}{a^2\,d^3\,{\left(a^2+b^2\right)}^3}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}-\frac{16\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6+11\,a^4\,b^2+7\,a^2\,b^4+b^6\right)}{a^2\,d^4\,{\left(a^2+b^2\right)}^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}-\frac{16\,b^6\,e^8\,\left(5\,a^2+b^2\right)}{a\,d^5\,{\left(a^2+b^2\right)}^4}\right)\,\sqrt{-\frac{1}{1{}\mathrm{i}\,e\,a^4\,d^2-4\,e\,a^3\,b\,d^2-6{}\mathrm{i}\,e\,a^2\,b^2\,d^2+4\,e\,a\,b^3\,d^2+1{}\mathrm{i}\,e\,b^4\,d^2}}}{2}-\ln\left(-\frac{\left(\frac{\left(\frac{\left(\frac{\left(\frac{128\,b^2\,e^{10}\,\left(-a^6+6\,a^4\,b^2+9\,a^2\,b^4+2\,b^6\right)}{a\,d}+256\,b^3\,e^{10}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}+\frac{64\,b^2\,e^9\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-a^8-a^6\,b^2+67\,a^4\,b^4+5\,a^2\,b^6+2\,b^8\right)}{a\,d^2\,{\left(a^2+b^2\right)}^2}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}-\frac{32\,b^5\,e^9\,\left(25\,a^6-85\,a^4\,b^2-13\,a^2\,b^4+b^6\right)}{a^2\,d^3\,{\left(a^2+b^2\right)}^3}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}+\frac{16\,b^5\,e^8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6+11\,a^4\,b^2+7\,a^2\,b^4+b^6\right)}{a^2\,d^4\,{\left(a^2+b^2\right)}^4}\right)\,\sqrt{\frac{1{}\mathrm{i}}{d^2\,e\,{\left(-b+a\,1{}\mathrm{i}\right)}^4}}}{2}-\frac{16\,b^6\,e^8\,\left(5\,a^2+b^2\right)}{a\,d^5\,{\left(a^2+b^2\right)}^4}\right)\,\sqrt{-\frac{1}{4\,\left(1{}\mathrm{i}\,e\,a^4\,d^2-4\,e\,a^3\,b\,d^2-6{}\mathrm{i}\,e\,a^2\,b^2\,d^2+4\,e\,a\,b^3\,d^2+1{}\mathrm{i}\,e\,b^4\,d^2\right)}}-\frac{b^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{a\,\left(a\,d\,e+b\,d\,e\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}+\mathrm{atan}\left(\frac{\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}-\frac{16\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)\,1{}\mathrm{i}-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{16\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)\,1{}\mathrm{i}}{\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}-\frac{16\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}+\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{16\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}-\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}\right)+\frac{32\,\left(5\,a^3\,b^6\,e^8+a\,b^8\,e^8\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}}\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(e\,a^4\,d^2-4{}\mathrm{i}\,e\,a^3\,b\,d^2-6\,e\,a^2\,b^2\,d^2+4{}\mathrm{i}\,e\,a\,b^3\,d^2+e\,b^4\,d^2\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(5\,a^2+b^2\right)\,\sqrt{-a^3\,b^3\,e}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)\,\left(a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}\,1{}\mathrm{i}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(5\,a^2+b^2\right)\,\sqrt{-a^3\,b^3\,e}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)\,\left(a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}\,1{}\mathrm{i}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}}{\frac{32\,\left(5\,a^3\,b^6\,e^8+a\,b^8\,e^8\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}+\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}-\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(5\,a^2+b^2\right)\,\sqrt{-a^3\,b^3\,e}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)\,\left(a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-27\,a^6\,b^5\,e^8+11\,a^4\,b^7\,e^8+7\,a^2\,b^9\,e^8+b^{11}\,e^8\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-50\,a^8\,b^5\,d^2\,e^9+120\,a^6\,b^7\,d^2\,e^9+196\,a^4\,b^9\,d^2\,e^9+24\,a^2\,b^{11}\,d^2\,e^9-2\,b^{13}\,d^2\,e^9\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-4\,a^{13}\,b^2\,d^2\,e^9-12\,a^{11}\,b^4\,d^2\,e^9+256\,a^9\,b^6\,d^2\,e^9+552\,a^7\,b^8\,d^2\,e^9+316\,a^5\,b^{10}\,d^2\,e^9+36\,a^3\,b^{12}\,d^2\,e^9+8\,a\,b^{14}\,d^2\,e^9\right)}{a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4}-\frac{\left(5\,a^2+b^2\right)\,\left(\frac{16\,\left(-8\,a^{15}\,b^2\,d^4\,e^{10}+16\,a^{13}\,b^4\,d^4\,e^{10}+216\,a^{11}\,b^6\,d^4\,e^{10}+560\,a^9\,b^8\,d^4\,e^{10}+680\,a^7\,b^{10}\,d^4\,e^{10}+432\,a^5\,b^{12}\,d^4\,e^{10}+136\,a^3\,b^{14}\,d^4\,e^{10}+16\,a\,b^{16}\,d^4\,e^{10}\right)}{a^{10}\,d^5+4\,a^8\,b^2\,d^5+6\,a^6\,b^4\,d^5+4\,a^4\,b^6\,d^5+a^2\,b^8\,d^5}+\frac{8\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(5\,a^2+b^2\right)\,\sqrt{-a^3\,b^3\,e}\,\left(-32\,a^{16}\,b^3\,d^4\,e^{10}-160\,a^{14}\,b^5\,d^4\,e^{10}-288\,a^{12}\,b^7\,d^4\,e^{10}-160\,a^{10}\,b^9\,d^4\,e^{10}+160\,a^8\,b^{11}\,d^4\,e^{10}+288\,a^6\,b^{13}\,d^4\,e^{10}+160\,a^4\,b^{15}\,d^4\,e^{10}+32\,a^2\,b^{17}\,d^4\,e^{10}\right)}{\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)\,\left(a^{10}\,d^4+4\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4+4\,a^4\,b^6\,d^4+a^2\,b^8\,d^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}\right)\,\sqrt{-a^3\,b^3\,e}}{2\,\left(d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4\right)}}\right)\,\left(5\,a^2+b^2\right)\,\sqrt{-a^3\,b^3\,e}\,1{}\mathrm{i}}{d\,e\,a^7+2\,d\,e\,a^5\,b^2+d\,e\,a^3\,b^4}","Not used",1,"(log(- (((((((((128*b^2*e^10*(2*b^6 - a^6 + 9*a^2*b^4 + 6*a^4*b^2))/(a*d) - 256*b^3*e^10*(e*cot(c + d*x))^(1/2)*(a^2 - b^2)*(a^2 + b^2)^2*(1i/(d^2*e*(a*1i - b)^4))^(1/2))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 - (64*b^2*e^9*(e*cot(c + d*x))^(1/2)*(2*b^8 - a^8 + 5*a^2*b^6 + 67*a^4*b^4 - a^6*b^2))/(a*d^2*(a^2 + b^2)^2))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 - (32*b^5*e^9*(25*a^6 + b^6 - 13*a^2*b^4 - 85*a^4*b^2))/(a^2*d^3*(a^2 + b^2)^3))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 - (16*b^5*e^8*(e*cot(c + d*x))^(1/2)*(b^6 - 27*a^6 + 7*a^2*b^4 + 11*a^4*b^2))/(a^2*d^4*(a^2 + b^2)^4))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 - (16*b^6*e^8*(5*a^2 + b^2))/(a*d^5*(a^2 + b^2)^4))*(-1/(a^4*d^2*e*1i + b^4*d^2*e*1i - a^2*b^2*d^2*e*6i + 4*a*b^3*d^2*e - 4*a^3*b*d^2*e))^(1/2))/2 - log(- (((((((((128*b^2*e^10*(2*b^6 - a^6 + 9*a^2*b^4 + 6*a^4*b^2))/(a*d) + 256*b^3*e^10*(e*cot(c + d*x))^(1/2)*(a^2 - b^2)*(a^2 + b^2)^2*(1i/(d^2*e*(a*1i - b)^4))^(1/2))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 + (64*b^2*e^9*(e*cot(c + d*x))^(1/2)*(2*b^8 - a^8 + 5*a^2*b^6 + 67*a^4*b^4 - a^6*b^2))/(a*d^2*(a^2 + b^2)^2))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 - (32*b^5*e^9*(25*a^6 + b^6 - 13*a^2*b^4 - 85*a^4*b^2))/(a^2*d^3*(a^2 + b^2)^3))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 + (16*b^5*e^8*(e*cot(c + d*x))^(1/2)*(b^6 - 27*a^6 + 7*a^2*b^4 + 11*a^4*b^2))/(a^2*d^4*(a^2 + b^2)^4))*(1i/(d^2*e*(a*1i - b)^4))^(1/2))/2 - (16*b^6*e^8*(5*a^2 + b^2))/(a*d^5*(a^2 + b^2)^4))*(-1/(4*(a^4*d^2*e*1i + b^4*d^2*e*1i - a^2*b^2*d^2*e*6i + 4*a*b^3*d^2*e - 4*a^3*b*d^2*e)))^(1/2) + atan(((-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) - (16*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)) + (16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4))*1i - (-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (16*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)) - (16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4))*1i)/((-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) - (16*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)) + (16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2) + (16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)) + (-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (16*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)) - (16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2) - (16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)) + (32*(a*b^8*e^8 + 5*a^3*b^6*e^8))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5)))*(-1i/(4*(a^4*d^2*e + b^4*d^2*e - 6*a^2*b^2*d^2*e + a*b^3*d^2*e*4i - a^3*b*d^2*e*4i)))^(1/2)*2i + (atan((((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) + ((5*a^2 + b^2)*((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) + ((5*a^2 + b^2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) - (8*(e*cot(c + d*x))^(1/2)*(5*a^2 + b^2)*(-a^3*b^3*e)^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/((a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)*(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2)*1i)/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)) + ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) - ((5*a^2 + b^2)*((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) - ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) - ((5*a^2 + b^2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (8*(e*cot(c + d*x))^(1/2)*(5*a^2 + b^2)*(-a^3*b^3*e)^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/((a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)*(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2)*1i)/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))/((32*(a*b^8*e^8 + 5*a^3*b^6*e^8))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) + ((5*a^2 + b^2)*((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) + ((5*a^2 + b^2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) - (8*(e*cot(c + d*x))^(1/2)*(5*a^2 + b^2)*(-a^3*b^3*e)^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/((a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)*(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)) - ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(b^11*e^8 + 7*a^2*b^9*e^8 + 11*a^4*b^7*e^8 - 27*a^6*b^5*e^8))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) - ((5*a^2 + b^2)*((16*(24*a^2*b^11*d^2*e^9 - 2*b^13*d^2*e^9 + 196*a^4*b^9*d^2*e^9 + 120*a^6*b^7*d^2*e^9 - 50*a^8*b^5*d^2*e^9))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) - ((5*a^2 + b^2)*((16*(e*cot(c + d*x))^(1/2)*(8*a*b^14*d^2*e^9 + 36*a^3*b^12*d^2*e^9 + 316*a^5*b^10*d^2*e^9 + 552*a^7*b^8*d^2*e^9 + 256*a^9*b^6*d^2*e^9 - 12*a^11*b^4*d^2*e^9 - 4*a^13*b^2*d^2*e^9))/(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4) - ((5*a^2 + b^2)*((16*(16*a*b^16*d^4*e^10 + 136*a^3*b^14*d^4*e^10 + 432*a^5*b^12*d^4*e^10 + 680*a^7*b^10*d^4*e^10 + 560*a^9*b^8*d^4*e^10 + 216*a^11*b^6*d^4*e^10 + 16*a^13*b^4*d^4*e^10 - 8*a^15*b^2*d^4*e^10))/(a^10*d^5 + a^2*b^8*d^5 + 4*a^4*b^6*d^5 + 6*a^6*b^4*d^5 + 4*a^8*b^2*d^5) + (8*(e*cot(c + d*x))^(1/2)*(5*a^2 + b^2)*(-a^3*b^3*e)^(1/2)*(32*a^2*b^17*d^4*e^10 + 160*a^4*b^15*d^4*e^10 + 288*a^6*b^13*d^4*e^10 + 160*a^8*b^11*d^4*e^10 - 160*a^10*b^9*d^4*e^10 - 288*a^12*b^7*d^4*e^10 - 160*a^14*b^5*d^4*e^10 - 32*a^16*b^3*d^4*e^10))/((a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)*(a^10*d^4 + a^2*b^8*d^4 + 4*a^4*b^6*d^4 + 6*a^6*b^4*d^4 + 4*a^8*b^2*d^4)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e)))*(-a^3*b^3*e)^(1/2))/(2*(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e))))*(5*a^2 + b^2)*(-a^3*b^3*e)^(1/2)*1i)/(a^7*d*e + a^3*b^4*d*e + 2*a^5*b^2*d*e) - (b^2*(e*cot(c + d*x))^(1/2))/(a*(a*d*e + b*d*e*cot(c + d*x))*(a^2 + b^2))","B"
80,1,15251,437,4.335323,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + b*cot(c + d*x))^2),x)","\frac{\frac{2}{a}+\frac{b\,\mathrm{cot}\left(c+d\,x\right)\,\left(2\,a^2+3\,b^2\right)}{a^2\,\left(a^2+b^2\right)}}{b\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}+a\,d\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}-\mathrm{atan}\left(\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(26496\,a^{25}\,b^{14}\,d^6\,e^{15}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(768\,a^{16}\,b^{27}\,d^8\,e^{18}-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,1{}\mathrm{i}+\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)-\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)-\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)+768\,a^{16}\,b^{27}\,d^8\,e^{18}+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}+26496\,a^{25}\,b^{14}\,d^6\,e^{15}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,1{}\mathrm{i}}{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(26496\,a^{25}\,b^{14}\,d^6\,e^{15}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(768\,a^{16}\,b^{27}\,d^8\,e^{18}-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}-\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)-\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)-\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)+768\,a^{16}\,b^{27}\,d^8\,e^{18}+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}+26496\,a^{25}\,b^{14}\,d^6\,e^{15}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}\right)\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}+144\,a^{14}\,b^{21}\,d^4\,e^{12}+1296\,a^{16}\,b^{19}\,d^4\,e^{12}+4880\,a^{18}\,b^{17}\,d^4\,e^{12}+10000\,a^{20}\,b^{15}\,d^4\,e^{12}+12080\,a^{22}\,b^{13}\,d^4\,e^{12}+8624\,a^{24}\,b^{11}\,d^4\,e^{12}+3376\,a^{26}\,b^9\,d^4\,e^{12}+560\,a^{28}\,b^7\,d^4\,e^{12}}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(a^4\,d^2\,e^3-a^3\,b\,d^2\,e^3\,4{}\mathrm{i}-6\,a^2\,b^2\,d^2\,e^3+a\,b^3\,d^2\,e^3\,4{}\mathrm{i}+b^4\,d^2\,e^3\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)}{2}+\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(13248\,a^{25}\,b^{14}\,d^6\,e^{15}-576\,a^{15}\,b^{24}\,d^6\,e^{15}-4224\,a^{17}\,b^{22}\,d^6\,e^{15}-11888\,a^{19}\,b^{20}\,d^6\,e^{15}-14832\,a^{21}\,b^{18}\,d^6\,e^{15}-3264\,a^{23}\,b^{16}\,d^6\,e^{15}-\frac{\left(\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(384\,a^{16}\,b^{27}\,d^8\,e^{18}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{4}+4352\,a^{18}\,b^{25}\,d^8\,e^{18}+22144\,a^{20}\,b^{23}\,d^8\,e^{18}+66560\,a^{22}\,b^{21}\,d^8\,e^{18}+130560\,a^{24}\,b^{19}\,d^8\,e^{18}+173568\,a^{26}\,b^{17}\,d^8\,e^{18}+155904\,a^{28}\,b^{15}\,d^8\,e^{18}+89088\,a^{30}\,b^{13}\,d^8\,e^{18}+24960\,a^{32}\,b^{11}\,d^8\,e^{18}-3840\,a^{34}\,b^9\,d^8\,e^{18}-6016\,a^{36}\,b^7\,d^8\,e^{18}-2048\,a^{38}\,b^5\,d^8\,e^{18}-256\,a^{40}\,b^3\,d^8\,e^{18}\right)}{2}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)}{2}\right)\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}}{2}+16992\,a^{27}\,b^{12}\,d^6\,e^{15}+9312\,a^{29}\,b^{10}\,d^6\,e^{15}+2688\,a^{31}\,b^8\,d^6\,e^{15}+576\,a^{33}\,b^6\,d^6\,e^{15}+144\,a^{35}\,b^4\,d^6\,e^{15}+16\,a^{37}\,b^2\,d^6\,e^{15}\right)}{2}\right)\,1{}\mathrm{i}+\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)}{2}-\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(13248\,a^{25}\,b^{14}\,d^6\,e^{15}-576\,a^{15}\,b^{24}\,d^6\,e^{15}-4224\,a^{17}\,b^{22}\,d^6\,e^{15}-11888\,a^{19}\,b^{20}\,d^6\,e^{15}-14832\,a^{21}\,b^{18}\,d^6\,e^{15}-3264\,a^{23}\,b^{16}\,d^6\,e^{15}-\frac{\left(\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{4}+384\,a^{16}\,b^{27}\,d^8\,e^{18}+4352\,a^{18}\,b^{25}\,d^8\,e^{18}+22144\,a^{20}\,b^{23}\,d^8\,e^{18}+66560\,a^{22}\,b^{21}\,d^8\,e^{18}+130560\,a^{24}\,b^{19}\,d^8\,e^{18}+173568\,a^{26}\,b^{17}\,d^8\,e^{18}+155904\,a^{28}\,b^{15}\,d^8\,e^{18}+89088\,a^{30}\,b^{13}\,d^8\,e^{18}+24960\,a^{32}\,b^{11}\,d^8\,e^{18}-3840\,a^{34}\,b^9\,d^8\,e^{18}-6016\,a^{36}\,b^7\,d^8\,e^{18}-2048\,a^{38}\,b^5\,d^8\,e^{18}-256\,a^{40}\,b^3\,d^8\,e^{18}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)}{2}\right)\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}}{2}+16992\,a^{27}\,b^{12}\,d^6\,e^{15}+9312\,a^{29}\,b^{10}\,d^6\,e^{15}+2688\,a^{31}\,b^8\,d^6\,e^{15}+576\,a^{33}\,b^6\,d^6\,e^{15}+144\,a^{35}\,b^4\,d^6\,e^{15}+16\,a^{37}\,b^2\,d^6\,e^{15}\right)}{2}\right)\,1{}\mathrm{i}}{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)}{2}+\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(13248\,a^{25}\,b^{14}\,d^6\,e^{15}-576\,a^{15}\,b^{24}\,d^6\,e^{15}-4224\,a^{17}\,b^{22}\,d^6\,e^{15}-11888\,a^{19}\,b^{20}\,d^6\,e^{15}-14832\,a^{21}\,b^{18}\,d^6\,e^{15}-3264\,a^{23}\,b^{16}\,d^6\,e^{15}-\frac{\left(\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(384\,a^{16}\,b^{27}\,d^8\,e^{18}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{4}+4352\,a^{18}\,b^{25}\,d^8\,e^{18}+22144\,a^{20}\,b^{23}\,d^8\,e^{18}+66560\,a^{22}\,b^{21}\,d^8\,e^{18}+130560\,a^{24}\,b^{19}\,d^8\,e^{18}+173568\,a^{26}\,b^{17}\,d^8\,e^{18}+155904\,a^{28}\,b^{15}\,d^8\,e^{18}+89088\,a^{30}\,b^{13}\,d^8\,e^{18}+24960\,a^{32}\,b^{11}\,d^8\,e^{18}-3840\,a^{34}\,b^9\,d^8\,e^{18}-6016\,a^{36}\,b^7\,d^8\,e^{18}-2048\,a^{38}\,b^5\,d^8\,e^{18}-256\,a^{40}\,b^3\,d^8\,e^{18}\right)}{2}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)}{2}\right)\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}}{2}+16992\,a^{27}\,b^{12}\,d^6\,e^{15}+9312\,a^{29}\,b^{10}\,d^6\,e^{15}+2688\,a^{31}\,b^8\,d^6\,e^{15}+576\,a^{33}\,b^6\,d^6\,e^{15}+144\,a^{35}\,b^4\,d^6\,e^{15}+16\,a^{37}\,b^2\,d^6\,e^{15}\right)}{2}\right)-\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)}{2}-\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(13248\,a^{25}\,b^{14}\,d^6\,e^{15}-576\,a^{15}\,b^{24}\,d^6\,e^{15}-4224\,a^{17}\,b^{22}\,d^6\,e^{15}-11888\,a^{19}\,b^{20}\,d^6\,e^{15}-14832\,a^{21}\,b^{18}\,d^6\,e^{15}-3264\,a^{23}\,b^{16}\,d^6\,e^{15}-\frac{\left(\frac{\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{4}+384\,a^{16}\,b^{27}\,d^8\,e^{18}+4352\,a^{18}\,b^{25}\,d^8\,e^{18}+22144\,a^{20}\,b^{23}\,d^8\,e^{18}+66560\,a^{22}\,b^{21}\,d^8\,e^{18}+130560\,a^{24}\,b^{19}\,d^8\,e^{18}+173568\,a^{26}\,b^{17}\,d^8\,e^{18}+155904\,a^{28}\,b^{15}\,d^8\,e^{18}+89088\,a^{30}\,b^{13}\,d^8\,e^{18}+24960\,a^{32}\,b^{11}\,d^8\,e^{18}-3840\,a^{34}\,b^9\,d^8\,e^{18}-6016\,a^{36}\,b^7\,d^8\,e^{18}-2048\,a^{38}\,b^5\,d^8\,e^{18}-256\,a^{40}\,b^3\,d^8\,e^{18}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)}{2}\right)\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}}{2}+16992\,a^{27}\,b^{12}\,d^6\,e^{15}+9312\,a^{29}\,b^{10}\,d^6\,e^{15}+2688\,a^{31}\,b^8\,d^6\,e^{15}+576\,a^{33}\,b^6\,d^6\,e^{15}+144\,a^{35}\,b^4\,d^6\,e^{15}+16\,a^{37}\,b^2\,d^6\,e^{15}\right)}{2}\right)+144\,a^{14}\,b^{21}\,d^4\,e^{12}+1296\,a^{16}\,b^{19}\,d^4\,e^{12}+4880\,a^{18}\,b^{17}\,d^4\,e^{12}+10000\,a^{20}\,b^{15}\,d^4\,e^{12}+12080\,a^{22}\,b^{13}\,d^4\,e^{12}+8624\,a^{24}\,b^{11}\,d^4\,e^{12}+3376\,a^{26}\,b^9\,d^4\,e^{12}+560\,a^{28}\,b^7\,d^4\,e^{12}}\right)\,\sqrt{\frac{1}{a^4\,d^2\,e^3\,1{}\mathrm{i}-4\,a^3\,b\,d^2\,e^3-a^2\,b^2\,d^2\,e^3\,6{}\mathrm{i}+4\,a\,b^3\,d^2\,e^3+b^4\,d^2\,e^3\,1{}\mathrm{i}}}\,1{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)+\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(26496\,a^{25}\,b^{14}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}-\frac{\left(7\,a^2+3\,b^2\right)\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)+\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(768\,a^{16}\,b^{27}\,d^8\,e^{18}+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\sqrt{-a^5\,b^5\,e^3}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,1{}\mathrm{i}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}+\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)-\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(26496\,a^{25}\,b^{14}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}+\frac{\left(7\,a^2+3\,b^2\right)\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)-\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(768\,a^{16}\,b^{27}\,d^8\,e^{18}+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\sqrt{-a^5\,b^5\,e^3}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,1{}\mathrm{i}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}}{\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)+\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(26496\,a^{25}\,b^{14}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}-\frac{\left(7\,a^2+3\,b^2\right)\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)+\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(768\,a^{16}\,b^{27}\,d^8\,e^{18}+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\sqrt{-a^5\,b^5\,e^3}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}-\frac{\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(32\,a^{32}\,b^5\,d^5\,e^{13}-560\,a^{30}\,b^7\,d^5\,e^{13}-3136\,a^{28}\,b^9\,d^5\,e^{13}-5632\,a^{26}\,b^{11}\,d^5\,e^{13}-2816\,a^{24}\,b^{13}\,d^5\,e^{13}+3872\,a^{22}\,b^{15}\,d^5\,e^{13}+6720\,a^{20}\,b^{17}\,d^5\,e^{13}+4224\,a^{18}\,b^{19}\,d^5\,e^{13}+1248\,a^{16}\,b^{21}\,d^5\,e^{13}+144\,a^{14}\,b^{23}\,d^5\,e^{13}\right)-\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(26496\,a^{25}\,b^{14}\,d^6\,e^{15}-8448\,a^{17}\,b^{22}\,d^6\,e^{15}-23776\,a^{19}\,b^{20}\,d^6\,e^{15}-29664\,a^{21}\,b^{18}\,d^6\,e^{15}-6528\,a^{23}\,b^{16}\,d^6\,e^{15}-1152\,a^{15}\,b^{24}\,d^6\,e^{15}+33984\,a^{27}\,b^{12}\,d^6\,e^{15}+18624\,a^{29}\,b^{10}\,d^6\,e^{15}+5376\,a^{31}\,b^8\,d^6\,e^{15}+1152\,a^{33}\,b^6\,d^6\,e^{15}+288\,a^{35}\,b^4\,d^6\,e^{15}+32\,a^{37}\,b^2\,d^6\,e^{15}+\frac{\left(7\,a^2+3\,b^2\right)\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{39}\,b^2\,d^7\,e^{16}+512\,a^{37}\,b^4\,d^7\,e^{16}+704\,a^{35}\,b^6\,d^7\,e^{16}+3200\,a^{33}\,b^8\,d^7\,e^{16}+37632\,a^{31}\,b^{10}\,d^7\,e^{16}+156160\,a^{29}\,b^{12}\,d^7\,e^{16}+337792\,a^{27}\,b^{14}\,d^7\,e^{16}+443136\,a^{25}\,b^{16}\,d^7\,e^{16}+372800\,a^{23}\,b^{18}\,d^7\,e^{16}+202752\,a^{21}\,b^{20}\,d^7\,e^{16}+69056\,a^{19}\,b^{22}\,d^7\,e^{16}+13440\,a^{17}\,b^{24}\,d^7\,e^{16}+1152\,a^{15}\,b^{26}\,d^7\,e^{16}\right)-\frac{\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(768\,a^{16}\,b^{27}\,d^8\,e^{18}+8704\,a^{18}\,b^{25}\,d^8\,e^{18}+44288\,a^{20}\,b^{23}\,d^8\,e^{18}+133120\,a^{22}\,b^{21}\,d^8\,e^{18}+261120\,a^{24}\,b^{19}\,d^8\,e^{18}+347136\,a^{26}\,b^{17}\,d^8\,e^{18}+311808\,a^{28}\,b^{15}\,d^8\,e^{18}+178176\,a^{30}\,b^{13}\,d^8\,e^{18}+49920\,a^{32}\,b^{11}\,d^8\,e^{18}-7680\,a^{34}\,b^9\,d^8\,e^{18}-12032\,a^{36}\,b^7\,d^8\,e^{18}-4096\,a^{38}\,b^5\,d^8\,e^{18}-512\,a^{40}\,b^3\,d^8\,e^{18}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,\left(-512\,a^{42}\,b^3\,d^9\,e^{19}-5120\,a^{40}\,b^5\,d^9\,e^{19}-22528\,a^{38}\,b^7\,d^9\,e^{19}-56320\,a^{36}\,b^9\,d^9\,e^{19}-84480\,a^{34}\,b^{11}\,d^9\,e^{19}-67584\,a^{32}\,b^{13}\,d^9\,e^{19}+67584\,a^{28}\,b^{17}\,d^9\,e^{19}+84480\,a^{26}\,b^{19}\,d^9\,e^{19}+56320\,a^{24}\,b^{21}\,d^9\,e^{19}+22528\,a^{22}\,b^{23}\,d^9\,e^{19}+5120\,a^{20}\,b^{25}\,d^9\,e^{19}+512\,a^{18}\,b^{27}\,d^9\,e^{19}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\sqrt{-a^5\,b^5\,e^3}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}\right)\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}}{2\,\left(d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3\right)}+144\,a^{14}\,b^{21}\,d^4\,e^{12}+1296\,a^{16}\,b^{19}\,d^4\,e^{12}+4880\,a^{18}\,b^{17}\,d^4\,e^{12}+10000\,a^{20}\,b^{15}\,d^4\,e^{12}+12080\,a^{22}\,b^{13}\,d^4\,e^{12}+8624\,a^{24}\,b^{11}\,d^4\,e^{12}+3376\,a^{26}\,b^9\,d^4\,e^{12}+560\,a^{28}\,b^7\,d^4\,e^{12}}\right)\,\left(7\,a^2+3\,b^2\right)\,\sqrt{-a^5\,b^5\,e^3}\,1{}\mathrm{i}}{d\,a^9\,e^3+2\,d\,a^7\,b^2\,e^3+d\,a^5\,b^4\,e^3}","Not used",1,"(2/a + (b*cot(c + d*x)*(2*a^2 + 3*b^2))/(a^2*(a^2 + b^2)))/(b*d*(e*cot(c + d*x))^(3/2) + a*d*e*(e*cot(c + d*x))^(1/2)) - atan((((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) + (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(26496*a^25*b^14*d^6*e^15 - 1152*a^15*b^24*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 - ((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) + (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(768*a^16*b^27*d^8*e^18 - (e*cot(c + d*x))^(1/2)*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19) + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2) + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*1i + ((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) - (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) - (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*((e*cot(c + d*x))^(1/2)*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19) + 768*a^16*b^27*d^8*e^18 + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2) - 1152*a^15*b^24*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 + 26496*a^25*b^14*d^6*e^15 + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*1i)/(((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) + (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(26496*a^25*b^14*d^6*e^15 - 1152*a^15*b^24*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 - ((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) + (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(768*a^16*b^27*d^8*e^18 - (e*cot(c + d*x))^(1/2)*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19) + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2) + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) - (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) - (1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*((e*cot(c + d*x))^(1/2)*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19) + 768*a^16*b^27*d^8*e^18 + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2) - 1152*a^15*b^24*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 + 26496*a^25*b^14*d^6*e^15 + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2) + 144*a^14*b^21*d^4*e^12 + 1296*a^16*b^19*d^4*e^12 + 4880*a^18*b^17*d^4*e^12 + 10000*a^20*b^15*d^4*e^12 + 12080*a^22*b^13*d^4*e^12 + 8624*a^24*b^11*d^4*e^12 + 3376*a^26*b^9*d^4*e^12 + 560*a^28*b^7*d^4*e^12))*(1i/(4*(a^4*d^2*e^3 + b^4*d^2*e^3 + a*b^3*d^2*e^3*4i - a^3*b*d^2*e^3*4i - 6*a^2*b^2*d^2*e^3)))^(1/2)*2i - atan(((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13))/2 + ((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(13248*a^25*b^14*d^6*e^15 - 576*a^15*b^24*d^6*e^15 - 4224*a^17*b^22*d^6*e^15 - 11888*a^19*b^20*d^6*e^15 - 14832*a^21*b^18*d^6*e^15 - 3264*a^23*b^16*d^6*e^15 - ((((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(384*a^16*b^27*d^8*e^18 - ((e*cot(c + d*x))^(1/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/4 + 4352*a^18*b^25*d^8*e^18 + 22144*a^20*b^23*d^8*e^18 + 66560*a^22*b^21*d^8*e^18 + 130560*a^24*b^19*d^8*e^18 + 173568*a^26*b^17*d^8*e^18 + 155904*a^28*b^15*d^8*e^18 + 89088*a^30*b^13*d^8*e^18 + 24960*a^32*b^11*d^8*e^18 - 3840*a^34*b^9*d^8*e^18 - 6016*a^36*b^7*d^8*e^18 - 2048*a^38*b^5*d^8*e^18 - 256*a^40*b^3*d^8*e^18))/2 + ((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16))/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2))/2 + 16992*a^27*b^12*d^6*e^15 + 9312*a^29*b^10*d^6*e^15 + 2688*a^31*b^8*d^6*e^15 + 576*a^33*b^6*d^6*e^15 + 144*a^35*b^4*d^6*e^15 + 16*a^37*b^2*d^6*e^15))/2)*1i + (1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13))/2 - ((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(13248*a^25*b^14*d^6*e^15 - 576*a^15*b^24*d^6*e^15 - 4224*a^17*b^22*d^6*e^15 - 11888*a^19*b^20*d^6*e^15 - 14832*a^21*b^18*d^6*e^15 - 3264*a^23*b^16*d^6*e^15 - ((((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/4 + 384*a^16*b^27*d^8*e^18 + 4352*a^18*b^25*d^8*e^18 + 22144*a^20*b^23*d^8*e^18 + 66560*a^22*b^21*d^8*e^18 + 130560*a^24*b^19*d^8*e^18 + 173568*a^26*b^17*d^8*e^18 + 155904*a^28*b^15*d^8*e^18 + 89088*a^30*b^13*d^8*e^18 + 24960*a^32*b^11*d^8*e^18 - 3840*a^34*b^9*d^8*e^18 - 6016*a^36*b^7*d^8*e^18 - 2048*a^38*b^5*d^8*e^18 - 256*a^40*b^3*d^8*e^18))/2 - ((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16))/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2))/2 + 16992*a^27*b^12*d^6*e^15 + 9312*a^29*b^10*d^6*e^15 + 2688*a^31*b^8*d^6*e^15 + 576*a^33*b^6*d^6*e^15 + 144*a^35*b^4*d^6*e^15 + 16*a^37*b^2*d^6*e^15))/2)*1i)/((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13))/2 + ((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(13248*a^25*b^14*d^6*e^15 - 576*a^15*b^24*d^6*e^15 - 4224*a^17*b^22*d^6*e^15 - 11888*a^19*b^20*d^6*e^15 - 14832*a^21*b^18*d^6*e^15 - 3264*a^23*b^16*d^6*e^15 - ((((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(384*a^16*b^27*d^8*e^18 - ((e*cot(c + d*x))^(1/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/4 + 4352*a^18*b^25*d^8*e^18 + 22144*a^20*b^23*d^8*e^18 + 66560*a^22*b^21*d^8*e^18 + 130560*a^24*b^19*d^8*e^18 + 173568*a^26*b^17*d^8*e^18 + 155904*a^28*b^15*d^8*e^18 + 89088*a^30*b^13*d^8*e^18 + 24960*a^32*b^11*d^8*e^18 - 3840*a^34*b^9*d^8*e^18 - 6016*a^36*b^7*d^8*e^18 - 2048*a^38*b^5*d^8*e^18 - 256*a^40*b^3*d^8*e^18))/2 + ((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16))/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2))/2 + 16992*a^27*b^12*d^6*e^15 + 9312*a^29*b^10*d^6*e^15 + 2688*a^31*b^8*d^6*e^15 + 576*a^33*b^6*d^6*e^15 + 144*a^35*b^4*d^6*e^15 + 16*a^37*b^2*d^6*e^15))/2) - (1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13))/2 - ((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(13248*a^25*b^14*d^6*e^15 - 576*a^15*b^24*d^6*e^15 - 4224*a^17*b^22*d^6*e^15 - 11888*a^19*b^20*d^6*e^15 - 14832*a^21*b^18*d^6*e^15 - 3264*a^23*b^16*d^6*e^15 - ((((1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(((e*cot(c + d*x))^(1/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/4 + 384*a^16*b^27*d^8*e^18 + 4352*a^18*b^25*d^8*e^18 + 22144*a^20*b^23*d^8*e^18 + 66560*a^22*b^21*d^8*e^18 + 130560*a^24*b^19*d^8*e^18 + 173568*a^26*b^17*d^8*e^18 + 155904*a^28*b^15*d^8*e^18 + 89088*a^30*b^13*d^8*e^18 + 24960*a^32*b^11*d^8*e^18 - 3840*a^34*b^9*d^8*e^18 - 6016*a^36*b^7*d^8*e^18 - 2048*a^38*b^5*d^8*e^18 - 256*a^40*b^3*d^8*e^18))/2 - ((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16))/2)*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2))/2 + 16992*a^27*b^12*d^6*e^15 + 9312*a^29*b^10*d^6*e^15 + 2688*a^31*b^8*d^6*e^15 + 576*a^33*b^6*d^6*e^15 + 144*a^35*b^4*d^6*e^15 + 16*a^37*b^2*d^6*e^15))/2) + 144*a^14*b^21*d^4*e^12 + 1296*a^16*b^19*d^4*e^12 + 4880*a^18*b^17*d^4*e^12 + 10000*a^20*b^15*d^4*e^12 + 12080*a^22*b^13*d^4*e^12 + 8624*a^24*b^11*d^4*e^12 + 3376*a^26*b^9*d^4*e^12 + 560*a^28*b^7*d^4*e^12))*(1/(a^4*d^2*e^3*1i + b^4*d^2*e^3*1i + 4*a*b^3*d^2*e^3 - 4*a^3*b*d^2*e^3 - a^2*b^2*d^2*e^3*6i))^(1/2)*1i - (atan(((((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) + ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(26496*a^25*b^14*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 - 1152*a^15*b^24*d^6*e^15 + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15 - ((7*a^2 + 3*b^2)*((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) + ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(768*a^16*b^27*d^8*e^18 + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18 - ((e*cot(c + d*x))^(1/2)*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(-a^5*b^5*e^3)^(1/2))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*1i)/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)) + (((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) - ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(26496*a^25*b^14*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 - 1152*a^15*b^24*d^6*e^15 + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15 + ((7*a^2 + 3*b^2)*((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) - ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(768*a^16*b^27*d^8*e^18 + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(-a^5*b^5*e^3)^(1/2))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*1i)/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))/((((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) + ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(26496*a^25*b^14*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 - 1152*a^15*b^24*d^6*e^15 + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15 - ((7*a^2 + 3*b^2)*((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) + ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(768*a^16*b^27*d^8*e^18 + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18 - ((e*cot(c + d*x))^(1/2)*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(-a^5*b^5*e^3)^(1/2))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)) - (((e*cot(c + d*x))^(1/2)*(144*a^14*b^23*d^5*e^13 + 1248*a^16*b^21*d^5*e^13 + 4224*a^18*b^19*d^5*e^13 + 6720*a^20*b^17*d^5*e^13 + 3872*a^22*b^15*d^5*e^13 - 2816*a^24*b^13*d^5*e^13 - 5632*a^26*b^11*d^5*e^13 - 3136*a^28*b^9*d^5*e^13 - 560*a^30*b^7*d^5*e^13 + 32*a^32*b^5*d^5*e^13) - ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(26496*a^25*b^14*d^6*e^15 - 8448*a^17*b^22*d^6*e^15 - 23776*a^19*b^20*d^6*e^15 - 29664*a^21*b^18*d^6*e^15 - 6528*a^23*b^16*d^6*e^15 - 1152*a^15*b^24*d^6*e^15 + 33984*a^27*b^12*d^6*e^15 + 18624*a^29*b^10*d^6*e^15 + 5376*a^31*b^8*d^6*e^15 + 1152*a^33*b^6*d^6*e^15 + 288*a^35*b^4*d^6*e^15 + 32*a^37*b^2*d^6*e^15 + ((7*a^2 + 3*b^2)*((e*cot(c + d*x))^(1/2)*(1152*a^15*b^26*d^7*e^16 + 13440*a^17*b^24*d^7*e^16 + 69056*a^19*b^22*d^7*e^16 + 202752*a^21*b^20*d^7*e^16 + 372800*a^23*b^18*d^7*e^16 + 443136*a^25*b^16*d^7*e^16 + 337792*a^27*b^14*d^7*e^16 + 156160*a^29*b^12*d^7*e^16 + 37632*a^31*b^10*d^7*e^16 + 3200*a^33*b^8*d^7*e^16 + 704*a^35*b^6*d^7*e^16 + 512*a^37*b^4*d^7*e^16 + 64*a^39*b^2*d^7*e^16) - ((7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(768*a^16*b^27*d^8*e^18 + 8704*a^18*b^25*d^8*e^18 + 44288*a^20*b^23*d^8*e^18 + 133120*a^22*b^21*d^8*e^18 + 261120*a^24*b^19*d^8*e^18 + 347136*a^26*b^17*d^8*e^18 + 311808*a^28*b^15*d^8*e^18 + 178176*a^30*b^13*d^8*e^18 + 49920*a^32*b^11*d^8*e^18 - 7680*a^34*b^9*d^8*e^18 - 12032*a^36*b^7*d^8*e^18 - 4096*a^38*b^5*d^8*e^18 - 512*a^40*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*(512*a^18*b^27*d^9*e^19 + 5120*a^20*b^25*d^9*e^19 + 22528*a^22*b^23*d^9*e^19 + 56320*a^24*b^21*d^9*e^19 + 84480*a^26*b^19*d^9*e^19 + 67584*a^28*b^17*d^9*e^19 - 67584*a^32*b^13*d^9*e^19 - 84480*a^34*b^11*d^9*e^19 - 56320*a^36*b^9*d^9*e^19 - 22528*a^38*b^7*d^9*e^19 - 5120*a^40*b^5*d^9*e^19 - 512*a^42*b^3*d^9*e^19))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(-a^5*b^5*e^3)^(1/2))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3))))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)))*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2))/(2*(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)) + 144*a^14*b^21*d^4*e^12 + 1296*a^16*b^19*d^4*e^12 + 4880*a^18*b^17*d^4*e^12 + 10000*a^20*b^15*d^4*e^12 + 12080*a^22*b^13*d^4*e^12 + 8624*a^24*b^11*d^4*e^12 + 3376*a^26*b^9*d^4*e^12 + 560*a^28*b^7*d^4*e^12))*(7*a^2 + 3*b^2)*(-a^5*b^5*e^3)^(1/2)*1i)/(a^9*d*e^3 + a^5*b^4*d*e^3 + 2*a^7*b^2*d*e^3)","B"
81,1,20651,529,10.398729,"\text{Not used}","int((e*cot(c + d*x))^(9/2)/(a + b*cot(c + d*x))^3,x)","-\frac{\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(7\,a^6\,e^6+15\,a^4\,b^2\,e^6\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(9\,a^5\,e^5+17\,a^3\,b^2\,e^5\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,a^2\,b^3\,e^2+2\,d\,a\,b^4\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,b^5\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}+\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}}{\frac{225\,a^{15}\,e^{33}+1380\,a^{13}\,b^2\,e^{33}+4006\,a^{11}\,b^4\,e^{33}+5916\,a^9\,b^6\,e^{33}+4457\,a^7\,b^8\,e^{33}+872\,a^5\,b^{10}\,e^{33}+504\,a^3\,b^{12}\,e^{33}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}}\right)\,\sqrt{-\frac{e^9\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\frac{225\,a^{15}\,e^{33}+1380\,a^{13}\,b^2\,e^{33}+4006\,a^{11}\,b^4\,e^{33}+5916\,a^9\,b^6\,e^{33}+4457\,a^7\,b^8\,e^{33}+872\,a^5\,b^{10}\,e^{33}+504\,a^3\,b^{12}\,e^{33}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}}\right)\,\sqrt{-\frac{e^9}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\frac{2\,e^4\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}-\frac{\left(\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}+\frac{\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)\,\left(a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,1{}\mathrm{i}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}+\frac{\left(\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}-\frac{\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)\,\left(a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,1{}\mathrm{i}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}}{\frac{225\,a^{15}\,e^{33}+1380\,a^{13}\,b^2\,e^{33}+4006\,a^{11}\,b^4\,e^{33}+5916\,a^9\,b^6\,e^{33}+4457\,a^7\,b^8\,e^{33}+872\,a^5\,b^{10}\,e^{33}+504\,a^3\,b^{12}\,e^{33}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}-\frac{\left(\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}+\frac{\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)\,\left(a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{18}\,e^{28}-30\,a^{16}\,b^2\,e^{28}+4049\,a^{14}\,b^4\,e^{28}+16860\,a^{12}\,b^6\,e^{28}+26801\,a^{10}\,b^8\,e^{28}+18050\,a^8\,b^{10}\,e^{28}-3841\,a^6\,b^{12}\,e^{28}+192\,a^4\,b^{14}\,e^{28}+128\,a^2\,b^{16}\,e^{28}+32\,b^{18}\,e^{28}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}+\frac{\left(\frac{2250\,a^{20}\,b\,d^2\,e^{24}+11550\,a^{18}\,b^3\,d^2\,e^{24}+22210\,a^{16}\,b^5\,d^2\,e^{24}-3578\,a^{14}\,b^7\,d^2\,e^{24}-85314\,a^{12}\,b^9\,d^2\,e^{24}-150758\,a^{10}\,b^{11}\,d^2\,e^{24}-105162\,a^8\,b^{13}\,d^2\,e^{24}-10974\,a^6\,b^{15}\,d^2\,e^{24}+12288\,a^4\,b^{17}\,d^2\,e^{24}+32\,a^2\,b^{19}\,d^2\,e^{24}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(1800\,a^{23}\,b\,d^2\,e^{19}+18240\,a^{21}\,b^3\,d^2\,e^{19}+87008\,a^{19}\,b^5\,d^2\,e^{19}+248064\,a^{17}\,b^7\,d^2\,e^{19}+455472\,a^{15}\,b^9\,d^2\,e^{19}+541632\,a^{13}\,b^{11}\,d^2\,e^{19}+402912\,a^{11}\,b^{13}\,d^2\,e^{19}+177344\,a^9\,b^{15}\,d^2\,e^{19}+46088\,a^7\,b^{17}\,d^2\,e^{19}+8448\,a^5\,b^{19}\,d^2\,e^{19}-1024\,a^3\,b^{21}\,d^2\,e^{19}-1472\,a\,b^{23}\,d^2\,e^{19}\right)}{a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4}-\frac{\left(\frac{960\,a^{21}\,b^6\,d^4\,e^{15}+10304\,a^{19}\,b^8\,d^4\,e^{15}+48000\,a^{17}\,b^{10}\,d^4\,e^{15}+128256\,a^{15}\,b^{12}\,d^4\,e^{15}+217728\,a^{13}\,b^{14}\,d^4\,e^{15}+244608\,a^{11}\,b^{16}\,d^4\,e^{15}+182784\,a^9\,b^{18}\,d^4\,e^{15}+88320\,a^7\,b^{20}\,d^4\,e^{15}+25536\,a^5\,b^{22}\,d^4\,e^{15}+3648\,a^3\,b^{24}\,d^4\,e^{15}+128\,a\,b^{26}\,d^4\,e^{15}}{a^{16}\,b^5\,d^5+8\,a^{14}\,b^7\,d^5+28\,a^{12}\,b^9\,d^5+56\,a^{10}\,b^{11}\,d^5+70\,a^8\,b^{13}\,d^5+56\,a^6\,b^{15}\,d^5+28\,a^4\,b^{17}\,d^5+8\,a^2\,b^{19}\,d^5+b^{21}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,\left(-512\,a^{22}\,b^8\,d^4\,e^{10}-4608\,a^{20}\,b^{10}\,d^4\,e^{10}-17920\,a^{18}\,b^{12}\,d^4\,e^{10}-38400\,a^{16}\,b^{14}\,d^4\,e^{10}-46080\,a^{14}\,b^{16}\,d^4\,e^{10}-21504\,a^{12}\,b^{18}\,d^4\,e^{10}+21504\,a^{10}\,b^{20}\,d^4\,e^{10}+46080\,a^8\,b^{22}\,d^4\,e^{10}+38400\,a^6\,b^{24}\,d^4\,e^{10}+17920\,a^4\,b^{26}\,d^4\,e^{10}+4608\,a^2\,b^{28}\,d^4\,e^{10}+512\,b^{30}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)\,\left(a^{16}\,b^5\,d^4+8\,a^{14}\,b^7\,d^4+28\,a^{12}\,b^9\,d^4+56\,a^{10}\,b^{11}\,d^4+70\,a^8\,b^{13}\,d^4+56\,a^6\,b^{15}\,d^4+28\,a^4\,b^{17}\,d^4+8\,a^2\,b^{19}\,d^4+b^{21}\,d^4\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}}{8\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}}\right)\,\left(15\,a^4+46\,a^2\,b^2+63\,b^4\right)\,\sqrt{-a^5\,b^7\,e^9}\,1{}\mathrm{i}}{4\,\left(d\,a^6\,b^7+3\,d\,a^4\,b^9+3\,d\,a^2\,b^{11}+d\,b^{13}\right)}","Not used",1,"atan(((((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((e*cot(c + d*x))^(1/2)*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i - (((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((e*cot(c + d*x))^(1/2)*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i)/((225*a^15*e^33 + 504*a^3*b^12*e^33 + 872*a^5*b^10*e^33 + 4457*a^7*b^8*e^33 + 5916*a^9*b^6*e^33 + 4006*a^11*b^4*e^33 + 1380*a^13*b^2*e^33)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + (((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((e*cot(c + d*x))^(1/2)*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((e*cot(c + d*x))^(1/2)*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)))*(-(e^9*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*2i - (((e*cot(c + d*x))^(1/2)*(7*a^6*e^6 + 15*a^4*b^2*e^6))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (b*(e*cot(c + d*x))^(3/2)*(9*a^5*e^5 + 17*a^3*b^2*e^5))/(4*(a^4 + b^4 + 2*a^2*b^2)))/(a^2*b^3*d*e^2 + b^5*d*e^2*cot(c + d*x)^2 + 2*a*b^4*d*e^2*cot(c + d*x)) + atan(((((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((e*cot(c + d*x))^(1/2)*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i - (((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((e*cot(c + d*x))^(1/2)*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i)/((225*a^15*e^33 + 504*a^3*b^12*e^33 + 872*a^5*b^10*e^33 + 4457*a^7*b^8*e^33 + 5916*a^9*b^6*e^33 + 4006*a^11*b^4*e^33 + 1380*a^13*b^2*e^33)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + (((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((e*cot(c + d*x))^(1/2)*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (((((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((e*cot(c + d*x))^(1/2)*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)))*(-e^9/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*2i - (2*e^4*(e*cot(c + d*x))^(1/2))/(b^3*d) + (atan((((((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) - (((2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) + (((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((e*cot(c + d*x))^(1/2)*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)*(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*1i)/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)) + ((((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) + (((2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) - (((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((e*cot(c + d*x))^(1/2)*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)*(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*1i)/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))/((225*a^15*e^33 + 504*a^3*b^12*e^33 + 872*a^5*b^10*e^33 + 4457*a^7*b^8*e^33 + 5916*a^9*b^6*e^33 + 4006*a^11*b^4*e^33 + 1380*a^13*b^2*e^33)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) - (((2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) + (((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((e*cot(c + d*x))^(1/2)*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)*(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)) + ((((e*cot(c + d*x))^(1/2)*(32*b^18*e^28 - 225*a^18*e^28 + 128*a^2*b^16*e^28 + 192*a^4*b^14*e^28 - 3841*a^6*b^12*e^28 + 18050*a^8*b^10*e^28 + 26801*a^10*b^8*e^28 + 16860*a^12*b^6*e^28 + 4049*a^14*b^4*e^28 - 30*a^16*b^2*e^28))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) + (((2250*a^20*b*d^2*e^24 + 32*a^2*b^19*d^2*e^24 + 12288*a^4*b^17*d^2*e^24 - 10974*a^6*b^15*d^2*e^24 - 105162*a^8*b^13*d^2*e^24 - 150758*a^10*b^11*d^2*e^24 - 85314*a^12*b^9*d^2*e^24 - 3578*a^14*b^7*d^2*e^24 + 22210*a^16*b^5*d^2*e^24 + 11550*a^18*b^3*d^2*e^24)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) - ((((e*cot(c + d*x))^(1/2)*(1800*a^23*b*d^2*e^19 - 1472*a*b^23*d^2*e^19 - 1024*a^3*b^21*d^2*e^19 + 8448*a^5*b^19*d^2*e^19 + 46088*a^7*b^17*d^2*e^19 + 177344*a^9*b^15*d^2*e^19 + 402912*a^11*b^13*d^2*e^19 + 541632*a^13*b^11*d^2*e^19 + 455472*a^15*b^9*d^2*e^19 + 248064*a^17*b^7*d^2*e^19 + 87008*a^19*b^5*d^2*e^19 + 18240*a^21*b^3*d^2*e^19))/(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4) - (((128*a*b^26*d^4*e^15 + 3648*a^3*b^24*d^4*e^15 + 25536*a^5*b^22*d^4*e^15 + 88320*a^7*b^20*d^4*e^15 + 182784*a^9*b^18*d^4*e^15 + 244608*a^11*b^16*d^4*e^15 + 217728*a^13*b^14*d^4*e^15 + 128256*a^15*b^12*d^4*e^15 + 48000*a^17*b^10*d^4*e^15 + 10304*a^19*b^8*d^4*e^15 + 960*a^21*b^6*d^4*e^15)/(b^21*d^5 + 8*a^2*b^19*d^5 + 28*a^4*b^17*d^5 + 56*a^6*b^15*d^5 + 70*a^8*b^13*d^5 + 56*a^10*b^11*d^5 + 28*a^12*b^9*d^5 + 8*a^14*b^7*d^5 + a^16*b^5*d^5) + ((e*cot(c + d*x))^(1/2)*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*(512*b^30*d^4*e^10 + 4608*a^2*b^28*d^4*e^10 + 17920*a^4*b^26*d^4*e^10 + 38400*a^6*b^24*d^4*e^10 + 46080*a^8*b^22*d^4*e^10 + 21504*a^10*b^20*d^4*e^10 - 21504*a^12*b^18*d^4*e^10 - 46080*a^14*b^16*d^4*e^10 - 38400*a^16*b^14*d^4*e^10 - 17920*a^18*b^12*d^4*e^10 - 4608*a^20*b^10*d^4*e^10 - 512*a^22*b^8*d^4*e^10))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)*(b^21*d^4 + 8*a^2*b^19*d^4 + 28*a^4*b^17*d^4 + 56*a^6*b^15*d^4 + 70*a^8*b^13*d^4 + 56*a^10*b^11*d^4 + 28*a^12*b^9*d^4 + 8*a^14*b^7*d^4 + a^16*b^5*d^4)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d)))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2))/(8*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d))))*(15*a^4 + 63*b^4 + 46*a^2*b^2)*(-a^5*b^7*e^9)^(1/2)*1i)/(4*(b^13*d + 3*a^2*b^11*d + 3*a^4*b^9*d + a^6*b^7*d))","B"
82,1,20089,476,7.261764,"\text{Not used}","int((e*cot(c + d*x))^(7/2)/(a + b*cot(c + d*x))^3,x)","\frac{\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^5\,e^5+11\,a^3\,b^2\,e^5\right)}{4\,b^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{e^4\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(5\,a^4+13\,a^2\,b^2\right)}{4\,b\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,a^2\,e^2+2\,d\,a\,b\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}-\mathrm{atan}\left(\frac{\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}}{\frac{9\,a^{12}\,b\,e^{28}+36\,a^{10}\,b^3\,e^{28}+270\,a^8\,b^5\,e^{28}+492\,a^6\,b^7\,e^{28}+1553\,a^4\,b^9\,e^{28}+280\,a^2\,b^{11}\,e^{28}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}}\right)\,\sqrt{\frac{e^7\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\frac{9\,a^{12}\,b\,e^{28}+36\,a^{10}\,b^3\,e^{28}+270\,a^8\,b^5\,e^{28}+492\,a^6\,b^7\,e^{28}+1553\,a^4\,b^9\,e^{28}+280\,a^2\,b^{11}\,e^{28}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\left(\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}}\right)\,\sqrt{\frac{e^7}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}-\frac{\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}+\frac{\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)\,\left(a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,1{}\mathrm{i}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}+\frac{\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}-\frac{\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)\,\left(a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,1{}\mathrm{i}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}}{\frac{9\,a^{12}\,b\,e^{28}+36\,a^{10}\,b^3\,e^{28}+270\,a^8\,b^5\,e^{28}+492\,a^6\,b^7\,e^{28}+1553\,a^4\,b^9\,e^{28}+280\,a^2\,b^{11}\,e^{28}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}-\frac{\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}+\frac{\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)\,\left(a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{16}\,e^{24}-18\,a^{14}\,b^2\,e^{24}+39\,a^{12}\,b^4\,e^{24}-1020\,a^{10}\,b^6\,e^{24}-1017\,a^8\,b^8\,e^{24}-6802\,a^6\,b^{10}\,e^{24}+1417\,a^4\,b^{12}\,e^{24}+128\,a^2\,b^{14}\,e^{24}+32\,b^{16}\,e^{24}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}+\frac{\left(\frac{-18\,a^{19}\,d^2\,e^{21}+90\,a^{17}\,b^2\,d^2\,e^{21}+246\,a^{15}\,b^4\,d^2\,e^{21}+3314\,a^{13}\,b^6\,d^2\,e^{21}+7594\,a^{11}\,b^8\,d^2\,e^{21}+21582\,a^9\,b^{10}\,d^2\,e^{21}+26482\,a^7\,b^{12}\,d^2\,e^{21}+2758\,a^5\,b^{14}\,d^2\,e^{21}-6528\,a^3\,b^{16}\,d^2\,e^{21}+32\,a\,b^{18}\,d^2\,e^{21}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(72\,a^{21}\,b\,d^2\,e^{17}+576\,a^{19}\,b^3\,d^2\,e^{17}+3488\,a^{17}\,b^5\,d^2\,e^{17}+13248\,a^{15}\,b^7\,d^2\,e^{17}+39088\,a^{13}\,b^9\,d^2\,e^{17}+72640\,a^{11}\,b^{11}\,d^2\,e^{17}+70240\,a^9\,b^{13}\,d^2\,e^{17}+28224\,a^7\,b^{15}\,d^2\,e^{17}+1352\,a^5\,b^{17}\,d^2\,e^{17}+1024\,a^3\,b^{19}\,d^2\,e^{17}+1472\,a\,b^{21}\,d^2\,e^{17}\right)}{a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4}-\frac{\left(\frac{64\,a^{20}\,b^5\,d^4\,e^{14}+2112\,a^{18}\,b^7\,d^4\,e^{14}+14592\,a^{16}\,b^9\,d^4\,e^{14}+48384\,a^{14}\,b^{11}\,d^4\,e^{14}+94080\,a^{12}\,b^{13}\,d^4\,e^{14}+115584\,a^{10}\,b^{15}\,d^4\,e^{14}+91392\,a^8\,b^{17}\,d^4\,e^{14}+45312\,a^6\,b^{19}\,d^4\,e^{14}+12864\,a^4\,b^{21}\,d^4\,e^{14}+1600\,a^2\,b^{23}\,d^4\,e^{14}}{a^{16}\,b^3\,d^5+8\,a^{14}\,b^5\,d^5+28\,a^{12}\,b^7\,d^5+56\,a^{10}\,b^9\,d^5+70\,a^8\,b^{11}\,d^5+56\,a^6\,b^{13}\,d^5+28\,a^4\,b^{15}\,d^5+8\,a^2\,b^{17}\,d^5+b^{19}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,\left(-512\,a^{22}\,b^6\,d^4\,e^{10}-4608\,a^{20}\,b^8\,d^4\,e^{10}-17920\,a^{18}\,b^{10}\,d^4\,e^{10}-38400\,a^{16}\,b^{12}\,d^4\,e^{10}-46080\,a^{14}\,b^{14}\,d^4\,e^{10}-21504\,a^{12}\,b^{16}\,d^4\,e^{10}+21504\,a^{10}\,b^{18}\,d^4\,e^{10}+46080\,a^8\,b^{20}\,d^4\,e^{10}+38400\,a^6\,b^{22}\,d^4\,e^{10}+17920\,a^4\,b^{24}\,d^4\,e^{10}+4608\,a^2\,b^{26}\,d^4\,e^{10}+512\,b^{28}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)\,\left(a^{16}\,b^3\,d^4+8\,a^{14}\,b^5\,d^4+28\,a^{12}\,b^7\,d^4+56\,a^{10}\,b^9\,d^4+70\,a^8\,b^{11}\,d^4+56\,a^6\,b^{13}\,d^4+28\,a^4\,b^{15}\,d^4+8\,a^2\,b^{17}\,d^4+b^{19}\,d^4\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}}{8\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}}\right)\,\left(3\,a^4+6\,a^2\,b^2+35\,b^4\right)\,\sqrt{-a^3\,b^5\,e^7}\,1{}\mathrm{i}}{4\,\left(d\,a^6\,b^5+3\,d\,a^4\,b^7+3\,d\,a^2\,b^9+d\,b^{11}\right)}","Not used",1,"(((e*cot(c + d*x))^(1/2)*(3*a^5*e^5 + 11*a^3*b^2*e^5))/(4*b^2*(a^4 + b^4 + 2*a^2*b^2)) + (e^4*(e*cot(c + d*x))^(3/2)*(5*a^4 + 13*a^2*b^2))/(4*b*(a^4 + b^4 + 2*a^2*b^2)))/(a^2*d*e^2 + b^2*d*e^2*cot(c + d*x)^2 + 2*a*b*d*e^2*cot(c + d*x)) - atan(((((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i - (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i)/((9*a^12*b*e^28 + 280*a^2*b^11*e^28 + 1553*a^4*b^9*e^28 + 492*a^6*b^7*e^28 + 270*a^8*b^5*e^28 + 36*a^10*b^3*e^28)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)))*((e^7*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*2i - atan(((((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i - (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i)/((9*a^12*b*e^28 + 280*a^2*b^11*e^28 + 1553*a^4*b^9*e^28 + 492*a^6*b^7*e^28 + 270*a^8*b^5*e^28 + 36*a^10*b^3*e^28)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)))*(e^7/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*2i - (atan((((((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) - (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)*(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*1i)/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)) + ((((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) + (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) - (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)*(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*1i)/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))/((9*a^12*b*e^28 + 280*a^2*b^11*e^28 + 1553*a^4*b^9*e^28 + 492*a^6*b^7*e^28 + 270*a^8*b^5*e^28 + 36*a^10*b^3*e^28)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) - (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) + (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)*(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)) + ((((e*cot(c + d*x))^(1/2)*(9*a^16*e^24 + 32*b^16*e^24 + 128*a^2*b^14*e^24 + 1417*a^4*b^12*e^24 - 6802*a^6*b^10*e^24 - 1017*a^8*b^8*e^24 - 1020*a^10*b^6*e^24 + 39*a^12*b^4*e^24 - 18*a^14*b^2*e^24))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) + (((32*a*b^18*d^2*e^21 - 18*a^19*d^2*e^21 - 6528*a^3*b^16*d^2*e^21 + 2758*a^5*b^14*d^2*e^21 + 26482*a^7*b^12*d^2*e^21 + 21582*a^9*b^10*d^2*e^21 + 7594*a^11*b^8*d^2*e^21 + 3314*a^13*b^6*d^2*e^21 + 246*a^15*b^4*d^2*e^21 + 90*a^17*b^2*d^2*e^21)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) - ((((e*cot(c + d*x))^(1/2)*(1472*a*b^21*d^2*e^17 + 72*a^21*b*d^2*e^17 + 1024*a^3*b^19*d^2*e^17 + 1352*a^5*b^17*d^2*e^17 + 28224*a^7*b^15*d^2*e^17 + 70240*a^9*b^13*d^2*e^17 + 72640*a^11*b^11*d^2*e^17 + 39088*a^13*b^9*d^2*e^17 + 13248*a^15*b^7*d^2*e^17 + 3488*a^17*b^5*d^2*e^17 + 576*a^19*b^3*d^2*e^17))/(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4) - (((1600*a^2*b^23*d^4*e^14 + 12864*a^4*b^21*d^4*e^14 + 45312*a^6*b^19*d^4*e^14 + 91392*a^8*b^17*d^4*e^14 + 115584*a^10*b^15*d^4*e^14 + 94080*a^12*b^13*d^4*e^14 + 48384*a^14*b^11*d^4*e^14 + 14592*a^16*b^9*d^4*e^14 + 2112*a^18*b^7*d^4*e^14 + 64*a^20*b^5*d^4*e^14)/(b^19*d^5 + 8*a^2*b^17*d^5 + 28*a^4*b^15*d^5 + 56*a^6*b^13*d^5 + 70*a^8*b^11*d^5 + 56*a^10*b^9*d^5 + 28*a^12*b^7*d^5 + 8*a^14*b^5*d^5 + a^16*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*(512*b^28*d^4*e^10 + 4608*a^2*b^26*d^4*e^10 + 17920*a^4*b^24*d^4*e^10 + 38400*a^6*b^22*d^4*e^10 + 46080*a^8*b^20*d^4*e^10 + 21504*a^10*b^18*d^4*e^10 - 21504*a^12*b^16*d^4*e^10 - 46080*a^14*b^14*d^4*e^10 - 38400*a^16*b^12*d^4*e^10 - 17920*a^18*b^10*d^4*e^10 - 4608*a^20*b^8*d^4*e^10 - 512*a^22*b^6*d^4*e^10))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)*(b^19*d^4 + 8*a^2*b^17*d^4 + 28*a^4*b^15*d^4 + 56*a^6*b^13*d^4 + 70*a^8*b^11*d^4 + 56*a^10*b^9*d^4 + 28*a^12*b^7*d^4 + 8*a^14*b^5*d^4 + a^16*b^3*d^4)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d)))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2))/(8*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d))))*(3*a^4 + 35*b^4 + 6*a^2*b^2)*(-a^3*b^5*e^7)^(1/2)*1i)/(4*(b^11*d + 3*a^2*b^9*d + 3*a^4*b^7*d + a^6*b^5*d))","B"
83,1,19256,470,6.514645,"\text{Not used}","int((e*cot(c + d*x))^(5/2)/(a + b*cot(c + d*x))^3,x)","-\frac{\frac{e^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(a^3+9\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4\,e^4-7\,a^2\,b^2\,e^4\right)}{4\,b\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,a^2\,e^2+2\,d\,a\,b\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}+\mathrm{atan}\left(\frac{\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{a^{11}\,e^{23}+36\,a^9\,b^2\,e^{23}+302\,a^7\,b^4\,e^{23}-388\,a^5\,b^6\,e^{23}+249\,a^3\,b^8\,e^{23}-120\,a\,b^{10}\,e^{23}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}}\right)\,\sqrt{-\frac{e^5\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\left(\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{a^{11}\,e^{23}+36\,a^9\,b^2\,e^{23}+302\,a^7\,b^4\,e^{23}-388\,a^5\,b^6\,e^{23}+249\,a^3\,b^8\,e^{23}-120\,a\,b^{10}\,e^{23}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}}\right)\,\sqrt{-\frac{e^5}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}-\frac{\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}+\frac{\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,1{}\mathrm{i}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}+\frac{\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}-\frac{\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,1{}\mathrm{i}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}}{\frac{a^{11}\,e^{23}+36\,a^9\,b^2\,e^{23}+302\,a^7\,b^4\,e^{23}-388\,a^5\,b^6\,e^{23}+249\,a^3\,b^8\,e^{23}-120\,a\,b^{10}\,e^{23}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}-\frac{\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}+\frac{\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^{14}\,e^{20}+30\,a^{12}\,b^2\,e^{20}+79\,a^{10}\,b^4\,e^{20}-2300\,a^8\,b^6\,e^{20}+3631\,a^6\,b^8\,e^{20}-2082\,a^4\,b^{10}\,e^{20}+97\,a^2\,b^{12}\,e^{20}-32\,b^{14}\,e^{20}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}+\frac{\left(\frac{10\,a^{16}\,b\,d^2\,e^{18}+382\,a^{14}\,b^3\,d^2\,e^{18}+2946\,a^{12}\,b^5\,d^2\,e^{18}-5498\,a^{10}\,b^7\,d^2\,e^{18}-8322\,a^8\,b^9\,d^2\,e^{18}+7386\,a^6\,b^{11}\,d^2\,e^{18}+5238\,a^4\,b^{13}\,d^2\,e^{18}-2398\,a^2\,b^{15}\,d^2\,e^{18}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{19}\,b\,d^2\,e^{15}+384\,a^{17}\,b^3\,d^2\,e^{15}+3552\,a^{15}\,b^5\,d^2\,e^{15}+4032\,a^{13}\,b^7\,d^2\,e^{15}-5328\,a^{11}\,b^9\,d^2\,e^{15}-5056\,a^9\,b^{11}\,d^2\,e^{15}+10208\,a^7\,b^{13}\,d^2\,e^{15}+11328\,a^5\,b^{15}\,d^2\,e^{15}+776\,a^3\,b^{17}\,d^2\,e^{15}-1472\,a\,b^{19}\,d^2\,e^{15}\right)}{a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4}-\frac{\left(\frac{-704\,a^{19}\,b^4\,d^4\,e^{13}-4800\,a^{17}\,b^6\,d^4\,e^{13}-13056\,a^{15}\,b^8\,d^4\,e^{13}-16128\,a^{13}\,b^{10}\,d^4\,e^{13}-2688\,a^{11}\,b^{12}\,d^4\,e^{13}+18816\,a^9\,b^{14}\,d^4\,e^{13}+26880\,a^7\,b^{16}\,d^4\,e^{13}+17664\,a^5\,b^{18}\,d^4\,e^{13}+5952\,a^3\,b^{20}\,d^4\,e^{13}+832\,a\,b^{22}\,d^4\,e^{13}}{a^{16}\,b\,d^5+8\,a^{14}\,b^3\,d^5+28\,a^{12}\,b^5\,d^5+56\,a^{10}\,b^7\,d^5+70\,a^8\,b^9\,d^5+56\,a^6\,b^{11}\,d^5+28\,a^4\,b^{13}\,d^5+8\,a^2\,b^{15}\,d^5+b^{17}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,\left(-512\,a^{22}\,b^4\,d^4\,e^{10}-4608\,a^{20}\,b^6\,d^4\,e^{10}-17920\,a^{18}\,b^8\,d^4\,e^{10}-38400\,a^{16}\,b^{10}\,d^4\,e^{10}-46080\,a^{14}\,b^{12}\,d^4\,e^{10}-21504\,a^{12}\,b^{14}\,d^4\,e^{10}+21504\,a^{10}\,b^{16}\,d^4\,e^{10}+46080\,a^8\,b^{18}\,d^4\,e^{10}+38400\,a^6\,b^{20}\,d^4\,e^{10}+17920\,a^4\,b^{22}\,d^4\,e^{10}+4608\,a^2\,b^{24}\,d^4\,e^{10}+512\,b^{26}\,d^4\,e^{10}\right)}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)\,\left(a^{16}\,b\,d^4+8\,a^{14}\,b^3\,d^4+28\,a^{12}\,b^5\,d^4+56\,a^{10}\,b^7\,d^4+70\,a^8\,b^9\,d^4+56\,a^6\,b^{11}\,d^4+28\,a^4\,b^{13}\,d^4+8\,a^2\,b^{15}\,d^4+b^{17}\,d^4\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}}{8\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}}\right)\,\left(a^4+18\,a^2\,b^2-15\,b^4\right)\,\sqrt{-a\,b^3\,e^5}\,1{}\mathrm{i}}{4\,\left(d\,a^6\,b^3+3\,d\,a^4\,b^5+3\,d\,a^2\,b^7+d\,b^9\right)}","Not used",1,"atan(((((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i - (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i)/((((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (a^11*e^23 - 120*a*b^10*e^23 + 249*a^3*b^8*e^23 - 388*a^5*b^6*e^23 + 302*a^7*b^4*e^23 + 36*a^9*b^2*e^23)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5)))*(-(e^5*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*2i - ((e^3*(e*cot(c + d*x))^(3/2)*(9*a*b^2 + a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - ((e*cot(c + d*x))^(1/2)*(a^4*e^4 - 7*a^2*b^2*e^4))/(4*b*(a^4 + b^4 + 2*a^2*b^2)))/(a^2*d*e^2 + b^2*d*e^2*cot(c + d*x)^2 + 2*a*b*d*e^2*cot(c + d*x)) + atan(((((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i - (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i)/((((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (a^11*e^23 - 120*a*b^10*e^23 + 249*a^3*b^8*e^23 - 388*a^5*b^6*e^23 + 302*a^7*b^4*e^23 + 36*a^9*b^2*e^23)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5)))*(-e^5/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*2i + (atan((((((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) - (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) + (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)*(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*1i)/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)) + ((((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) + (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)*(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*1i)/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))/((a^11*e^23 - 120*a*b^10*e^23 + 249*a^3*b^8*e^23 - 388*a^5*b^6*e^23 + 302*a^7*b^4*e^23 + 36*a^9*b^2*e^23)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) - (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) + (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) - ((e*cot(c + d*x))^(1/2)*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)*(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)) + ((((e*cot(c + d*x))^(1/2)*(a^14*e^20 - 32*b^14*e^20 + 97*a^2*b^12*e^20 - 2082*a^4*b^10*e^20 + 3631*a^6*b^8*e^20 - 2300*a^8*b^6*e^20 + 79*a^10*b^4*e^20 + 30*a^12*b^2*e^20))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) + (((10*a^16*b*d^2*e^18 - 2398*a^2*b^15*d^2*e^18 + 5238*a^4*b^13*d^2*e^18 + 7386*a^6*b^11*d^2*e^18 - 8322*a^8*b^9*d^2*e^18 - 5498*a^10*b^7*d^2*e^18 + 2946*a^12*b^5*d^2*e^18 + 382*a^14*b^3*d^2*e^18)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((((e*cot(c + d*x))^(1/2)*(8*a^19*b*d^2*e^15 - 1472*a*b^19*d^2*e^15 + 776*a^3*b^17*d^2*e^15 + 11328*a^5*b^15*d^2*e^15 + 10208*a^7*b^13*d^2*e^15 - 5056*a^9*b^11*d^2*e^15 - 5328*a^11*b^9*d^2*e^15 + 4032*a^13*b^7*d^2*e^15 + 3552*a^15*b^5*d^2*e^15 + 384*a^17*b^3*d^2*e^15))/(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4) - (((832*a*b^22*d^4*e^13 + 5952*a^3*b^20*d^4*e^13 + 17664*a^5*b^18*d^4*e^13 + 26880*a^7*b^16*d^4*e^13 + 18816*a^9*b^14*d^4*e^13 - 2688*a^11*b^12*d^4*e^13 - 16128*a^13*b^10*d^4*e^13 - 13056*a^15*b^8*d^4*e^13 - 4800*a^17*b^6*d^4*e^13 - 704*a^19*b^4*d^4*e^13)/(b^17*d^5 + a^16*b*d^5 + 8*a^2*b^15*d^5 + 28*a^4*b^13*d^5 + 56*a^6*b^11*d^5 + 70*a^8*b^9*d^5 + 56*a^10*b^7*d^5 + 28*a^12*b^5*d^5 + 8*a^14*b^3*d^5) + ((e*cot(c + d*x))^(1/2)*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*(512*b^26*d^4*e^10 + 4608*a^2*b^24*d^4*e^10 + 17920*a^4*b^22*d^4*e^10 + 38400*a^6*b^20*d^4*e^10 + 46080*a^8*b^18*d^4*e^10 + 21504*a^10*b^16*d^4*e^10 - 21504*a^12*b^14*d^4*e^10 - 46080*a^14*b^12*d^4*e^10 - 38400*a^16*b^10*d^4*e^10 - 17920*a^18*b^8*d^4*e^10 - 4608*a^20*b^6*d^4*e^10 - 512*a^22*b^4*d^4*e^10))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)*(b^17*d^4 + a^16*b*d^4 + 8*a^2*b^15*d^4 + 28*a^4*b^13*d^4 + 56*a^6*b^11*d^4 + 70*a^8*b^9*d^4 + 56*a^10*b^7*d^4 + 28*a^12*b^5*d^4 + 8*a^14*b^3*d^4)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d)))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2))/(8*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d))))*(a^4 - 15*b^4 + 18*a^2*b^2)*(-a*b^3*e^5)^(1/2)*1i)/(4*(b^9*d + 3*a^2*b^7*d + 3*a^4*b^5*d + a^6*b^3*d))","B"
84,1,19000,461,6.213352,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + b*cot(c + d*x))^3,x)","\mathrm{atan}\left(\frac{\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{9\,a^8\,b^2\,e^{18}-180\,a^6\,b^4\,e^{18}+878\,a^4\,b^6\,e^{18}+28\,a^2\,b^8\,e^{18}-15\,b^{10}\,e^{18}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}}\right)\,\sqrt{\frac{e^3\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\left(\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{9\,a^8\,b^2\,e^{18}-180\,a^6\,b^4\,e^{18}+878\,a^4\,b^6\,e^{18}+28\,a^2\,b^8\,e^{18}-15\,b^{10}\,e^{18}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}}\right)\,\sqrt{\frac{e^3}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\frac{\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(5\,a^3\,e^3-3\,a\,b^2\,e^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b\,e^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(3\,a^2-5\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,a^2\,e^2+2\,d\,a\,b\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}-\frac{\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}+\frac{\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)\,\left(a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,1{}\mathrm{i}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}+\frac{\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}-\frac{\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)\,\left(a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,1{}\mathrm{i}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}}{\frac{9\,a^8\,b^2\,e^{18}-180\,a^6\,b^4\,e^{18}+878\,a^4\,b^6\,e^{18}+28\,a^2\,b^8\,e^{18}-15\,b^{10}\,e^{18}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}-\frac{\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}+\frac{\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)\,\left(a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^{12}\,b\,e^{16}-210\,a^{10}\,b^3\,e^{16}+1671\,a^8\,b^5\,e^{16}-4348\,a^6\,b^7\,e^{16}+1831\,a^4\,b^9\,e^{16}-82\,a^2\,b^{11}\,e^{16}+41\,b^{13}\,e^{16}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}+\frac{\left(\frac{-18\,a^{15}\,b\,d^2\,e^{15}+506\,a^{13}\,b^3\,d^2\,e^{15}-3338\,a^{11}\,b^5\,d^2\,e^{15}+5298\,a^9\,b^7\,d^2\,e^{15}+17194\,a^7\,b^9\,d^2\,e^{15}+3022\,a^5\,b^{11}\,d^2\,e^{15}-4494\,a^3\,b^{13}\,d^2\,e^{15}+518\,a\,b^{15}\,d^2\,e^{15}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8\,a^{17}\,b^2\,d^2\,e^{13}-960\,a^{15}\,b^4\,d^2\,e^{13}+3808\,a^{13}\,b^6\,d^2\,e^{13}+18880\,a^{11}\,b^8\,d^2\,e^{13}+19504\,a^9\,b^{10}\,d^2\,e^{13}-576\,a^7\,b^{12}\,d^2\,e^{13}-7456\,a^5\,b^{14}\,d^2\,e^{13}+64\,a^3\,b^{16}\,d^2\,e^{13}+1544\,a\,b^{18}\,d^2\,e^{13}\right)}{a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4}-\frac{\left(\frac{-128\,a^{20}\,b^2\,d^4\,e^{12}+192\,a^{18}\,b^4\,d^4\,e^{12}+5952\,a^{16}\,b^6\,d^4\,e^{12}+25344\,a^{14}\,b^8\,d^4\,e^{12}+53760\,a^{12}\,b^{10}\,d^4\,e^{12}+67200\,a^{10}\,b^{12}\,d^4\,e^{12}+51072\,a^8\,b^{14}\,d^4\,e^{12}+22272\,a^6\,b^{16}\,d^4\,e^{12}+4224\,a^4\,b^{18}\,d^4\,e^{12}-320\,a^2\,b^{20}\,d^4\,e^{12}-192\,b^{22}\,d^4\,e^{12}}{a^{16}\,d^5+8\,a^{14}\,b^2\,d^5+28\,a^{12}\,b^4\,d^5+56\,a^{10}\,b^6\,d^5+70\,a^8\,b^8\,d^5+56\,a^6\,b^{10}\,d^5+28\,a^4\,b^{12}\,d^5+8\,a^2\,b^{14}\,d^5+b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,\left(-512\,a^{22}\,b^3\,d^4\,e^{10}-4608\,a^{20}\,b^5\,d^4\,e^{10}-17920\,a^{18}\,b^7\,d^4\,e^{10}-38400\,a^{16}\,b^9\,d^4\,e^{10}-46080\,a^{14}\,b^{11}\,d^4\,e^{10}-21504\,a^{12}\,b^{13}\,d^4\,e^{10}+21504\,a^{10}\,b^{15}\,d^4\,e^{10}+46080\,a^8\,b^{17}\,d^4\,e^{10}+38400\,a^6\,b^{19}\,d^4\,e^{10}+17920\,a^4\,b^{21}\,d^4\,e^{10}+4608\,a^2\,b^{23}\,d^4\,e^{10}+512\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)\,\left(a^{16}\,d^4+8\,a^{14}\,b^2\,d^4+28\,a^{12}\,b^4\,d^4+56\,a^{10}\,b^6\,d^4+70\,a^8\,b^8\,d^4+56\,a^6\,b^{10}\,d^4+28\,a^4\,b^{12}\,d^4+8\,a^2\,b^{14}\,d^4+b^{16}\,d^4\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}}{8\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}}\right)\,\left(3\,a^4-26\,a^2\,b^2+3\,b^4\right)\,\sqrt{-a\,b\,e^3}\,1{}\mathrm{i}}{4\,\left(d\,a^7\,b+3\,d\,a^5\,b^3+3\,d\,a^3\,b^5+d\,a\,b^7\right)}","Not used",1,"atan(((((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i - (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i)/((((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (28*a^2*b^8*e^18 - 15*b^10*e^18 + 878*a^4*b^6*e^18 - 180*a^6*b^4*e^18 + 9*a^8*b^2*e^18)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5)))*((e^3*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*2i + atan(((((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i - (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i)/((((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (28*a^2*b^8*e^18 - 15*b^10*e^18 + 878*a^4*b^6*e^18 - 180*a^6*b^4*e^18 + 9*a^8*b^2*e^18)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5)))*(e^3/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*2i - (((e*cot(c + d*x))^(1/2)*(5*a^3*e^3 - 3*a*b^2*e^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (b*e^2*(e*cot(c + d*x))^(3/2)*(3*a^2 - 5*b^2))/(4*(a^4 + b^4 + 2*a^2*b^2)))/(a^2*d*e^2 + b^2*d*e^2*cot(c + d*x)^2 + 2*a*b*d*e^2*cot(c + d*x)) + (atan((((((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) - (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)*(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*1i)/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)) + ((((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) + (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) - (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)*(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*1i)/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))/((28*a^2*b^8*e^18 - 15*b^10*e^18 + 878*a^4*b^6*e^18 - 180*a^6*b^4*e^18 + 9*a^8*b^2*e^18)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) - (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) + (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)*(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)) + ((((e*cot(c + d*x))^(1/2)*(41*b^13*e^16 + 9*a^12*b*e^16 - 82*a^2*b^11*e^16 + 1831*a^4*b^9*e^16 - 4348*a^6*b^7*e^16 + 1671*a^8*b^5*e^16 - 210*a^10*b^3*e^16))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) + (((518*a*b^15*d^2*e^15 - 18*a^15*b*d^2*e^15 - 4494*a^3*b^13*d^2*e^15 + 3022*a^5*b^11*d^2*e^15 + 17194*a^7*b^9*d^2*e^15 + 5298*a^9*b^7*d^2*e^15 - 3338*a^11*b^5*d^2*e^15 + 506*a^13*b^3*d^2*e^15)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(1544*a*b^18*d^2*e^13 + 64*a^3*b^16*d^2*e^13 - 7456*a^5*b^14*d^2*e^13 - 576*a^7*b^12*d^2*e^13 + 19504*a^9*b^10*d^2*e^13 + 18880*a^11*b^8*d^2*e^13 + 3808*a^13*b^6*d^2*e^13 - 960*a^15*b^4*d^2*e^13 + 8*a^17*b^2*d^2*e^13))/(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4) - (((4224*a^4*b^18*d^4*e^12 - 320*a^2*b^20*d^4*e^12 - 192*b^22*d^4*e^12 + 22272*a^6*b^16*d^4*e^12 + 51072*a^8*b^14*d^4*e^12 + 67200*a^10*b^12*d^4*e^12 + 53760*a^12*b^10*d^4*e^12 + 25344*a^14*b^8*d^4*e^12 + 5952*a^16*b^6*d^4*e^12 + 192*a^18*b^4*d^4*e^12 - 128*a^20*b^2*d^4*e^12)/(a^16*d^5 + b^16*d^5 + 8*a^2*b^14*d^5 + 28*a^4*b^12*d^5 + 56*a^6*b^10*d^5 + 70*a^8*b^8*d^5 + 56*a^10*b^6*d^5 + 28*a^12*b^4*d^5 + 8*a^14*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*(512*b^25*d^4*e^10 + 4608*a^2*b^23*d^4*e^10 + 17920*a^4*b^21*d^4*e^10 + 38400*a^6*b^19*d^4*e^10 + 46080*a^8*b^17*d^4*e^10 + 21504*a^10*b^15*d^4*e^10 - 21504*a^12*b^13*d^4*e^10 - 46080*a^14*b^11*d^4*e^10 - 38400*a^16*b^9*d^4*e^10 - 17920*a^18*b^7*d^4*e^10 - 4608*a^20*b^5*d^4*e^10 - 512*a^22*b^3*d^4*e^10))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)*(a^16*d^4 + b^16*d^4 + 8*a^2*b^14*d^4 + 28*a^4*b^12*d^4 + 56*a^6*b^10*d^4 + 70*a^8*b^8*d^4 + 56*a^10*b^6*d^4 + 28*a^12*b^4*d^4 + 8*a^14*b^2*d^4)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d)))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2))/(8*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d))))*(3*a^4 + 3*b^4 - 26*a^2*b^2)*(-a*b*e^3)^(1/2)*1i)/(4*(3*a^3*b^5*d + 3*a^5*b^3*d + a*b^7*d + a^7*b*d))","B"
85,1,19534,463,6.127345,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + b*cot(c + d*x))^3,x)","\frac{\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(9\,a^2\,b\,e^2+b^3\,e^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b^2\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(7\,a^2-b^2\right)}{4\,a\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,a^2\,e^2+2\,d\,a\,b\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,1{}\mathrm{i}}{\frac{-225\,a^9\,b^3\,e^{13}+420\,a^7\,b^5\,e^{13}-270\,a^5\,b^7\,e^{13}+116\,a^3\,b^9\,e^{13}+7\,a\,b^{11}\,e^{13}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}}\right)\,\sqrt{-\frac{e}{4\,\left(-a^6\,d^2\,1{}\mathrm{i}+6\,a^5\,b\,d^2+a^4\,b^2\,d^2\,15{}\mathrm{i}-20\,a^3\,b^3\,d^2-a^2\,b^4\,d^2\,15{}\mathrm{i}+6\,a\,b^5\,d^2+b^6\,d^2\,1{}\mathrm{i}\right)}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}-\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,1{}\mathrm{i}}{\frac{-225\,a^9\,b^3\,e^{13}+420\,a^7\,b^5\,e^{13}-270\,a^5\,b^7\,e^{13}+116\,a^3\,b^9\,e^{13}+7\,a\,b^{11}\,e^{13}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\left(\left(\left(\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}}\right)\,\sqrt{-\frac{e\,1{}\mathrm{i}}{4\,\left(-a^6\,d^2+a^5\,b\,d^2\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2-a^3\,b^3\,d^2\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2+a\,b^5\,d^2\,6{}\mathrm{i}+b^6\,d^2\right)}}\,2{}\mathrm{i}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}+\frac{\left(\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}+\frac{\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)\,\left(a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,1{}\mathrm{i}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}-\frac{\left(\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}-\frac{\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)\,\left(a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,1{}\mathrm{i}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}}{\frac{-225\,a^9\,b^3\,e^{13}+420\,a^7\,b^5\,e^{13}-270\,a^5\,b^7\,e^{13}+116\,a^3\,b^9\,e^{13}+7\,a\,b^{11}\,e^{13}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}+\frac{\left(\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}+\frac{\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)\,\left(a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-225\,a^{12}\,b^3\,e^{12}+1922\,a^{10}\,b^5\,e^{12}-3631\,a^8\,b^7\,e^{12}+2460\,a^6\,b^9\,e^{12}+49\,a^4\,b^{11}\,e^{12}+2\,a^2\,b^{13}\,e^{12}-b^{15}\,e^{12}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}-\frac{\left(\frac{32\,a^{16}\,b^2\,d^2\,e^{12}+2442\,a^{14}\,b^4\,d^2\,e^{12}-4290\,a^{12}\,b^6\,d^2\,e^{12}-5246\,a^{10}\,b^8\,d^2\,e^{12}+9222\,a^8\,b^{10}\,d^2\,e^{12}+4862\,a^6\,b^{12}\,d^2\,e^{12}-3046\,a^4\,b^{14}\,d^2\,e^{12}-138\,a^2\,b^{16}\,d^2\,e^{12}+2\,b^{18}\,d^2\,e^{12}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{19}\,b^2\,d^2\,e^{11}+1800\,a^{17}\,b^4\,d^2\,e^{11}+64\,a^{15}\,b^6\,d^2\,e^{11}-9248\,a^{13}\,b^8\,d^2\,e^{11}-5056\,a^{11}\,b^{10}\,d^2\,e^{11}+14128\,a^9\,b^{12}\,d^2\,e^{11}+15296\,a^7\,b^{14}\,d^2\,e^{11}+2528\,a^5\,b^{16}\,d^2\,e^{11}-1152\,a^3\,b^{18}\,d^2\,e^{11}+8\,a\,b^{20}\,d^2\,e^{11}\right)}{a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4}-\frac{\left(\frac{-640\,a^{21}\,b^3\,d^4\,e^{11}-4160\,a^{19}\,b^5\,d^4\,e^{11}-10176\,a^{17}\,b^7\,d^4\,e^{11}-8448\,a^{15}\,b^9\,d^4\,e^{11}+10752\,a^{13}\,b^{11}\,d^4\,e^{11}+34944\,a^{11}\,b^{13}\,d^4\,e^{11}+40320\,a^9\,b^{15}\,d^4\,e^{11}+25344\,a^7\,b^{17}\,d^4\,e^{11}+8832\,a^5\,b^{19}\,d^4\,e^{11}+1472\,a^3\,b^{21}\,d^4\,e^{11}+64\,a\,b^{23}\,d^4\,e^{11}}{a^{18}\,d^5+8\,a^{16}\,b^2\,d^5+28\,a^{14}\,b^4\,d^5+56\,a^{12}\,b^6\,d^5+70\,a^{10}\,b^8\,d^5+56\,a^8\,b^{10}\,d^5+28\,a^6\,b^{12}\,d^5+8\,a^4\,b^{14}\,d^5+a^2\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,\left(-512\,a^{24}\,b^3\,d^4\,e^{10}-4608\,a^{22}\,b^5\,d^4\,e^{10}-17920\,a^{20}\,b^7\,d^4\,e^{10}-38400\,a^{18}\,b^9\,d^4\,e^{10}-46080\,a^{16}\,b^{11}\,d^4\,e^{10}-21504\,a^{14}\,b^{13}\,d^4\,e^{10}+21504\,a^{12}\,b^{15}\,d^4\,e^{10}+46080\,a^{10}\,b^{17}\,d^4\,e^{10}+38400\,a^8\,b^{19}\,d^4\,e^{10}+17920\,a^6\,b^{21}\,d^4\,e^{10}+4608\,a^4\,b^{23}\,d^4\,e^{10}+512\,a^2\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)\,\left(a^{18}\,d^4+8\,a^{16}\,b^2\,d^4+28\,a^{14}\,b^4\,d^4+56\,a^{12}\,b^6\,d^4+70\,a^{10}\,b^8\,d^4+56\,a^8\,b^{10}\,d^4+28\,a^6\,b^{12}\,d^4+8\,a^4\,b^{14}\,d^4+a^2\,b^{16}\,d^4\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}}{8\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}}\right)\,\left(-15\,a^4+18\,a^2\,b^2+b^4\right)\,\sqrt{-a^3\,b\,e}\,1{}\mathrm{i}}{4\,\left(d\,a^9+3\,d\,a^7\,b^2+3\,d\,a^5\,b^4+d\,a^3\,b^6\right)}","Not used",1,"(((e*cot(c + d*x))^(1/2)*(b^3*e^2 + 9*a^2*b*e^2))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (b^2*e*(e*cot(c + d*x))^(3/2)*(7*a^2 - b^2))/(4*a*(a^4 + b^4 + 2*a^2*b^2)))/(a^2*d*e^2 + b^2*d*e^2*cot(c + d*x)^2 + 2*a*b*d*e^2*cot(c + d*x)) - atan(((((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i - (((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*1i)/((7*a*b^11*e^13 + 116*a^3*b^9*e^13 - 270*a^5*b^7*e^13 + 420*a^7*b^5*e^13 - 225*a^9*b^3*e^13)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + (((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + (((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)))*(-e/(4*(b^6*d^2*1i - a^6*d^2*1i + 6*a*b^5*d^2 + 6*a^5*b*d^2 - a^2*b^4*d^2*15i - 20*a^3*b^3*d^2 + a^4*b^2*d^2*15i)))^(1/2)*2i - atan(((((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i - (((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*1i)/((7*a*b^11*e^13 + 116*a^3*b^9*e^13 - 270*a^5*b^7*e^13 + 420*a^7*b^5*e^13 - 225*a^9*b^3*e^13)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + (((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + (((((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) + ((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - (2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2) - ((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)))*(-(e*1i)/(4*(b^6*d^2 - a^6*d^2 + a*b^5*d^2*6i + a^5*b*d^2*6i - 15*a^2*b^4*d^2 - a^3*b^3*d^2*20i + 15*a^4*b^2*d^2)))^(1/2)*2i - (atan((((((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) + (((2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) + (((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)*(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*1i)/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)) + ((((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) - (((2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) - (((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)*(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*1i)/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))/((7*a*b^11*e^13 + 116*a^3*b^9*e^13 - 270*a^5*b^7*e^13 + 420*a^7*b^5*e^13 - 225*a^9*b^3*e^13)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) + (((2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) + (((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)*(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)) + ((((e*cot(c + d*x))^(1/2)*(2*a^2*b^13*e^12 - b^15*e^12 + 49*a^4*b^11*e^12 + 2460*a^6*b^9*e^12 - 3631*a^8*b^7*e^12 + 1922*a^10*b^5*e^12 - 225*a^12*b^3*e^12))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) - (((2*b^18*d^2*e^12 - 138*a^2*b^16*d^2*e^12 - 3046*a^4*b^14*d^2*e^12 + 4862*a^6*b^12*d^2*e^12 + 9222*a^8*b^10*d^2*e^12 - 5246*a^10*b^8*d^2*e^12 - 4290*a^12*b^6*d^2*e^12 + 2442*a^14*b^4*d^2*e^12 + 32*a^16*b^2*d^2*e^12)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(8*a*b^20*d^2*e^11 - 1152*a^3*b^18*d^2*e^11 + 2528*a^5*b^16*d^2*e^11 + 15296*a^7*b^14*d^2*e^11 + 14128*a^9*b^12*d^2*e^11 - 5056*a^11*b^10*d^2*e^11 - 9248*a^13*b^8*d^2*e^11 + 64*a^15*b^6*d^2*e^11 + 1800*a^17*b^4*d^2*e^11 + 64*a^19*b^2*d^2*e^11))/(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4) - (((64*a*b^23*d^4*e^11 + 1472*a^3*b^21*d^4*e^11 + 8832*a^5*b^19*d^4*e^11 + 25344*a^7*b^17*d^4*e^11 + 40320*a^9*b^15*d^4*e^11 + 34944*a^11*b^13*d^4*e^11 + 10752*a^13*b^11*d^4*e^11 - 8448*a^15*b^9*d^4*e^11 - 10176*a^17*b^7*d^4*e^11 - 4160*a^19*b^5*d^4*e^11 - 640*a^21*b^3*d^4*e^11)/(a^18*d^5 + a^2*b^16*d^5 + 8*a^4*b^14*d^5 + 28*a^6*b^12*d^5 + 56*a^8*b^10*d^5 + 70*a^10*b^8*d^5 + 56*a^12*b^6*d^5 + 28*a^14*b^4*d^5 + 8*a^16*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*(512*a^2*b^25*d^4*e^10 + 4608*a^4*b^23*d^4*e^10 + 17920*a^6*b^21*d^4*e^10 + 38400*a^8*b^19*d^4*e^10 + 46080*a^10*b^17*d^4*e^10 + 21504*a^12*b^15*d^4*e^10 - 21504*a^14*b^13*d^4*e^10 - 46080*a^16*b^11*d^4*e^10 - 38400*a^18*b^9*d^4*e^10 - 17920*a^20*b^7*d^4*e^10 - 4608*a^22*b^5*d^4*e^10 - 512*a^24*b^3*d^4*e^10))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)*(a^18*d^4 + a^2*b^16*d^4 + 8*a^4*b^14*d^4 + 28*a^6*b^12*d^4 + 56*a^8*b^10*d^4 + 70*a^10*b^8*d^4 + 56*a^12*b^6*d^4 + 28*a^14*b^4*d^4 + 8*a^16*b^2*d^4)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d)))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2))/(8*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d))))*(b^4 - 15*a^4 + 18*a^2*b^2)*(-a^3*b*e)^(1/2)*1i)/(4*(a^9*d + a^3*b^6*d + 3*a^5*b^4*d + 3*a^7*b^2*d))","B"
86,1,20155,476,6.788845,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + b*cot(c + d*x))^3),x)","-\frac{\frac{b^3\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(11\,a^2+3\,b^2\right)}{4\,a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b^2\,e\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(13\,a^2+5\,b^2\right)}{4\,a\,{\left(a^2+b^2\right)}^2}}{d\,a^2\,e^2+2\,d\,a\,b\,e^2\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}+\mathrm{atan}\left(\frac{\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}-\frac{\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}\right)+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)\,1{}\mathrm{i}-\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}\right)-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)\,1{}\mathrm{i}}{\frac{1505\,a^8\,b^6\,e^8+748\,a^6\,b^8\,e^8+318\,a^4\,b^{10}\,e^8+60\,a^2\,b^{12}\,e^8+9\,b^{14}\,e^8}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}-\frac{\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}\right)+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)+\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}\right)-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}\right)}\right)\,\sqrt{\frac{1{}\mathrm{i}}{4\,\left(-e\,a^6\,d^2+6{}\mathrm{i}\,e\,a^5\,b\,d^2+15\,e\,a^4\,b^2\,d^2-20{}\mathrm{i}\,e\,a^3\,b^3\,d^2-15\,e\,a^2\,b^4\,d^2+6{}\mathrm{i}\,e\,a\,b^5\,d^2+e\,b^6\,d^2\right)}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\frac{\left(\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{4\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)}{2}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,1{}\mathrm{i}-\left(\frac{\left(\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{4\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,1{}\mathrm{i}}{\frac{1505\,a^8\,b^6\,e^8+748\,a^6\,b^8\,e^8+318\,a^4\,b^{10}\,e^8+60\,a^2\,b^{12}\,e^8+9\,b^{14}\,e^8}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\left(\frac{\left(\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{4\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)}{2}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}+\left(\frac{\left(\frac{\left(\frac{\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{4\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}-\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{2\,\left(a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}{2}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{2\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}}\right)\,\sqrt{\frac{1}{-1{}\mathrm{i}\,e\,a^6\,d^2+6\,e\,a^5\,b\,d^2+15{}\mathrm{i}\,e\,a^4\,b^2\,d^2-20\,e\,a^3\,b^3\,d^2-15{}\mathrm{i}\,e\,a^2\,b^4\,d^2+6\,e\,a\,b^5\,d^2+1{}\mathrm{i}\,e\,b^6\,d^2}}\,1{}\mathrm{i}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}-\frac{\left(\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}+\frac{\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,1{}\mathrm{i}}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}+\frac{\left(\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}-\frac{\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,1{}\mathrm{i}}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}}{\frac{1505\,a^8\,b^6\,e^8+748\,a^6\,b^8\,e^8+318\,a^4\,b^{10}\,e^8+60\,a^2\,b^{12}\,e^8+9\,b^{14}\,e^8}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}-\frac{\left(\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}+\frac{\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}-\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}-\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-1257\,a^{12}\,b^5\,e^8+6802\,a^{10}\,b^7\,e^8+857\,a^8\,b^9\,e^8+892\,a^6\,b^{11}\,e^8-71\,a^4\,b^{13}\,e^8+18\,a^2\,b^{15}\,e^8-9\,b^{17}\,e^8\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}+\frac{\left(\frac{-32\,a^{17}\,b^3\,d^2\,e^9+2258\,a^{15}\,b^5\,d^2\,e^9-14970\,a^{13}\,b^7\,d^2\,e^9-34486\,a^{11}\,b^9\,d^2\,e^9-14578\,a^9\,b^{11}\,d^2\,e^9+3606\,a^7\,b^{13}\,d^2\,e^9+1714\,a^5\,b^{15}\,d^2\,e^9+846\,a^3\,b^{17}\,d^2\,e^9+90\,a\,b^{19}\,d^2\,e^9}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\left(\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-64\,a^{21}\,b^2\,d^2\,e^9+12616\,a^{17}\,b^6\,d^2\,e^9+47680\,a^{15}\,b^8\,d^2\,e^9+70240\,a^{13}\,b^{10}\,d^2\,e^9+53184\,a^{11}\,b^{12}\,d^2\,e^9+27824\,a^9\,b^{14}\,d^2\,e^9+14272\,a^7\,b^{16}\,d^2\,e^9+5024\,a^5\,b^{18}\,d^2\,e^9+576\,a^3\,b^{20}\,d^2\,e^9+72\,a\,b^{22}\,d^2\,e^9\right)}{a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4}-\frac{\left(\frac{-128\,a^{24}\,b^2\,d^4\,e^{10}+384\,a^{22}\,b^4\,d^4\,e^{10}+7872\,a^{20}\,b^6\,d^4\,e^{10}+33984\,a^{18}\,b^8\,d^4\,e^{10}+76800\,a^{16}\,b^{10}\,d^4\,e^{10}+107520\,a^{14}\,b^{12}\,d^4\,e^{10}+99456\,a^{12}\,b^{14}\,d^4\,e^{10}+62592\,a^{10}\,b^{16}\,d^4\,e^{10}+27264\,a^8\,b^{18}\,d^4\,e^{10}+8320\,a^6\,b^{20}\,d^4\,e^{10}+1728\,a^4\,b^{22}\,d^4\,e^{10}+192\,a^2\,b^{24}\,d^4\,e^{10}}{a^{20}\,d^5+8\,a^{18}\,b^2\,d^5+28\,a^{16}\,b^4\,d^5+56\,a^{14}\,b^6\,d^5+70\,a^{12}\,b^8\,d^5+56\,a^{10}\,b^{10}\,d^5+28\,a^8\,b^{12}\,d^5+8\,a^6\,b^{14}\,d^5+a^4\,b^{16}\,d^5}+\frac{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,\left(-512\,a^{26}\,b^3\,d^4\,e^{10}-4608\,a^{24}\,b^5\,d^4\,e^{10}-17920\,a^{22}\,b^7\,d^4\,e^{10}-38400\,a^{20}\,b^9\,d^4\,e^{10}-46080\,a^{18}\,b^{11}\,d^4\,e^{10}-21504\,a^{16}\,b^{13}\,d^4\,e^{10}+21504\,a^{14}\,b^{15}\,d^4\,e^{10}+46080\,a^{12}\,b^{17}\,d^4\,e^{10}+38400\,a^{10}\,b^{19}\,d^4\,e^{10}+17920\,a^8\,b^{21}\,d^4\,e^{10}+4608\,a^6\,b^{23}\,d^4\,e^{10}+512\,a^4\,b^{25}\,d^4\,e^{10}\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)\,\left(a^{20}\,d^4+8\,a^{18}\,b^2\,d^4+28\,a^{16}\,b^4\,d^4+56\,a^{14}\,b^6\,d^4+70\,a^{12}\,b^8\,d^4+56\,a^{10}\,b^{10}\,d^4+28\,a^8\,b^{12}\,d^4+8\,a^6\,b^{14}\,d^4+a^4\,b^{16}\,d^4\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)}{8\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}}\right)\,\sqrt{-a^5\,b^3\,e}\,\left(35\,a^4+6\,a^2\,b^2+3\,b^4\right)\,1{}\mathrm{i}}{4\,\left(d\,e\,a^{11}+3\,d\,e\,a^9\,b^2+3\,d\,e\,a^7\,b^4+d\,e\,a^5\,b^6\right)}","Not used",1,"atan(((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) - ((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) + ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) + ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))*1i - (1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) - ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) - ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))*1i)/((9*b^14*e^8 + 60*a^2*b^12*e^8 + 318*a^4*b^10*e^8 + 748*a^6*b^8*e^8 + 1505*a^8*b^6*e^8)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + (1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) - ((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) + ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) + ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) + (1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*(e*cot(c + d*x))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) - ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)) - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) - ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))))*(1i/(4*(b^6*d^2*e - a^6*d^2*e - 15*a^2*b^4*d^2*e - a^3*b^3*d^2*e*20i + 15*a^4*b^2*d^2*e + a*b^5*d^2*e*6i + a^5*b*d^2*e*6i)))^(1/2)*2i - ((b^3*(e*cot(c + d*x))^(3/2)*(11*a^2 + 3*b^2))/(4*a^2*(a^4 + b^4 + 2*a^2*b^2)) + (b^2*e*(e*cot(c + d*x))^(1/2)*(13*a^2 + 5*b^2))/(4*a*(a^2 + b^2)^2))/(a^2*d*e^2 + b^2*d*e^2*cot(c + d*x)^2 + 2*a*b*d*e^2*cot(c + d*x)) + atan(((((((((1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) - ((e*cot(c + d*x))^(1/2)*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(4*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))))/2 + ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 + ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*1i - (((((((1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) + ((e*cot(c + d*x))^(1/2)*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(4*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))))/2 - ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 - ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*1i)/((9*b^14*e^8 + 60*a^2*b^12*e^8 + 318*a^4*b^10*e^8 + 748*a^6*b^8*e^8 + 1505*a^8*b^6*e^8)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + (((((((1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) - ((e*cot(c + d*x))^(1/2)*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(4*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))))/2 + ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 + ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2) + (((((((1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)) + ((e*cot(c + d*x))^(1/2)*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(4*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4))))/2 - ((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 - (90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(2*(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2))/2 - ((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(2*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)))*(1/(b^6*d^2*e*1i - a^6*d^2*e*1i - a^2*b^4*d^2*e*15i - 20*a^3*b^3*d^2*e + a^4*b^2*d^2*e*15i + 6*a*b^5*d^2*e + 6*a^5*b*d^2*e))^(1/2)*1i + (atan((((((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) - (((90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) + (((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*1i)/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)) + ((((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) + (((90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) - (((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*1i)/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))/((9*b^14*e^8 + 60*a^2*b^12*e^8 + 318*a^4*b^10*e^8 + 748*a^6*b^8*e^8 + 1505*a^8*b^6*e^8)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) - (((90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) - ((((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) + (((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) - ((e*cot(c + d*x))^(1/2)*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)) - ((((e*cot(c + d*x))^(1/2)*(18*a^2*b^15*e^8 - 9*b^17*e^8 - 71*a^4*b^13*e^8 + 892*a^6*b^11*e^8 + 857*a^8*b^9*e^8 + 6802*a^10*b^7*e^8 - 1257*a^12*b^5*e^8))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) + (((90*a*b^19*d^2*e^9 + 846*a^3*b^17*d^2*e^9 + 1714*a^5*b^15*d^2*e^9 + 3606*a^7*b^13*d^2*e^9 - 14578*a^9*b^11*d^2*e^9 - 34486*a^11*b^9*d^2*e^9 - 14970*a^13*b^7*d^2*e^9 + 2258*a^15*b^5*d^2*e^9 - 32*a^17*b^3*d^2*e^9)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((((e*cot(c + d*x))^(1/2)*(72*a*b^22*d^2*e^9 + 576*a^3*b^20*d^2*e^9 + 5024*a^5*b^18*d^2*e^9 + 14272*a^7*b^16*d^2*e^9 + 27824*a^9*b^14*d^2*e^9 + 53184*a^11*b^12*d^2*e^9 + 70240*a^13*b^10*d^2*e^9 + 47680*a^15*b^8*d^2*e^9 + 12616*a^17*b^6*d^2*e^9 - 64*a^21*b^2*d^2*e^9))/(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4) - (((192*a^2*b^24*d^4*e^10 + 1728*a^4*b^22*d^4*e^10 + 8320*a^6*b^20*d^4*e^10 + 27264*a^8*b^18*d^4*e^10 + 62592*a^10*b^16*d^4*e^10 + 99456*a^12*b^14*d^4*e^10 + 107520*a^14*b^12*d^4*e^10 + 76800*a^16*b^10*d^4*e^10 + 33984*a^18*b^8*d^4*e^10 + 7872*a^20*b^6*d^4*e^10 + 384*a^22*b^4*d^4*e^10 - 128*a^24*b^2*d^4*e^10)/(a^20*d^5 + a^4*b^16*d^5 + 8*a^6*b^14*d^5 + 28*a^8*b^12*d^5 + 56*a^10*b^10*d^5 + 70*a^12*b^8*d^5 + 56*a^14*b^6*d^5 + 28*a^16*b^4*d^5 + 8*a^18*b^2*d^5) + ((e*cot(c + d*x))^(1/2)*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*(512*a^4*b^25*d^4*e^10 + 4608*a^6*b^23*d^4*e^10 + 17920*a^8*b^21*d^4*e^10 + 38400*a^10*b^19*d^4*e^10 + 46080*a^12*b^17*d^4*e^10 + 21504*a^14*b^15*d^4*e^10 - 21504*a^16*b^13*d^4*e^10 - 46080*a^18*b^11*d^4*e^10 - 38400*a^20*b^9*d^4*e^10 - 17920*a^22*b^7*d^4*e^10 - 4608*a^24*b^5*d^4*e^10 - 512*a^26*b^3*d^4*e^10))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)*(a^20*d^4 + a^4*b^16*d^4 + 8*a^6*b^14*d^4 + 28*a^8*b^12*d^4 + 56*a^10*b^10*d^4 + 70*a^12*b^8*d^4 + 56*a^14*b^6*d^4 + 28*a^16*b^4*d^4 + 8*a^18*b^2*d^4)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e)))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2))/(8*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e))))*(-a^5*b^3*e)^(1/2)*(35*a^4 + 3*b^4 + 6*a^2*b^2)*1i)/(4*(a^11*d*e + a^5*b^6*d*e + 3*a^7*b^4*d*e + 3*a^9*b^2*d*e))","B"
87,1,21158,529,9.998799,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + b*cot(c + d*x))^3),x)","\frac{\frac{2\,e}{a}+\frac{e\,\mathrm{cot}\left(c+d\,x\right)\,\left(16\,a^4\,b+49\,a^2\,b^3+25\,b^5\right)}{4\,a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b^2\,e^2\,{\mathrm{cot}\left(c+d\,x\right)}^2\,\left(8\,a^4+31\,a^2\,b^2+15\,b^4\right)}{4\,a^3\,\left(e\,a^4+2\,e\,a^2\,b^2+e\,b^4\right)}}{b^2\,d\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}+a^2\,d\,e^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}+2\,a\,b\,d\,e\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}+\mathrm{atan}\left(\frac{\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,\left(\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16777216\,a^{64}\,b^2\,d^7\,e^{16}+167772160\,a^{62}\,b^4\,d^7\,e^{16}+16777216\,a^{60}\,b^6\,d^7\,e^{16}+1612709888\,a^{58}\,b^8\,d^7\,e^{16}+86608183296\,a^{56}\,b^{10}\,d^7\,e^{16}+805425905664\,a^{54}\,b^{12}\,d^7\,e^{16}+4030457708544\,a^{52}\,b^{14}\,d^7\,e^{16}+13411815522304\,a^{50}\,b^{16}\,d^7\,e^{16}+32432589897728\,a^{48}\,b^{18}\,d^7\,e^{16}+59767095558144\,a^{46}\,b^{20}\,d^7\,e^{16}+86342935511040\,a^{44}\,b^{22}\,d^7\,e^{16}+99508717355008\,a^{42}\,b^{24}\,d^7\,e^{16}+92434029608960\,a^{40}\,b^{26}\,d^7\,e^{16}+69534945902592\,a^{38}\,b^{28}\,d^7\,e^{16}+42351565209600\,a^{36}\,b^{30}\,d^7\,e^{16}+20769933361152\,a^{34}\,b^{32}\,d^7\,e^{16}+8104469069824\,a^{32}\,b^{34}\,d^7\,e^{16}+2464648527872\,a^{30}\,b^{36}\,d^7\,e^{16}+564502986752\,a^{28}\,b^{38}\,d^7\,e^{16}+91857354752\,a^{26}\,b^{40}\,d^7\,e^{16}+9500098560\,a^{24}\,b^{42}\,d^7\,e^{16}+471859200\,a^{22}\,b^{44}\,d^7\,e^{16}\right)+\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,\left(251658240\,a^{24}\,b^{45}\,d^8\,e^{18}-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,\left(-134217728\,a^{69}\,b^3\,d^9\,e^{19}-2550136832\,a^{67}\,b^5\,d^9\,e^{19}-22817013760\,a^{65}\,b^7\,d^9\,e^{19}-127506841600\,a^{63}\,b^9\,d^9\,e^{19}-497276682240\,a^{61}\,b^{11}\,d^9\,e^{19}-1430626762752\,a^{59}\,b^{13}\,d^9\,e^{19}-3121367482368\,a^{57}\,b^{15}\,d^9\,e^{19}-5202279137280\,a^{55}\,b^{17}\,d^9\,e^{19}-6502848921600\,a^{53}\,b^{19}\,d^9\,e^{19}-5635802398720\,a^{51}\,b^{21}\,d^9\,e^{19}-2254320959488\,a^{49}\,b^{23}\,d^9\,e^{19}+2254320959488\,a^{47}\,b^{25}\,d^9\,e^{19}+5635802398720\,a^{45}\,b^{27}\,d^9\,e^{19}+6502848921600\,a^{43}\,b^{29}\,d^9\,e^{19}+5202279137280\,a^{41}\,b^{31}\,d^9\,e^{19}+3121367482368\,a^{39}\,b^{33}\,d^9\,e^{19}+1430626762752\,a^{37}\,b^{35}\,d^9\,e^{19}+497276682240\,a^{35}\,b^{37}\,d^9\,e^{19}+127506841600\,a^{33}\,b^{39}\,d^9\,e^{19}+22817013760\,a^{31}\,b^{41}\,d^9\,e^{19}+2550136832\,a^{29}\,b^{43}\,d^9\,e^{19}+134217728\,a^{27}\,b^{45}\,d^9\,e^{19}\right)+5049942016\,a^{26}\,b^{43}\,d^8\,e^{18}+48368713728\,a^{28}\,b^{41}\,d^8\,e^{18}+293819383808\,a^{30}\,b^{39}\,d^8\,e^{18}+1268458192896\,a^{32}\,b^{37}\,d^8\,e^{18}+4132731617280\,a^{34}\,b^{35}\,d^8\,e^{18}+10531192700928\,a^{36}\,b^{33}\,d^8\,e^{18}+21462823993344\,a^{38}\,b^{31}\,d^8\,e^{18}+35469618315264\,a^{40}\,b^{29}\,d^8\,e^{18}+47896904859648\,a^{42}\,b^{27}\,d^8\,e^{18}+52983958077440\,a^{44}\,b^{25}\,d^8\,e^{18}+47896904859648\,a^{46}\,b^{23}\,d^8\,e^{18}+35090285461504\,a^{48}\,b^{21}\,d^8\,e^{18}+20487396655104\,a^{50}\,b^{19}\,d^8\,e^{18}+9230622916608\,a^{52}\,b^{17}\,d^8\,e^{18}+2994733056000\,a^{54}\,b^{15}\,d^8\,e^{18}+565576728576\,a^{56}\,b^{13}\,d^8\,e^{18}-18572378112\,a^{58}\,b^{11}\,d^8\,e^{18}-50281316352\,a^{60}\,b^9\,d^8\,e^{18}-16089350144\,a^{62}\,b^7\,d^8\,e^{18}-2516582400\,a^{64}\,b^5\,d^8\,e^{18}-167772160\,a^{66}\,b^3\,d^8\,e^{18}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}-117964800\,a^{21}\,b^{42}\,d^6\,e^{15}-841482240\,a^{23}\,b^{40}\,d^6\,e^{15}+3829399552\,a^{25}\,b^{38}\,d^6\,e^{15}+78068580352\,a^{27}\,b^{36}\,d^6\,e^{15}+497438162944\,a^{29}\,b^{34}\,d^6\,e^{15}+1899895980032\,a^{31}\,b^{32}\,d^6\,e^{15}+4972695519232\,a^{33}\,b^{30}\,d^6\,e^{15}+9371195015168\,a^{35}\,b^{28}\,d^6\,e^{15}+12890720436224\,a^{37}\,b^{26}\,d^6\,e^{15}+12726089809920\,a^{39}\,b^{24}\,d^6\,e^{15}+8366961197056\,a^{41}\,b^{22}\,d^6\,e^{15}+2597662490624\,a^{43}\,b^{20}\,d^6\,e^{15}-1171836108800\,a^{45}\,b^{18}\,d^6\,e^{15}-1986881650688\,a^{47}\,b^{16}\,d^6\,e^{15}-1237583921152\,a^{49}\,b^{14}\,d^6\,e^{15}-449507753984\,a^{51}\,b^{12}\,d^6\,e^{15}-97476149248\,a^{53}\,b^{10}\,d^6\,e^{15}-11931222016\,a^{55}\,b^8\,d^6\,e^{15}-1006632960\,a^{57}\,b^6\,d^6\,e^{15}-134217728\,a^{59}\,b^4\,d^6\,e^{15}-8388608\,a^{61}\,b^2\,d^6\,e^{15}\right)-\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(8388608\,a^{55}\,b^5\,d^5\,e^{13}-923009024\,a^{53}\,b^7\,d^5\,e^{13}-4917821440\,a^{51}\,b^9\,d^5\,e^{13}+10492051456\,a^{49}\,b^{11}\,d^5\,e^{13}+170768990208\,a^{47}\,b^{13}\,d^5\,e^{13}+726513221632\,a^{45}\,b^{15}\,d^5\,e^{13}+1807474491392\,a^{43}\,b^{17}\,d^5\,e^{13}+3053967114240\,a^{41}\,b^{19}\,d^5\,e^{13}+3717287903232\,a^{39}\,b^{21}\,d^5\,e^{13}+3345249468416\,a^{37}\,b^{23}\,d^5\,e^{13}+2240523796480\,a^{35}\,b^{25}\,d^5\,e^{13}+1104303620096\,a^{33}\,b^{27}\,d^5\,e^{13}+385487994880\,a^{31}\,b^{29}\,d^5\,e^{13}+85774565376\,a^{29}\,b^{31}\,d^5\,e^{13}+7610564608\,a^{27}\,b^{33}\,d^5\,e^{13}-1671430144\,a^{25}\,b^{35}\,d^5\,e^{13}-597688320\,a^{23}\,b^{37}\,d^5\,e^{13}-58982400\,a^{21}\,b^{39}\,d^5\,e^{13}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,1{}\mathrm{i}+\left(\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,\left(\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(16777216\,a^{64}\,b^2\,d^7\,e^{16}+167772160\,a^{62}\,b^4\,d^7\,e^{16}+16777216\,a^{60}\,b^6\,d^7\,e^{16}+1612709888\,a^{58}\,b^8\,d^7\,e^{16}+86608183296\,a^{56}\,b^{10}\,d^7\,e^{16}+805425905664\,a^{54}\,b^{12}\,d^7\,e^{16}+4030457708544\,a^{52}\,b^{14}\,d^7\,e^{16}+13411815522304\,a^{50}\,b^{16}\,d^7\,e^{16}+32432589897728\,a^{48}\,b^{18}\,d^7\,e^{16}+59767095558144\,a^{46}\,b^{20}\,d^7\,e^{16}+86342935511040\,a^{44}\,b^{22}\,d^7\,e^{16}+99508717355008\,a^{42}\,b^{24}\,d^7\,e^{16}+92434029608960\,a^{40}\,b^{26}\,d^7\,e^{16}+69534945902592\,a^{38}\,b^{28}\,d^7\,e^{16}+42351565209600\,a^{36}\,b^{30}\,d^7\,e^{16}+20769933361152\,a^{34}\,b^{32}\,d^7\,e^{16}+8104469069824\,a^{32}\,b^{34}\,d^7\,e^{16}+2464648527872\,a^{30}\,b^{36}\,d^7\,e^{16}+564502986752\,a^{28}\,b^{38}\,d^7\,e^{16}+91857354752\,a^{26}\,b^{40}\,d^7\,e^{16}+9500098560\,a^{24}\,b^{42}\,d^7\,e^{16}+471859200\,a^{22}\,b^{44}\,d^7\,e^{16}\right)-\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,\left(\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}\,\left(-134217728\,a^{69}\,b^3\,d^9\,e^{19}-2550136832\,a^{67}\,b^5\,d^9\,e^{19}-22817013760\,a^{65}\,b^7\,d^9\,e^{19}-127506841600\,a^{63}\,b^9\,d^9\,e^{19}-497276682240\,a^{61}\,b^{11}\,d^9\,e^{19}-1430626762752\,a^{59}\,b^{13}\,d^9\,e^{19}-3121367482368\,a^{57}\,b^{15}\,d^9\,e^{19}-5202279137280\,a^{55}\,b^{17}\,d^9\,e^{19}-6502848921600\,a^{53}\,b^{19}\,d^9\,e^{19}-5635802398720\,a^{51}\,b^{21}\,d^9\,e^{19}-2254320959488\,a^{49}\,b^{23}\,d^9\,e^{19}+2254320959488\,a^{47}\,b^{25}\,d^9\,e^{19}+5635802398720\,a^{45}\,b^{27}\,d^9\,e^{19}+6502848921600\,a^{43}\,b^{29}\,d^9\,e^{19}+5202279137280\,a^{41}\,b^{31}\,d^9\,e^{19}+3121367482368\,a^{39}\,b^{33}\,d^9\,e^{19}+1430626762752\,a^{37}\,b^{35}\,d^9\,e^{19}+497276682240\,a^{35}\,b^{37}\,d^9\,e^{19}+127506841600\,a^{33}\,b^{39}\,d^9\,e^{19}+22817013760\,a^{31}\,b^{41}\,d^9\,e^{19}+2550136832\,a^{29}\,b^{43}\,d^9\,e^{19}+134217728\,a^{27}\,b^{45}\,d^9\,e^{19}\right)+251658240\,a^{24}\,b^{45}\,d^8\,e^{18}+5049942016\,a^{26}\,b^{43}\,d^8\,e^{18}+48368713728\,a^{28}\,b^{41}\,d^8\,e^{18}+293819383808\,a^{30}\,b^{39}\,d^8\,e^{18}+1268458192896\,a^{32}\,b^{37}\,d^8\,e^{18}+4132731617280\,a^{34}\,b^{35}\,d^8\,e^{18}+10531192700928\,a^{36}\,b^{33}\,d^8\,e^{18}+21462823993344\,a^{38}\,b^{31}\,d^8\,e^{18}+35469618315264\,a^{40}\,b^{29}\,d^8\,e^{18}+47896904859648\,a^{42}\,b^{27}\,d^8\,e^{18}+52983958077440\,a^{44}\,b^{25}\,d^8\,e^{18}+47896904859648\,a^{46}\,b^{23}\,d^8\,e^{18}+35090285461504\,a^{48}\,b^{21}\,d^8\,e^{18}+20487396655104\,a^{50}\,b^{19}\,d^8\,e^{18}+9230622916608\,a^{52}\,b^{17}\,d^8\,e^{18}+2994733056000\,a^{54}\,b^{15}\,d^8\,e^{18}+565576728576\,a^{56}\,b^{13}\,d^8\,e^{18}-18572378112\,a^{58}\,b^{11}\,d^8\,e^{18}-50281316352\,a^{60}\,b^9\,d^8\,e^{18}-16089350144\,a^{62}\,b^7\,d^8\,e^{18}-2516582400\,a^{64}\,b^5\,d^8\,e^{18}-167772160\,a^{66}\,b^3\,d^8\,e^{18}\right)\right)\,\sqrt{-\frac{1{}\mathrm{i}}{4\,\left(-a^6\,d^2\,e^3+a^5\,b\,d^2\,e^3\,6{}\mathrm{i}+15\,a^4\,b^2\,d^2\,e^3-a^3\,b^3\,d^2\,e^3\,20{}\mathrm{i}-15\,a^2\,b^4\,d^2\,e^3+a\,b^5\,d^2\,e^3\,6{}\mathrm{i}+b^6\,d^2\,e^3\right)}}+117964800\,a^{21}\,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used",1,"((2*e)/a + (e*cot(c + d*x)*(16*a^4*b + 25*b^5 + 49*a^2*b^3))/(4*a^2*(a^4 + b^4 + 2*a^2*b^2)) + (b^2*e^2*cot(c + d*x)^2*(8*a^4 + 15*b^4 + 31*a^2*b^2))/(4*a^3*(a^4*e + b^4*e + 2*a^2*b^2*e)))/(b^2*d*(e*cot(c + d*x))^(5/2) + a^2*d*e^2*(e*cot(c + d*x))^(1/2) + 2*a*b*d*e*(e*cot(c + d*x))^(3/2)) + atan((((-1i/(4*(b^6*d^2*e^3 - a^6*d^2*e^3 + a*b^5*d^2*e^3*6i + a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2)*(((e*cot(c + d*x))^(1/2)*(471859200*a^22*b^44*d^7*e^16 + 9500098560*a^24*b^42*d^7*e^16 + 91857354752*a^26*b^40*d^7*e^16 + 564502986752*a^28*b^38*d^7*e^16 + 2464648527872*a^30*b^36*d^7*e^16 + 8104469069824*a^32*b^34*d^7*e^16 + 20769933361152*a^34*b^32*d^7*e^16 + 42351565209600*a^36*b^30*d^7*e^16 + 69534945902592*a^38*b^28*d^7*e^16 + 92434029608960*a^40*b^26*d^7*e^16 + 99508717355008*a^42*b^24*d^7*e^16 + 86342935511040*a^44*b^22*d^7*e^16 + 59767095558144*a^46*b^20*d^7*e^16 + 32432589897728*a^48*b^18*d^7*e^16 + 13411815522304*a^50*b^16*d^7*e^16 + 4030457708544*a^52*b^14*d^7*e^16 + 805425905664*a^54*b^12*d^7*e^16 + 86608183296*a^56*b^10*d^7*e^16 + 1612709888*a^58*b^8*d^7*e^16 + 16777216*a^60*b^6*d^7*e^16 + 167772160*a^62*b^4*d^7*e^16 + 16777216*a^64*b^2*d^7*e^16) + (-1i/(4*(b^6*d^2*e^3 - a^6*d^2*e^3 + a*b^5*d^2*e^3*6i + a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2)*(251658240*a^24*b^45*d^8*e^18 - (e*cot(c + d*x))^(1/2)*(-1i/(4*(b^6*d^2*e^3 - a^6*d^2*e^3 + a*b^5*d^2*e^3*6i + a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2)*(134217728*a^27*b^45*d^9*e^19 + 2550136832*a^29*b^43*d^9*e^19 + 22817013760*a^31*b^41*d^9*e^19 + 127506841600*a^33*b^39*d^9*e^19 + 497276682240*a^35*b^37*d^9*e^19 + 1430626762752*a^37*b^35*d^9*e^19 + 3121367482368*a^39*b^33*d^9*e^19 + 5202279137280*a^41*b^31*d^9*e^19 + 6502848921600*a^43*b^29*d^9*e^19 + 5635802398720*a^45*b^27*d^9*e^19 + 2254320959488*a^47*b^25*d^9*e^19 - 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16089350144*a^62*b^7*d^8*e^18 - 2516582400*a^64*b^5*d^8*e^18 - 167772160*a^66*b^3*d^8*e^18))*(-1i/(4*(b^6*d^2*e^3 - a^6*d^2*e^3 + a*b^5*d^2*e^3*6i + a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2) - 117964800*a^21*b^42*d^6*e^15 - 841482240*a^23*b^40*d^6*e^15 + 3829399552*a^25*b^38*d^6*e^15 + 78068580352*a^27*b^36*d^6*e^15 + 497438162944*a^29*b^34*d^6*e^15 + 1899895980032*a^31*b^32*d^6*e^15 + 4972695519232*a^33*b^30*d^6*e^15 + 9371195015168*a^35*b^28*d^6*e^15 + 12890720436224*a^37*b^26*d^6*e^15 + 12726089809920*a^39*b^24*d^6*e^15 + 8366961197056*a^41*b^22*d^6*e^15 + 2597662490624*a^43*b^20*d^6*e^15 - 1171836108800*a^45*b^18*d^6*e^15 - 1986881650688*a^47*b^16*d^6*e^15 - 1237583921152*a^49*b^14*d^6*e^15 - 449507753984*a^51*b^12*d^6*e^15 - 97476149248*a^53*b^10*d^6*e^15 - 11931222016*a^55*b^8*d^6*e^15 - 1006632960*a^57*b^6*d^6*e^15 - 134217728*a^59*b^4*d^6*e^15 - 8388608*a^61*b^2*d^6*e^15) - (e*cot(c + d*x))^(1/2)*(7610564608*a^27*b^33*d^5*e^13 - 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2550136832*a^29*b^43*d^9*e^19 + 22817013760*a^31*b^41*d^9*e^19 + 127506841600*a^33*b^39*d^9*e^19 + 497276682240*a^35*b^37*d^9*e^19 + 1430626762752*a^37*b^35*d^9*e^19 + 3121367482368*a^39*b^33*d^9*e^19 + 5202279137280*a^41*b^31*d^9*e^19 + 6502848921600*a^43*b^29*d^9*e^19 + 5635802398720*a^45*b^27*d^9*e^19 + 2254320959488*a^47*b^25*d^9*e^19 - 2254320959488*a^49*b^23*d^9*e^19 - 5635802398720*a^51*b^21*d^9*e^19 - 6502848921600*a^53*b^19*d^9*e^19 - 5202279137280*a^55*b^17*d^9*e^19 - 3121367482368*a^57*b^15*d^9*e^19 - 1430626762752*a^59*b^13*d^9*e^19 - 497276682240*a^61*b^11*d^9*e^19 - 127506841600*a^63*b^9*d^9*e^19 - 22817013760*a^65*b^7*d^9*e^19 - 2550136832*a^67*b^5*d^9*e^19 - 134217728*a^69*b^3*d^9*e^19) + 251658240*a^24*b^45*d^8*e^18 + 5049942016*a^26*b^43*d^8*e^18 + 48368713728*a^28*b^41*d^8*e^18 + 293819383808*a^30*b^39*d^8*e^18 + 1268458192896*a^32*b^37*d^8*e^18 + 4132731617280*a^34*b^35*d^8*e^18 + 10531192700928*a^36*b^33*d^8*e^18 + 21462823993344*a^38*b^31*d^8*e^18 + 35469618315264*a^40*b^29*d^8*e^18 + 47896904859648*a^42*b^27*d^8*e^18 + 52983958077440*a^44*b^25*d^8*e^18 + 47896904859648*a^46*b^23*d^8*e^18 + 35090285461504*a^48*b^21*d^8*e^18 + 20487396655104*a^50*b^19*d^8*e^18 + 9230622916608*a^52*b^17*d^8*e^18 + 2994733056000*a^54*b^15*d^8*e^18 + 565576728576*a^56*b^13*d^8*e^18 - 18572378112*a^58*b^11*d^8*e^18 - 50281316352*a^60*b^9*d^8*e^18 - 16089350144*a^62*b^7*d^8*e^18 - 2516582400*a^64*b^5*d^8*e^18 - 167772160*a^66*b^3*d^8*e^18))*(-1i/(4*(b^6*d^2*e^3 - a^6*d^2*e^3 + a*b^5*d^2*e^3*6i + a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2) + 117964800*a^21*b^42*d^6*e^15 + 841482240*a^23*b^40*d^6*e^15 - 3829399552*a^25*b^38*d^6*e^15 - 78068580352*a^27*b^36*d^6*e^15 - 497438162944*a^29*b^34*d^6*e^15 - 1899895980032*a^31*b^32*d^6*e^15 - 4972695519232*a^33*b^30*d^6*e^15 - 9371195015168*a^35*b^28*d^6*e^15 - 12890720436224*a^37*b^26*d^6*e^15 - 12726089809920*a^39*b^24*d^6*e^15 - 8366961197056*a^41*b^22*d^6*e^15 - 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a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2)*1i)/(((-1i/(4*(b^6*d^2*e^3 - a^6*d^2*e^3 + a*b^5*d^2*e^3*6i + a^5*b*d^2*e^3*6i - 15*a^2*b^4*d^2*e^3 - a^3*b^3*d^2*e^3*20i + 15*a^4*b^2*d^2*e^3)))^(1/2)*(((e*cot(c + d*x))^(1/2)*(471859200*a^22*b^44*d^7*e^16 + 9500098560*a^24*b^42*d^7*e^16 + 91857354752*a^26*b^40*d^7*e^16 + 564502986752*a^28*b^38*d^7*e^16 + 2464648527872*a^30*b^36*d^7*e^16 + 8104469069824*a^32*b^34*d^7*e^16 + 20769933361152*a^34*b^32*d^7*e^16 + 42351565209600*a^36*b^30*d^7*e^16 + 69534945902592*a^38*b^28*d^7*e^16 + 92434029608960*a^40*b^26*d^7*e^16 + 99508717355008*a^42*b^24*d^7*e^16 + 86342935511040*a^44*b^22*d^7*e^16 + 59767095558144*a^46*b^20*d^7*e^16 + 32432589897728*a^48*b^18*d^7*e^16 + 13411815522304*a^50*b^16*d^7*e^16 + 4030457708544*a^52*b^14*d^7*e^16 + 805425905664*a^54*b^12*d^7*e^16 + 86608183296*a^56*b^10*d^7*e^16 + 1612709888*a^58*b^8*d^7*e^16 + 16777216*a^60*b^6*d^7*e^16 + 167772160*a^62*b^4*d^7*e^16 + 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497276682240*a^35*b^37*d^9*e^19 + 1430626762752*a^37*b^35*d^9*e^19 + 3121367482368*a^39*b^33*d^9*e^19 + 5202279137280*a^41*b^31*d^9*e^19 + 6502848921600*a^43*b^29*d^9*e^19 + 5635802398720*a^45*b^27*d^9*e^19 + 2254320959488*a^47*b^25*d^9*e^19 - 2254320959488*a^49*b^23*d^9*e^19 - 5635802398720*a^51*b^21*d^9*e^19 - 6502848921600*a^53*b^19*d^9*e^19 - 5202279137280*a^55*b^17*d^9*e^19 - 3121367482368*a^57*b^15*d^9*e^19 - 1430626762752*a^59*b^13*d^9*e^19 - 497276682240*a^61*b^11*d^9*e^19 - 127506841600*a^63*b^9*d^9*e^19 - 22817013760*a^65*b^7*d^9*e^19 - 2550136832*a^67*b^5*d^9*e^19 - 134217728*a^69*b^3*d^9*e^19) + 251658240*a^24*b^45*d^8*e^18 + 5049942016*a^26*b^43*d^8*e^18 + 48368713728*a^28*b^41*d^8*e^18 + 293819383808*a^30*b^39*d^8*e^18 + 1268458192896*a^32*b^37*d^8*e^18 + 4132731617280*a^34*b^35*d^8*e^18 + 10531192700928*a^36*b^33*d^8*e^18 + 21462823993344*a^38*b^31*d^8*e^18 + 35469618315264*a^40*b^29*d^8*e^18 + 47896904859648*a^42*b^27*d^8*e^18 + 52983958077440*a^44*b^25*d^8*e^18 + 47896904859648*a^46*b^23*d^8*e^18 + 35090285461504*a^48*b^21*d^8*e^18 + 20487396655104*a^50*b^19*d^8*e^18 + 9230622916608*a^52*b^17*d^8*e^18 + 2994733056000*a^54*b^15*d^8*e^18 + 565576728576*a^56*b^13*d^8*e^18 - 18572378112*a^58*b^11*d^8*e^18 - 50281316352*a^60*b^9*d^8*e^18 - 16089350144*a^62*b^7*d^8*e^18 - 2516582400*a^64*b^5*d^8*e^18 - 167772160*a^66*b^3*d^8*e^18))*(-1/(4*(b^6*d^2*e^3*1i - a^6*d^2*e^3*1i + 6*a*b^5*d^2*e^3 + 6*a^5*b*d^2*e^3 - a^2*b^4*d^2*e^3*15i - 20*a^3*b^3*d^2*e^3 + a^4*b^2*d^2*e^3*15i)))^(1/2) + 117964800*a^21*b^42*d^6*e^15 + 841482240*a^23*b^40*d^6*e^15 - 3829399552*a^25*b^38*d^6*e^15 - 78068580352*a^27*b^36*d^6*e^15 - 497438162944*a^29*b^34*d^6*e^15 - 1899895980032*a^31*b^32*d^6*e^15 - 4972695519232*a^33*b^30*d^6*e^15 - 9371195015168*a^35*b^28*d^6*e^15 - 12890720436224*a^37*b^26*d^6*e^15 - 12726089809920*a^39*b^24*d^6*e^15 - 8366961197056*a^41*b^22*d^6*e^15 - 2597662490624*a^43*b^20*d^6*e^15 + 1171836108800*a^45*b^18*d^6*e^15 + 1986881650688*a^47*b^16*d^6*e^15 + 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2516582400*a^64*b^5*d^8*e^18 - 167772160*a^66*b^3*d^8*e^18 - ((e*cot(c + d*x))^(1/2)*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2)*(134217728*a^27*b^45*d^9*e^19 + 2550136832*a^29*b^43*d^9*e^19 + 22817013760*a^31*b^41*d^9*e^19 + 127506841600*a^33*b^39*d^9*e^19 + 497276682240*a^35*b^37*d^9*e^19 + 1430626762752*a^37*b^35*d^9*e^19 + 3121367482368*a^39*b^33*d^9*e^19 + 5202279137280*a^41*b^31*d^9*e^19 + 6502848921600*a^43*b^29*d^9*e^19 + 5635802398720*a^45*b^27*d^9*e^19 + 2254320959488*a^47*b^25*d^9*e^19 - 2254320959488*a^49*b^23*d^9*e^19 - 5635802398720*a^51*b^21*d^9*e^19 - 6502848921600*a^53*b^19*d^9*e^19 - 5202279137280*a^55*b^17*d^9*e^19 - 3121367482368*a^57*b^15*d^9*e^19 - 1430626762752*a^59*b^13*d^9*e^19 - 497276682240*a^61*b^11*d^9*e^19 - 127506841600*a^63*b^9*d^9*e^19 - 22817013760*a^65*b^7*d^9*e^19 - 2550136832*a^67*b^5*d^9*e^19 - 134217728*a^69*b^3*d^9*e^19))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3))))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)))*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)) - 117964800*a^21*b^42*d^6*e^15 - 841482240*a^23*b^40*d^6*e^15 + 3829399552*a^25*b^38*d^6*e^15 + 78068580352*a^27*b^36*d^6*e^15 + 497438162944*a^29*b^34*d^6*e^15 + 1899895980032*a^31*b^32*d^6*e^15 + 4972695519232*a^33*b^30*d^6*e^15 + 9371195015168*a^35*b^28*d^6*e^15 + 12890720436224*a^37*b^26*d^6*e^15 + 12726089809920*a^39*b^24*d^6*e^15 + 8366961197056*a^41*b^22*d^6*e^15 + 2597662490624*a^43*b^20*d^6*e^15 - 1171836108800*a^45*b^18*d^6*e^15 - 1986881650688*a^47*b^16*d^6*e^15 - 1237583921152*a^49*b^14*d^6*e^15 - 449507753984*a^51*b^12*d^6*e^15 - 97476149248*a^53*b^10*d^6*e^15 - 11931222016*a^55*b^8*d^6*e^15 - 1006632960*a^57*b^6*d^6*e^15 - 134217728*a^59*b^4*d^6*e^15 - 8388608*a^61*b^2*d^6*e^15))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)))*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)) - (((e*cot(c + d*x))^(1/2)*(7610564608*a^27*b^33*d^5*e^13 - 597688320*a^23*b^37*d^5*e^13 - 1671430144*a^25*b^35*d^5*e^13 - 58982400*a^21*b^39*d^5*e^13 + 85774565376*a^29*b^31*d^5*e^13 + 385487994880*a^31*b^29*d^5*e^13 + 1104303620096*a^33*b^27*d^5*e^13 + 2240523796480*a^35*b^25*d^5*e^13 + 3345249468416*a^37*b^23*d^5*e^13 + 3717287903232*a^39*b^21*d^5*e^13 + 3053967114240*a^41*b^19*d^5*e^13 + 1807474491392*a^43*b^17*d^5*e^13 + 726513221632*a^45*b^15*d^5*e^13 + 170768990208*a^47*b^13*d^5*e^13 + 10492051456*a^49*b^11*d^5*e^13 - 4917821440*a^51*b^9*d^5*e^13 - 923009024*a^53*b^7*d^5*e^13 + 8388608*a^55*b^5*d^5*e^13) - ((63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2)*((((e*cot(c + d*x))^(1/2)*(471859200*a^22*b^44*d^7*e^16 + 9500098560*a^24*b^42*d^7*e^16 + 91857354752*a^26*b^40*d^7*e^16 + 564502986752*a^28*b^38*d^7*e^16 + 2464648527872*a^30*b^36*d^7*e^16 + 8104469069824*a^32*b^34*d^7*e^16 + 20769933361152*a^34*b^32*d^7*e^16 + 42351565209600*a^36*b^30*d^7*e^16 + 69534945902592*a^38*b^28*d^7*e^16 + 92434029608960*a^40*b^26*d^7*e^16 + 99508717355008*a^42*b^24*d^7*e^16 + 86342935511040*a^44*b^22*d^7*e^16 + 59767095558144*a^46*b^20*d^7*e^16 + 32432589897728*a^48*b^18*d^7*e^16 + 13411815522304*a^50*b^16*d^7*e^16 + 4030457708544*a^52*b^14*d^7*e^16 + 805425905664*a^54*b^12*d^7*e^16 + 86608183296*a^56*b^10*d^7*e^16 + 1612709888*a^58*b^8*d^7*e^16 + 16777216*a^60*b^6*d^7*e^16 + 167772160*a^62*b^4*d^7*e^16 + 16777216*a^64*b^2*d^7*e^16) - ((63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2)*(251658240*a^24*b^45*d^8*e^18 + 5049942016*a^26*b^43*d^8*e^18 + 48368713728*a^28*b^41*d^8*e^18 + 293819383808*a^30*b^39*d^8*e^18 + 1268458192896*a^32*b^37*d^8*e^18 + 4132731617280*a^34*b^35*d^8*e^18 + 10531192700928*a^36*b^33*d^8*e^18 + 21462823993344*a^38*b^31*d^8*e^18 + 35469618315264*a^40*b^29*d^8*e^18 + 47896904859648*a^42*b^27*d^8*e^18 + 52983958077440*a^44*b^25*d^8*e^18 + 47896904859648*a^46*b^23*d^8*e^18 + 35090285461504*a^48*b^21*d^8*e^18 + 20487396655104*a^50*b^19*d^8*e^18 + 9230622916608*a^52*b^17*d^8*e^18 + 2994733056000*a^54*b^15*d^8*e^18 + 565576728576*a^56*b^13*d^8*e^18 - 18572378112*a^58*b^11*d^8*e^18 - 50281316352*a^60*b^9*d^8*e^18 - 16089350144*a^62*b^7*d^8*e^18 - 2516582400*a^64*b^5*d^8*e^18 - 167772160*a^66*b^3*d^8*e^18 + ((e*cot(c + d*x))^(1/2)*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2)*(134217728*a^27*b^45*d^9*e^19 + 2550136832*a^29*b^43*d^9*e^19 + 22817013760*a^31*b^41*d^9*e^19 + 127506841600*a^33*b^39*d^9*e^19 + 497276682240*a^35*b^37*d^9*e^19 + 1430626762752*a^37*b^35*d^9*e^19 + 3121367482368*a^39*b^33*d^9*e^19 + 5202279137280*a^41*b^31*d^9*e^19 + 6502848921600*a^43*b^29*d^9*e^19 + 5635802398720*a^45*b^27*d^9*e^19 + 2254320959488*a^47*b^25*d^9*e^19 - 2254320959488*a^49*b^23*d^9*e^19 - 5635802398720*a^51*b^21*d^9*e^19 - 6502848921600*a^53*b^19*d^9*e^19 - 5202279137280*a^55*b^17*d^9*e^19 - 3121367482368*a^57*b^15*d^9*e^19 - 1430626762752*a^59*b^13*d^9*e^19 - 497276682240*a^61*b^11*d^9*e^19 - 127506841600*a^63*b^9*d^9*e^19 - 22817013760*a^65*b^7*d^9*e^19 - 2550136832*a^67*b^5*d^9*e^19 - 134217728*a^69*b^3*d^9*e^19))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3))))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)))*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)) + 117964800*a^21*b^42*d^6*e^15 + 841482240*a^23*b^40*d^6*e^15 - 3829399552*a^25*b^38*d^6*e^15 - 78068580352*a^27*b^36*d^6*e^15 - 497438162944*a^29*b^34*d^6*e^15 - 1899895980032*a^31*b^32*d^6*e^15 - 4972695519232*a^33*b^30*d^6*e^15 - 9371195015168*a^35*b^28*d^6*e^15 - 12890720436224*a^37*b^26*d^6*e^15 - 12726089809920*a^39*b^24*d^6*e^15 - 8366961197056*a^41*b^22*d^6*e^15 - 2597662490624*a^43*b^20*d^6*e^15 + 1171836108800*a^45*b^18*d^6*e^15 + 1986881650688*a^47*b^16*d^6*e^15 + 1237583921152*a^49*b^14*d^6*e^15 + 449507753984*a^51*b^12*d^6*e^15 + 97476149248*a^53*b^10*d^6*e^15 + 11931222016*a^55*b^8*d^6*e^15 + 1006632960*a^57*b^6*d^6*e^15 + 134217728*a^59*b^4*d^6*e^15 + 8388608*a^61*b^2*d^6*e^15))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3)))*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2))/(8*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3))))*(63*a^4 + 15*b^4 + 46*a^2*b^2)*(-a^7*b^5*e^3)^(1/2)*1i)/(4*(a^13*d*e^3 + a^7*b^6*d*e^3 + 3*a^9*b^4*d*e^3 + 3*a^11*b^2*d*e^3))","B"
88,0,-1,167,0.000000,"\text{Not used}","int((a + b*cot(c + d*x))^n,x)","\int {\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((a + b*cot(c + d*x))^n, x)","F"
89,0,-1,193,0.000000,"\text{Not used}","int((d*tan(e + f*x))^n*(a + b*cot(e + f*x))^m,x)","\int {\left(d\,\mathrm{tan}\left(e+f\,x\right)\right)}^n\,{\left(a+b\,\mathrm{cot}\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((d*tan(e + f*x))^n*(a + b*cot(e + f*x))^m, x)","F"
90,1,1410,45,2.536429,"\text{Not used}","int((cot(c + d*x)*1i + 1)/(a + b*cot(c + d*x))^(1/2),x)","\frac{\ln\left(d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}+1{}\mathrm{i}\right)\,\sqrt{-\frac{1}{a\,d^2-b\,d^2\,1{}\mathrm{i}}}}{2}-\ln\left(1+d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{1}{4\,\left(a\,d^2-b\,d^2\,1{}\mathrm{i}\right)}}+\frac{\ln\left(-16\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}+16\,b^3\,d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}+\frac{16\,a\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{a-b\,1{}\mathrm{i}}\right)\,\sqrt{-\frac{1}{a\,d^2-b\,d^2\,1{}\mathrm{i}}}}{2}-\ln\left(16\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}+16\,b^3\,d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}-\frac{16\,a\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{a-b\,1{}\mathrm{i}}\right)\,\sqrt{-\frac{1}{4\,\left(a\,d^2-b\,d^2\,1{}\mathrm{i}\right)}}-2\,\mathrm{atanh}\left(\frac{32\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{-\frac{64\,a\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{b^4\,d^2\,64{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}+\frac{a\,b^3\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}\,128{}\mathrm{i}}{-\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{b^6\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}-\frac{128\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{-\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{b^6\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}\right)\,\sqrt{-\frac{a-b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}-2\,\mathrm{atanh}\left(\frac{32\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{\frac{64\,a\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{b^2\,16{}\mathrm{i}}{d}+\frac{a^2\,b^2\,d^2\,64{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}-\frac{128\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{b^4\,64{}\mathrm{i}}{d}-\frac{a^2\,b^2\,64{}\mathrm{i}}{d}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^4\,b^2\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}+\frac{a\,b^3\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}\,128{}\mathrm{i}}{\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{b^4\,64{}\mathrm{i}}{d}-\frac{a^2\,b^2\,64{}\mathrm{i}}{d}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^4\,b^2\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}\right)\,\sqrt{-\frac{a-b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}","Not used",1,"(log(d*(-1/(d^2*(a - b*1i)))^(1/2)*(a + b*cot(c + d*x))^(1/2) + 1i)*(-1/(a*d^2 - b*d^2*1i))^(1/2))/2 - log(d*(-1/(d^2*(a - b*1i)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*1i + 1)*(-1/(4*(a*d^2 - b*d^2*1i)))^(1/2) + (log(16*b^3*d*(-1/(d^2*(a - b*1i)))^(1/2) - 16*b^2*(a + b*cot(c + d*x))^(1/2) + (16*a*b^2*(a + b*cot(c + d*x))^(1/2))/(a - b*1i))*(-1/(a*d^2 - b*d^2*1i))^(1/2))/2 - log(16*b^2*(a + b*cot(c + d*x))^(1/2) + 16*b^3*d*(-1/(d^2*(a - b*1i)))^(1/2) - (16*a*b^2*(a + b*cot(c + d*x))^(1/2))/(a - b*1i))*(-1/(4*(a*d^2 - b*d^2*1i)))^(1/2) - 2*atanh((32*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((b^4*d^2*64i)/(4*a^2*d^3 + 4*b^2*d^3) - (64*a*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) + (a*b^3*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2)*128i)/((b^6*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) - (128*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((b^6*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)))*(-(a - b*1i)/(4*a^2*d^2 + 4*b^2*d^2))^(1/2) - 2*atanh((32*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((a^2*b^2*d^2*64i)/(4*a^2*d^3 + 4*b^2*d^3) - (b^2*16i)/d + (64*a*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) - (128*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (a^2*b^2*64i)/d - (b^4*64i)/d + (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) + (a^4*b^2*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) + (a*b^3*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2)*128i)/((a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (a^2*b^2*64i)/d - (b^4*64i)/d + (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) + (a^4*b^2*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)))*(-(a - b*1i)/(4*a^2*d^2 + 4*b^2*d^2))^(1/2)","B"
91,1,1410,45,1.402573,"\text{Not used}","int(-(cot(c + d*x)*1i - 1)/(a + b*cot(c + d*x))^(1/2),x)","\frac{\ln\left(1+d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{1}{a\,d^2-b\,d^2\,1{}\mathrm{i}}}}{2}-\ln\left(d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}+1{}\mathrm{i}\right)\,\sqrt{-\frac{1}{4\,\left(a\,d^2-b\,d^2\,1{}\mathrm{i}\right)}}+\frac{\ln\left(-16\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}+16\,b^3\,d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}+\frac{16\,a\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{a-b\,1{}\mathrm{i}}\right)\,\sqrt{-\frac{1}{a\,d^2-b\,d^2\,1{}\mathrm{i}}}}{2}-\ln\left(16\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}+16\,b^3\,d\,\sqrt{-\frac{1}{d^2\,\left(a-b\,1{}\mathrm{i}\right)}}-\frac{16\,a\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{a-b\,1{}\mathrm{i}}\right)\,\sqrt{-\frac{1}{4\,\left(a\,d^2-b\,d^2\,1{}\mathrm{i}\right)}}-2\,\mathrm{atanh}\left(\frac{32\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{-\frac{64\,a\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{b^4\,d^2\,64{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}+\frac{a\,b^3\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}\,128{}\mathrm{i}}{-\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{b^6\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}-\frac{128\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{-\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{b^6\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}\right)\,\sqrt{-\frac{a-b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}+2\,\mathrm{atanh}\left(\frac{32\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{\frac{64\,a\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{b^2\,16{}\mathrm{i}}{d}+\frac{a^2\,b^2\,d^2\,64{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}-\frac{128\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}}{\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{b^4\,64{}\mathrm{i}}{d}-\frac{a^2\,b^2\,64{}\mathrm{i}}{d}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^4\,b^2\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}+\frac{a\,b^3\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{a}{4\,a^2\,d^2+4\,b^2\,d^2}+\frac{b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}\,128{}\mathrm{i}}{\frac{256\,a^3\,b^3\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{256\,a\,b^5\,d^2}{4\,a^2\,d^3+4\,b^2\,d^3}-\frac{b^4\,64{}\mathrm{i}}{d}-\frac{a^2\,b^2\,64{}\mathrm{i}}{d}+\frac{a^2\,b^4\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}+\frac{a^4\,b^2\,d^2\,256{}\mathrm{i}}{4\,a^2\,d^3+4\,b^2\,d^3}}\right)\,\sqrt{-\frac{a-b\,1{}\mathrm{i}}{4\,a^2\,d^2+4\,b^2\,d^2}}","Not used",1,"(log(d*(-1/(d^2*(a - b*1i)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*1i + 1)*(-1/(a*d^2 - b*d^2*1i))^(1/2))/2 - log(d*(-1/(d^2*(a - b*1i)))^(1/2)*(a + b*cot(c + d*x))^(1/2) + 1i)*(-1/(4*(a*d^2 - b*d^2*1i)))^(1/2) + (log(16*b^3*d*(-1/(d^2*(a - b*1i)))^(1/2) - 16*b^2*(a + b*cot(c + d*x))^(1/2) + (16*a*b^2*(a + b*cot(c + d*x))^(1/2))/(a - b*1i))*(-1/(a*d^2 - b*d^2*1i))^(1/2))/2 - log(16*b^2*(a + b*cot(c + d*x))^(1/2) + 16*b^3*d*(-1/(d^2*(a - b*1i)))^(1/2) - (16*a*b^2*(a + b*cot(c + d*x))^(1/2))/(a - b*1i))*(-1/(4*(a*d^2 - b*d^2*1i)))^(1/2) - 2*atanh((32*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((b^4*d^2*64i)/(4*a^2*d^3 + 4*b^2*d^3) - (64*a*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) + (a*b^3*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2)*128i)/((b^6*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) - (128*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((b^6*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) - (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)))*(-(a - b*1i)/(4*a^2*d^2 + 4*b^2*d^2))^(1/2) + 2*atanh((32*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((a^2*b^2*d^2*64i)/(4*a^2*d^3 + 4*b^2*d^3) - (b^2*16i)/d + (64*a*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) - (128*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2))/((a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (a^2*b^2*64i)/d - (b^4*64i)/d + (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) + (a^4*b^2*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)) + (a*b^3*(a + b*cot(c + d*x))^(1/2)*((b*1i)/(4*a^2*d^2 + 4*b^2*d^2) - a/(4*a^2*d^2 + 4*b^2*d^2))^(1/2)*128i)/((a^2*b^4*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) - (a^2*b^2*64i)/d - (b^4*64i)/d + (256*a^3*b^3*d^2)/(4*a^2*d^3 + 4*b^2*d^3) + (a^4*b^2*d^2*256i)/(4*a^2*d^3 + 4*b^2*d^3) + (256*a*b^5*d^2)/(4*a^2*d^3 + 4*b^2*d^3)))*(-(a - b*1i)/(4*a^2*d^2 + 4*b^2*d^2))^(1/2)","B"
92,1,155,59,0.995468,"\text{Not used}","int((A + B*cot(c + d*x))/(a + b*cot(c + d*x)),x)","\frac{A\,\ln\left(\mathrm{cot}\left(c+d\,x\right)+1{}\mathrm{i}\right)}{2\,\left(b\,d+a\,d\,1{}\mathrm{i}\right)}-\frac{B\,\ln\left(\mathrm{cot}\left(c+d\,x\right)+1{}\mathrm{i}\right)}{2\,\left(a\,d-b\,d\,1{}\mathrm{i}\right)}-\frac{A\,b\,\ln\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{d\,\left(a^2+b^2\right)}+\frac{B\,a\,\ln\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{d\,\left(a^2+b^2\right)}+\frac{A\,\ln\left(\mathrm{cot}\left(c+d\,x\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{2\,\left(a\,d+b\,d\,1{}\mathrm{i}\right)}-\frac{B\,\ln\left(\mathrm{cot}\left(c+d\,x\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{2\,\left(-b\,d+a\,d\,1{}\mathrm{i}\right)}","Not used",1,"(A*log(cot(c + d*x) - 1i)*1i)/(2*(a*d + b*d*1i)) + (A*log(cot(c + d*x) + 1i))/(2*(a*d*1i + b*d)) - (B*log(cot(c + d*x) + 1i))/(2*(a*d - b*d*1i)) - (B*log(cot(c + d*x) - 1i)*1i)/(2*(a*d*1i - b*d)) - (A*b*log(a + b*cot(c + d*x)))/(d*(a^2 + b^2)) + (B*a*log(a + b*cot(c + d*x)))/(d*(a^2 + b^2))","B"
93,1,268,111,1.460473,"\text{Not used}","int((A + B*cot(c + d*x))/(a + b*cot(c + d*x))^2,x)","\ln\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(\frac{B}{d\,\left(a^2+b^2\right)}-\frac{2\,B\,b^2}{d\,{\left(a^2+b^2\right)}^2}\right)+\frac{A\,\ln\left(\mathrm{cot}\left(c+d\,x\right)-\mathrm{i}\right)}{2\,\left(-1{}\mathrm{i}\,d\,a^2+2\,d\,a\,b+1{}\mathrm{i}\,d\,b^2\right)}-\frac{B\,\ln\left(\mathrm{cot}\left(c+d\,x\right)-\mathrm{i}\right)}{2\,\left(d\,a^2+2{}\mathrm{i}\,d\,a\,b-d\,b^2\right)}+\frac{A\,b}{\left(a\,d+b\,d\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}-\frac{B\,a}{\left(a\,d+b\,d\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(a^2+b^2\right)}-\frac{2\,A\,a\,b\,\ln\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{d\,{\left(a^2+b^2\right)}^2}+\frac{A\,\ln\left(\mathrm{cot}\left(c+d\,x\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,\left(-d\,a^2+2{}\mathrm{i}\,d\,a\,b+d\,b^2\right)}-\frac{B\,\ln\left(\mathrm{cot}\left(c+d\,x\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,\left(1{}\mathrm{i}\,d\,a^2+2\,d\,a\,b-1{}\mathrm{i}\,d\,b^2\right)}","Not used",1,"log(a + b*cot(c + d*x))*(B/(d*(a^2 + b^2)) - (2*B*b^2)/(d*(a^2 + b^2)^2)) + (A*log(cot(c + d*x) + 1i)*1i)/(2*(b^2*d - a^2*d + a*b*d*2i)) + (A*log(cot(c + d*x) - 1i))/(2*(b^2*d*1i - a^2*d*1i + 2*a*b*d)) - (B*log(cot(c + d*x) - 1i))/(2*(a^2*d - b^2*d + a*b*d*2i)) - (B*log(cot(c + d*x) + 1i)*1i)/(2*(a^2*d*1i - b^2*d*1i + 2*a*b*d)) + (A*b)/((a*d + b*d*cot(c + d*x))*(a^2 + b^2)) - (B*a)/((a*d + b*d*cot(c + d*x))*(a^2 + b^2)) - (2*A*a*b*log(a + b*cot(c + d*x)))/(d*(a^2 + b^2)^2)","B"
94,1,481,175,2.601922,"\text{Not used}","int((A + B*cot(c + d*x))/(a + b*cot(c + d*x))^3,x)","\frac{\frac{5\,A\,a^2\,b+A\,b^3}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,A\,a\,b^2\,\mathrm{cot}\left(c+d\,x\right)}{a^4+2\,a^2\,b^2+b^4}}{d\,a^2+2\,d\,a\,b\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}-\ln\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(\frac{3\,A\,b}{d\,{\left(a^2+b^2\right)}^2}-\frac{4\,A\,b^3}{d\,{\left(a^2+b^2\right)}^3}\right)-\frac{\frac{3\,B\,a^3-B\,a\,b^2}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{\mathrm{cot}\left(c+d\,x\right)\,\left(B\,b^3-B\,a^2\,b\right)}{a^4+2\,a^2\,b^2+b^4}}{d\,a^2+2\,d\,a\,b\,\mathrm{cot}\left(c+d\,x\right)+d\,b^2\,{\mathrm{cot}\left(c+d\,x\right)}^2}+\ln\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)\,\left(\frac{B\,a}{d\,{\left(a^2+b^2\right)}^2}-\frac{4\,B\,a\,b^2}{d\,{\left(a^2+b^2\right)}^3}\right)+\frac{A\,\ln\left(\mathrm{cot}\left(c+d\,x\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{2\,\left(d\,a^3+3{}\mathrm{i}\,d\,a^2\,b-3\,d\,a\,b^2-1{}\mathrm{i}\,d\,b^3\right)}+\frac{A\,\ln\left(\mathrm{cot}\left(c+d\,x\right)+1{}\mathrm{i}\right)}{2\,\left(1{}\mathrm{i}\,d\,a^3+3\,d\,a^2\,b-3{}\mathrm{i}\,d\,a\,b^2-d\,b^3\right)}-\frac{B\,\ln\left(\mathrm{cot}\left(c+d\,x\right)-\mathrm{i}\right)\,1{}\mathrm{i}}{2\,\left(1{}\mathrm{i}\,d\,a^3-3\,d\,a^2\,b-3{}\mathrm{i}\,d\,a\,b^2+d\,b^3\right)}-\frac{B\,\ln\left(\mathrm{cot}\left(c+d\,x\right)+1{}\mathrm{i}\right)}{2\,\left(d\,a^3-3{}\mathrm{i}\,d\,a^2\,b-3\,d\,a\,b^2+1{}\mathrm{i}\,d\,b^3\right)}","Not used",1,"((A*b^3 + 5*A*a^2*b)/(2*(a^4 + b^4 + 2*a^2*b^2)) + (2*A*a*b^2*cot(c + d*x))/(a^4 + b^4 + 2*a^2*b^2))/(a^2*d + b^2*d*cot(c + d*x)^2 + 2*a*b*d*cot(c + d*x)) - log(a + b*cot(c + d*x))*((3*A*b)/(d*(a^2 + b^2)^2) - (4*A*b^3)/(d*(a^2 + b^2)^3)) - ((3*B*a^3 - B*a*b^2)/(2*(a^4 + b^4 + 2*a^2*b^2)) - (cot(c + d*x)*(B*b^3 - B*a^2*b))/(a^4 + b^4 + 2*a^2*b^2))/(a^2*d + b^2*d*cot(c + d*x)^2 + 2*a*b*d*cot(c + d*x)) + log(a + b*cot(c + d*x))*((B*a)/(d*(a^2 + b^2)^2) - (4*B*a*b^2)/(d*(a^2 + b^2)^3)) + (A*log(cot(c + d*x) - 1i)*1i)/(2*(a^3*d - b^3*d*1i - 3*a*b^2*d + a^2*b*d*3i)) + (A*log(cot(c + d*x) + 1i))/(2*(a^3*d*1i - b^3*d - a*b^2*d*3i + 3*a^2*b*d)) - (B*log(cot(c + d*x) - 1i)*1i)/(2*(a^3*d*1i + b^3*d - a*b^2*d*3i - 3*a^2*b*d)) - (B*log(cot(c + d*x) + 1i))/(2*(a^3*d + b^3*d*1i - 3*a*b^2*d - a^2*b*d*3i))","B"
95,1,3864,188,31.594415,"\text{Not used}","int((A + B*cot(c + d*x))*(a + b*cot(c + d*x))^(5/2),x)","\ln\left(\frac{8\,B^3\,a\,b^2\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\left(\frac{\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{d^4}}\,\left(32\,B\,a^4\,b^2-32\,B\,b^6+32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{\sqrt{-25\,B^4\,a^8\,b^2\,d^4+100\,B^4\,a^6\,b^4\,d^4-110\,B^4\,a^4\,b^6\,d^4+20\,B^4\,a^2\,b^8\,d^4-B^4\,b^{10}\,d^4}}{4\,d^4}+\frac{B^2\,a^5}{4\,d^2}-\frac{5\,B^2\,a^3\,b^2}{2\,d^2}+\frac{5\,B^2\,a\,b^4}{4\,d^2}}-\ln\left(\frac{\left(\frac{\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{d^4}}\,\left(32\,B\,b^6-32\,B\,a^4\,b^2+32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{d^4}}}{2}+\frac{8\,B^3\,a\,b^2\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{\frac{\sqrt{-25\,B^4\,a^8\,b^2\,d^4+100\,B^4\,a^6\,b^4\,d^4-110\,B^4\,a^4\,b^6\,d^4+20\,B^4\,a^2\,b^8\,d^4-B^4\,b^{10}\,d^4}+B^2\,a^5\,d^2-10\,B^2\,a^3\,b^2\,d^2+5\,B^2\,a\,b^4\,d^2}{4\,d^4}}-\ln\left(\frac{\left(\frac{\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{d^4}}\,\left(32\,B\,b^6-32\,B\,a^4\,b^2+32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{d^4}}}{2}+\frac{8\,B^3\,a\,b^2\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{-\frac{\sqrt{-25\,B^4\,a^8\,b^2\,d^4+100\,B^4\,a^6\,b^4\,d^4-110\,B^4\,a^4\,b^6\,d^4+20\,B^4\,a^2\,b^8\,d^4-B^4\,b^{10}\,d^4}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{4\,d^4}}+\ln\left(\frac{8\,B^3\,a\,b^2\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\left(\frac{\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{d^4}}\,\left(32\,B\,a^4\,b^2-32\,B\,b^6+32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-B^2\,a^5\,d^2+10\,B^2\,a^3\,b^2\,d^2-5\,B^2\,a\,b^4\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{B^2\,a^5}{4\,d^2}-\frac{\sqrt{-25\,B^4\,a^8\,b^2\,d^4+100\,B^4\,a^6\,b^4\,d^4-110\,B^4\,a^4\,b^6\,d^4+20\,B^4\,a^2\,b^8\,d^4-B^4\,b^{10}\,d^4}}{4\,d^4}-\frac{5\,B^2\,a^3\,b^2}{2\,d^2}+\frac{5\,B^2\,a\,b^4}{4\,d^2}}-\left(\frac{4\,B\,a^2}{d}-\frac{2\,B\,\left(a^2+b^2\right)}{d}\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}-\ln\left(\frac{8\,A^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(64\,A\,a^3\,b^3+64\,A\,a\,b^5-32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}\right)\,\sqrt{-\frac{\sqrt{-25\,A^4\,a^8\,b^2\,d^4+100\,A^4\,a^6\,b^4\,d^4-110\,A^4\,a^4\,b^6\,d^4+20\,A^4\,a^2\,b^8\,d^4-A^4\,b^{10}\,d^4}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{4\,d^4}}-\ln\left(\frac{8\,A^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(64\,A\,a^3\,b^3+64\,A\,a\,b^5-32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}\right)\,\sqrt{\frac{\sqrt{-25\,A^4\,a^8\,b^2\,d^4+100\,A^4\,a^6\,b^4\,d^4-110\,A^4\,a^4\,b^6\,d^4+20\,A^4\,a^2\,b^8\,d^4-A^4\,b^{10}\,d^4}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{4\,d^4}}+\ln\left(\frac{8\,A^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(64\,A\,a^3\,b^3+64\,A\,a\,b^5+32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-A^2\,a^5\,d^2+10\,A^2\,a^3\,b^2\,d^2-5\,A^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}\right)\,\sqrt{\frac{\sqrt{-25\,A^4\,a^8\,b^2\,d^4+100\,A^4\,a^6\,b^4\,d^4-110\,A^4\,a^4\,b^6\,d^4+20\,A^4\,a^2\,b^8\,d^4-A^4\,b^{10}\,d^4}}{4\,d^4}-\frac{A^2\,a^5}{4\,d^2}+\frac{5\,A^2\,a^3\,b^2}{2\,d^2}-\frac{5\,A^2\,a\,b^4}{4\,d^2}}+\ln\left(\frac{8\,A^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{d^4}}\,\left(64\,A\,a^3\,b^3+64\,A\,a\,b^5+32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+A^2\,a^5\,d^2-10\,A^2\,a^3\,b^2\,d^2+5\,A^2\,a\,b^4\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}\right)\,\sqrt{\frac{5\,A^2\,a^3\,b^2}{2\,d^2}-\frac{A^2\,a^5}{4\,d^2}-\frac{\sqrt{-25\,A^4\,a^8\,b^2\,d^4+100\,A^4\,a^6\,b^4\,d^4-110\,A^4\,a^4\,b^6\,d^4+20\,A^4\,a^2\,b^8\,d^4-A^4\,b^{10}\,d^4}}{4\,d^4}-\frac{5\,A^2\,a\,b^4}{4\,d^2}}-\frac{2\,B\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d}-\frac{2\,A\,b\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{2\,B\,a\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{4\,A\,a\,b\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d}","Not used",1,"log((8*B^3*a*b^2*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3 - ((((((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(32*B*a^4*b^2 - 32*B*b^6 + 32*a*b^2*d*(((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2)*(((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/d^4)^(1/2))/2)*((20*B^4*a^2*b^8*d^4 - B^4*b^10*d^4 - 110*B^4*a^4*b^6*d^4 + 100*B^4*a^6*b^4*d^4 - 25*B^4*a^8*b^2*d^4)^(1/2)/(4*d^4) + (B^2*a^5)/(4*d^2) - (5*B^2*a^3*b^2)/(2*d^2) + (5*B^2*a*b^4)/(4*d^2))^(1/2) - log(((((((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(32*B*b^6 - 32*B*a^4*b^2 + 32*a*b^2*d*(((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2)*(((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/d^4)^(1/2))/2 + (8*B^3*a*b^2*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3)*(((20*B^4*a^2*b^8*d^4 - B^4*b^10*d^4 - 110*B^4*a^4*b^6*d^4 + 100*B^4*a^6*b^4*d^4 - 25*B^4*a^8*b^2*d^4)^(1/2) + B^2*a^5*d^2 - 10*B^2*a^3*b^2*d^2 + 5*B^2*a*b^4*d^2)/(4*d^4))^(1/2) - log(((((-((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(32*B*b^6 - 32*B*a^4*b^2 + 32*a*b^2*d*(-((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2)*(-((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/d^4)^(1/2))/2 + (8*B^3*a*b^2*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3)*(-((20*B^4*a^2*b^8*d^4 - B^4*b^10*d^4 - 110*B^4*a^4*b^6*d^4 + 100*B^4*a^6*b^4*d^4 - 25*B^4*a^8*b^2*d^4)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/(4*d^4))^(1/2) + log((8*B^3*a*b^2*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3 - ((((-((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(32*B*a^4*b^2 - 32*B*b^6 + 32*a*b^2*d*(-((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2)*(-((-B^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - B^2*a^5*d^2 + 10*B^2*a^3*b^2*d^2 - 5*B^2*a*b^4*d^2)/d^4)^(1/2))/2)*((B^2*a^5)/(4*d^2) - (20*B^4*a^2*b^8*d^4 - B^4*b^10*d^4 - 110*B^4*a^4*b^6*d^4 + 100*B^4*a^6*b^4*d^4 - 25*B^4*a^8*b^2*d^4)^(1/2)/(4*d^4) - (5*B^2*a^3*b^2)/(2*d^2) + (5*B^2*a*b^4)/(4*d^2))^(1/2) - ((4*B*a^2)/d - (2*B*(a^2 + b^2))/d)*(a + b*cot(c + d*x))^(1/2) - log((8*A^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3 - ((-((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(((-((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(64*A*a^3*b^3 + 64*A*a*b^5 - 32*a*b^2*d*(-((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2)*(-((20*A^4*a^2*b^8*d^4 - A^4*b^10*d^4 - 110*A^4*a^4*b^6*d^4 + 100*A^4*a^6*b^4*d^4 - 25*A^4*a^8*b^2*d^4)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/(4*d^4))^(1/2) - log((8*A^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3 - ((((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(((((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(64*A*a^3*b^3 + 64*A*a*b^5 - 32*a*b^2*d*(((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2)*(((20*A^4*a^2*b^8*d^4 - A^4*b^10*d^4 - 110*A^4*a^4*b^6*d^4 + 100*A^4*a^6*b^4*d^4 - 25*A^4*a^8*b^2*d^4)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/(4*d^4))^(1/2) + log((8*A^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3 - ((((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(((((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(64*A*a^3*b^3 + 64*A*a*b^5 + 32*a*b^2*d*(((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - A^2*a^5*d^2 + 10*A^2*a^3*b^2*d^2 - 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2)*((20*A^4*a^2*b^8*d^4 - A^4*b^10*d^4 - 110*A^4*a^4*b^6*d^4 + 100*A^4*a^6*b^4*d^4 - 25*A^4*a^8*b^2*d^4)^(1/2)/(4*d^4) - (A^2*a^5)/(4*d^2) + (5*A^2*a^3*b^2)/(2*d^2) - (5*A^2*a*b^4)/(4*d^2))^(1/2) + log((8*A^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3 - ((-((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(((-((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(64*A*a^3*b^3 + 64*A*a*b^5 + 32*a*b^2*d*(-((-A^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + A^2*a^5*d^2 - 10*A^2*a^3*b^2*d^2 + 5*A^2*a*b^4*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2)*((5*A^2*a^3*b^2)/(2*d^2) - (A^2*a^5)/(4*d^2) - (20*A^4*a^2*b^8*d^4 - A^4*b^10*d^4 - 110*A^4*a^4*b^6*d^4 + 100*A^4*a^6*b^4*d^4 - 25*A^4*a^8*b^2*d^4)^(1/2)/(4*d^4) - (5*A^2*a*b^4)/(4*d^2))^(1/2) - (2*B*(a + b*cot(c + d*x))^(5/2))/(5*d) - (2*A*b*(a + b*cot(c + d*x))^(3/2))/(3*d) - (2*B*a*(a + b*cot(c + d*x))^(3/2))/(3*d) - (4*A*a*b*(a + b*cot(c + d*x))^(1/2))/d","B"
96,1,2823,150,13.758118,"\text{Not used}","int((A + B*cot(c + d*x))*(a + b*cot(c + d*x))^(3/2),x)","\ln\left(\frac{16\,A^3\,a\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,b^2\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{d^4}}\,\left(A\,b^3+A\,a^2\,b+a\,d\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}+\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}\right)\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{\sqrt{-9\,A^4\,a^4\,b^2\,d^4+6\,A^4\,a^2\,b^4\,d^4-A^4\,b^6\,d^4}}{4\,d^4}-\frac{A^2\,a^3}{4\,d^2}+\frac{3\,A^2\,a\,b^2}{4\,d^2}}-\ln\left(\frac{16\,A^3\,a\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,b^2\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{d^4}}\,\left(A\,b^3+A\,a^2\,b-a\,d\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}-\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}\right)\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{\sqrt{-9\,A^4\,a^4\,b^2\,d^4+6\,A^4\,a^2\,b^4\,d^4-A^4\,b^6\,d^4}-A^2\,a^3\,d^2+3\,A^2\,a\,b^2\,d^2}{4\,d^4}}-\ln\left(\frac{16\,A^3\,a\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,b^2\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{d^4}}\,\left(A\,b^3+A\,a^2\,b-a\,d\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}-\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}\right)\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{-\frac{\sqrt{-9\,A^4\,a^4\,b^2\,d^4+6\,A^4\,a^2\,b^4\,d^4-A^4\,b^6\,d^4}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{4\,d^4}}+\ln\left(\frac{16\,A^3\,a\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,b^2\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{d^4}}\,\left(A\,b^3+A\,a^2\,b+a\,d\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}+\frac{16\,A^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}\right)\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+A^2\,a^3\,d^2-3\,A^2\,a\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{3\,A^2\,a\,b^2}{4\,d^2}-\frac{A^2\,a^3}{4\,d^2}-\frac{\sqrt{-9\,A^4\,a^4\,b^2\,d^4+6\,A^4\,a^2\,b^4\,d^4-A^4\,b^6\,d^4}}{4\,d^4}}-\ln\left(\frac{8\,B^3\,b^2\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}+\frac{16\,a\,b^2\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{d^4}}\,\left(B\,a^2+B\,b^2-d\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{\sqrt{-9\,B^4\,a^4\,b^2\,d^4+6\,B^4\,a^2\,b^4\,d^4-B^4\,b^6\,d^4}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{4\,d^4}}-\ln\left(\frac{8\,B^3\,b^2\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}+\frac{16\,a\,b^2\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{d^4}}\,\left(B\,a^2+B\,b^2-d\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{-\frac{\sqrt{-9\,B^4\,a^4\,b^2\,d^4+6\,B^4\,a^2\,b^4\,d^4-B^4\,b^6\,d^4}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{4\,d^4}}+\ln\left(\frac{\left(\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}-\frac{16\,a\,b^2\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{d^4}}\,\left(B\,a^2+B\,b^2+d\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+B^2\,a^3\,d^2-3\,B^2\,a\,b^2\,d^2}{d^4}}}{2}+\frac{8\,B^3\,b^2\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{\sqrt{-9\,B^4\,a^4\,b^2\,d^4+6\,B^4\,a^2\,b^4\,d^4-B^4\,b^6\,d^4}}{4\,d^4}+\frac{B^2\,a^3}{4\,d^2}-\frac{3\,B^2\,a\,b^2}{4\,d^2}}+\ln\left(\frac{\left(\frac{16\,B^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}-\frac{16\,a\,b^2\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{d^4}}\,\left(B\,a^2+B\,b^2+d\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-B^2\,a^3\,d^2+3\,B^2\,a\,b^2\,d^2}{d^4}}}{2}+\frac{8\,B^3\,b^2\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{B^2\,a^3}{4\,d^2}-\frac{\sqrt{-9\,B^4\,a^4\,b^2\,d^4+6\,B^4\,a^2\,b^4\,d^4-B^4\,b^6\,d^4}}{4\,d^4}-\frac{3\,B^2\,a\,b^2}{4\,d^2}}-\frac{2\,B\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}-\frac{2\,A\,b\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d}-\frac{2\,B\,a\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d}","Not used",1,"log((16*A^3*a*b^3*(a^2 + b^2)^2)/d^3 - (((16*b^2*(((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(A*b^3 + A*a^2*b + a*d*(((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d + (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2)*(((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/d^4)^(1/2))/2)*((6*A^4*a^2*b^4*d^4 - A^4*b^6*d^4 - 9*A^4*a^4*b^2*d^4)^(1/2)/(4*d^4) - (A^2*a^3)/(4*d^2) + (3*A^2*a*b^2)/(4*d^2))^(1/2) - log((16*A^3*a*b^3*(a^2 + b^2)^2)/d^3 - (((16*b^2*(((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(A*b^3 + A*a^2*b - a*d*(((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d - (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2)*(((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/d^4)^(1/2))/2)*(((6*A^4*a^2*b^4*d^4 - A^4*b^6*d^4 - 9*A^4*a^4*b^2*d^4)^(1/2) - A^2*a^3*d^2 + 3*A^2*a*b^2*d^2)/(4*d^4))^(1/2) - log((16*A^3*a*b^3*(a^2 + b^2)^2)/d^3 - (((16*b^2*(-((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(A*b^3 + A*a^2*b - a*d*(-((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d - (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2)*(-((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/d^4)^(1/2))/2)*(-((6*A^4*a^2*b^4*d^4 - A^4*b^6*d^4 - 9*A^4*a^4*b^2*d^4)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/(4*d^4))^(1/2) + log((16*A^3*a*b^3*(a^2 + b^2)^2)/d^3 - (((16*b^2*(-((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(A*b^3 + A*a^2*b + a*d*(-((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d + (16*A^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2)*(-((-A^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + A^2*a^3*d^2 - 3*A^2*a*b^2*d^2)/d^4)^(1/2))/2)*((3*A^2*a*b^2)/(4*d^2) - (A^2*a^3)/(4*d^2) - (6*A^4*a^2*b^4*d^4 - A^4*b^6*d^4 - 9*A^4*a^4*b^2*d^4)^(1/2)/(4*d^4))^(1/2) - log((8*B^3*b^2*(a^2 - b^2)*(a^2 + b^2)^2)/d^3 - (((16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 + (16*a*b^2*(((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(B*a^2 + B*b^2 - d*(((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/d^4)^(1/2))/2)*(((6*B^4*a^2*b^4*d^4 - B^4*b^6*d^4 - 9*B^4*a^4*b^2*d^4)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/(4*d^4))^(1/2) - log((8*B^3*b^2*(a^2 - b^2)*(a^2 + b^2)^2)/d^3 - (((16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 + (16*a*b^2*(-((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(B*a^2 + B*b^2 - d*(-((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(-((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/d^4)^(1/2))/2)*(-((6*B^4*a^2*b^4*d^4 - B^4*b^6*d^4 - 9*B^4*a^4*b^2*d^4)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/(4*d^4))^(1/2) + log((((16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 - (16*a*b^2*(((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(B*a^2 + B*b^2 + d*(((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + B^2*a^3*d^2 - 3*B^2*a*b^2*d^2)/d^4)^(1/2))/2 + (8*B^3*b^2*(a^2 - b^2)*(a^2 + b^2)^2)/d^3)*((6*B^4*a^2*b^4*d^4 - B^4*b^6*d^4 - 9*B^4*a^4*b^2*d^4)^(1/2)/(4*d^4) + (B^2*a^3)/(4*d^2) - (3*B^2*a*b^2)/(4*d^2))^(1/2) + log((((16*B^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 - (16*a*b^2*(-((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(B*a^2 + B*b^2 + d*(-((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(-((-B^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - B^2*a^3*d^2 + 3*B^2*a*b^2*d^2)/d^4)^(1/2))/2 + (8*B^3*b^2*(a^2 - b^2)*(a^2 + b^2)^2)/d^3)*((B^2*a^3)/(4*d^2) - (6*B^4*a^2*b^4*d^4 - B^4*b^6*d^4 - 9*B^4*a^4*b^2*d^4)^(1/2)/(4*d^4) - (3*B^2*a*b^2)/(4*d^2))^(1/2) - (2*B*(a + b*cot(c + d*x))^(3/2))/(3*d) - (2*A*b*(a + b*cot(c + d*x))^(1/2))/d - (2*B*a*(a + b*cot(c + d*x))^(1/2))/d","B"
97,1,843,122,3.029213,"\text{Not used}","int((A + B*cot(c + d*x))*(a + b*cot(c + d*x))^(1/2),x)","\mathrm{atanh}\left(\frac{d^3\,\left(\frac{16\,\left(A^2\,b^4-A^2\,a^2\,b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^2}+\frac{16\,a\,b^2\,\left(\sqrt{-A^4\,b^2\,d^4}+A^2\,a\,d^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4}+A^2\,a\,d^2}{d^4}}}{16\,\left(A^3\,a^2\,b^3+A^3\,b^5\right)}\right)\,\sqrt{-\frac{\sqrt{-A^4\,b^2\,d^4}+A^2\,a\,d^2}{d^4}}+\mathrm{atanh}\left(\frac{d^3\,\left(\frac{16\,\left(A^2\,b^4-A^2\,a^2\,b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^2}-\frac{16\,a\,b^2\,\left(\sqrt{-A^4\,b^2\,d^4}-A^2\,a\,d^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^4}\right)\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4}-A^2\,a\,d^2}{d^4}}}{16\,\left(A^3\,a^2\,b^3+A^3\,b^5\right)}\right)\,\sqrt{\frac{\sqrt{-A^4\,b^2\,d^4}-A^2\,a\,d^2}{d^4}}+2\,\mathrm{atanh}\left(\frac{32\,B^2\,b^4\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4}}{4\,d^4}+\frac{B^2\,a}{4\,d^2}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,B\,b^4\,\sqrt{-B^4\,b^2\,d^4}}{d^3}+\frac{16\,B\,a^2\,b^2\,\sqrt{-B^4\,b^2\,d^4}}{d^3}}+\frac{32\,a\,b^2\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4}}{4\,d^4}+\frac{B^2\,a}{4\,d^2}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-B^4\,b^2\,d^4}}{\frac{16\,B\,b^4\,\sqrt{-B^4\,b^2\,d^4}}{d}+\frac{16\,B\,a^2\,b^2\,\sqrt{-B^4\,b^2\,d^4}}{d}}\right)\,\sqrt{\frac{\sqrt{-B^4\,b^2\,d^4}+B^2\,a\,d^2}{4\,d^4}}-2\,\mathrm{atanh}\left(\frac{32\,B^2\,b^4\,\sqrt{\frac{B^2\,a}{4\,d^2}-\frac{\sqrt{-B^4\,b^2\,d^4}}{4\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,B\,b^4\,\sqrt{-B^4\,b^2\,d^4}}{d^3}+\frac{16\,B\,a^2\,b^2\,\sqrt{-B^4\,b^2\,d^4}}{d^3}}-\frac{32\,a\,b^2\,\sqrt{\frac{B^2\,a}{4\,d^2}-\frac{\sqrt{-B^4\,b^2\,d^4}}{4\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-B^4\,b^2\,d^4}}{\frac{16\,B\,b^4\,\sqrt{-B^4\,b^2\,d^4}}{d}+\frac{16\,B\,a^2\,b^2\,\sqrt{-B^4\,b^2\,d^4}}{d}}\right)\,\sqrt{-\frac{\sqrt{-B^4\,b^2\,d^4}-B^2\,a\,d^2}{4\,d^4}}-\frac{2\,B\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d}","Not used",1,"atanh((d^3*((16*(A^2*b^4 - A^2*a^2*b^2)*(a + b*cot(c + d*x))^(1/2))/d^2 + (16*a*b^2*((-A^4*b^2*d^4)^(1/2) + A^2*a*d^2)*(a + b*cot(c + d*x))^(1/2))/d^4)*(-((-A^4*b^2*d^4)^(1/2) + A^2*a*d^2)/d^4)^(1/2))/(16*(A^3*b^5 + A^3*a^2*b^3)))*(-((-A^4*b^2*d^4)^(1/2) + A^2*a*d^2)/d^4)^(1/2) + atanh((d^3*((16*(A^2*b^4 - A^2*a^2*b^2)*(a + b*cot(c + d*x))^(1/2))/d^2 - (16*a*b^2*((-A^4*b^2*d^4)^(1/2) - A^2*a*d^2)*(a + b*cot(c + d*x))^(1/2))/d^4)*(((-A^4*b^2*d^4)^(1/2) - A^2*a*d^2)/d^4)^(1/2))/(16*(A^3*b^5 + A^3*a^2*b^3)))*(((-A^4*b^2*d^4)^(1/2) - A^2*a*d^2)/d^4)^(1/2) + 2*atanh((32*B^2*b^4*((-B^4*b^2*d^4)^(1/2)/(4*d^4) + (B^2*a)/(4*d^2))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*B*b^4*(-B^4*b^2*d^4)^(1/2))/d^3 + (16*B*a^2*b^2*(-B^4*b^2*d^4)^(1/2))/d^3) + (32*a*b^2*((-B^4*b^2*d^4)^(1/2)/(4*d^4) + (B^2*a)/(4*d^2))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-B^4*b^2*d^4)^(1/2))/((16*B*b^4*(-B^4*b^2*d^4)^(1/2))/d + (16*B*a^2*b^2*(-B^4*b^2*d^4)^(1/2))/d))*(((-B^4*b^2*d^4)^(1/2) + B^2*a*d^2)/(4*d^4))^(1/2) - 2*atanh((32*B^2*b^4*((B^2*a)/(4*d^2) - (-B^4*b^2*d^4)^(1/2)/(4*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*B*b^4*(-B^4*b^2*d^4)^(1/2))/d^3 + (16*B*a^2*b^2*(-B^4*b^2*d^4)^(1/2))/d^3) - (32*a*b^2*((B^2*a)/(4*d^2) - (-B^4*b^2*d^4)^(1/2)/(4*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-B^4*b^2*d^4)^(1/2))/((16*B*b^4*(-B^4*b^2*d^4)^(1/2))/d + (16*B*a^2*b^2*(-B^4*b^2*d^4)^(1/2))/d))*(-((-B^4*b^2*d^4)^(1/2) - B^2*a*d^2)/(4*d^4))^(1/2) - (2*B*(a + b*cot(c + d*x))^(1/2))/d","B"
98,1,3442,151,26.556073,"\text{Not used}","int(-(a + b*cot(c + d*x))^(5/2)*(a - b*cot(c + d*x)),x)","\ln\left(\frac{\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-a^7\,d^2-5\,a^3\,b^4\,d^2+10\,a^5\,b^2\,d^2}{d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-a^7\,d^2-5\,a^3\,b^4\,d^2+10\,a^5\,b^2\,d^2}{d^4}}\,\left(64\,a^2\,b^5+64\,a^4\,b^3-32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-a^7\,d^2-5\,a^3\,b^4\,d^2+10\,a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}-\frac{8\,a^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{\frac{\sqrt{-25\,a^{12}\,b^2\,d^4+100\,a^{10}\,b^4\,d^4-110\,a^8\,b^6\,d^4+20\,a^6\,b^8\,d^4-a^4\,b^{10}\,d^4}}{4\,d^4}-\frac{a^7}{4\,d^2}-\frac{5\,a^3\,b^4}{4\,d^2}+\frac{5\,a^5\,b^2}{2\,d^2}}-\ln\left(\frac{\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+a^7\,d^2+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+a^7\,d^2+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{d^4}}\,\left(64\,a^2\,b^5+64\,a^4\,b^3+32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+a^7\,d^2+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}-\frac{8\,a^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{-\frac{a^7\,d^2+\sqrt{-25\,a^{12}\,b^2\,d^4+100\,a^{10}\,b^4\,d^4-110\,a^8\,b^6\,d^4+20\,a^6\,b^8\,d^4-a^4\,b^{10}\,d^4}+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{4\,d^4}}+\ln\left(\frac{\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+a^7\,d^2+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+a^7\,d^2+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{d^4}}\,\left(64\,a^2\,b^5+64\,a^4\,b^3-32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+a^7\,d^2+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}-\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}-\frac{8\,a^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{\frac{5\,a^5\,b^2}{2\,d^2}-\frac{a^7}{4\,d^2}-\frac{5\,a^3\,b^4}{4\,d^2}-\frac{\sqrt{-25\,a^{12}\,b^2\,d^4+100\,a^{10}\,b^4\,d^4-110\,a^8\,b^6\,d^4+20\,a^6\,b^8\,d^4-a^4\,b^{10}\,d^4}}{4\,d^4}}-\left(\frac{4\,a^2\,b}{d}-\frac{2\,b\,\left(a^2+b^2\right)}{d}\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}-\ln\left(\frac{\left(\frac{\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{d^4}}\,\left(32\,b^7-32\,a^4\,b^3+32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-a^6\,b^4+15\,a^4\,b^6-15\,a^2\,b^8+b^{10}\right)}{d^2}\right)\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{d^4}}}{2}+\frac{8\,a\,b^5\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{\frac{\sqrt{-25\,a^8\,b^6\,d^4+100\,a^6\,b^8\,d^4-110\,a^4\,b^{10}\,d^4+20\,a^2\,b^{12}\,d^4-b^{14}\,d^4}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{4\,d^4}}+\ln\left(\frac{8\,a\,b^5\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\left(\frac{\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{d^4}}\,\left(32\,a^4\,b^3-32\,b^7+32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-a^6\,b^4+15\,a^4\,b^6-15\,a^2\,b^8+b^{10}\right)}{d^2}\right)\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}+5\,a\,b^6\,d^2-10\,a^3\,b^4\,d^2+a^5\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{\sqrt{-25\,a^8\,b^6\,d^4+100\,a^6\,b^8\,d^4-110\,a^4\,b^{10}\,d^4+20\,a^2\,b^{12}\,d^4-b^{14}\,d^4}}{4\,d^4}+\frac{5\,a\,b^6}{4\,d^2}-\frac{5\,a^3\,b^4}{2\,d^2}+\frac{a^5\,b^2}{4\,d^2}}-\ln\left(\frac{\left(\frac{\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{d^4}}\,\left(32\,b^7-32\,a^4\,b^3+32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-a^6\,b^4+15\,a^4\,b^6-15\,a^2\,b^8+b^{10}\right)}{d^2}\right)\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{d^4}}}{2}+\frac{8\,a\,b^5\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{-\frac{\sqrt{-25\,a^8\,b^6\,d^4+100\,a^6\,b^8\,d^4-110\,a^4\,b^{10}\,d^4+20\,a^2\,b^{12}\,d^4-b^{14}\,d^4}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{4\,d^4}}+\ln\left(\frac{8\,a\,b^5\,\left(a^2-3\,b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}-\frac{\left(\frac{\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{d^4}}\,\left(32\,a^4\,b^3-32\,b^7+32\,a\,b^2\,d\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-a^6\,b^4+15\,a^4\,b^6-15\,a^2\,b^8+b^{10}\right)}{d^2}\right)\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-5\,a\,b^6\,d^2+10\,a^3\,b^4\,d^2-a^5\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{5\,a\,b^6}{4\,d^2}-\frac{\sqrt{-25\,a^8\,b^6\,d^4+100\,a^6\,b^8\,d^4-110\,a^4\,b^{10}\,d^4+20\,a^2\,b^{12}\,d^4-b^{14}\,d^4}}{4\,d^4}-\frac{5\,a^3\,b^4}{2\,d^2}+\frac{a^5\,b^2}{4\,d^2}}-\ln\left(\frac{\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-a^7\,d^2-5\,a^3\,b^4\,d^2+10\,a^5\,b^2\,d^2}{d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-a^7\,d^2-5\,a^3\,b^4\,d^2+10\,a^5\,b^2\,d^2}{d^4}}\,\left(64\,a^2\,b^5+64\,a^4\,b^3+32\,a\,b^2\,d\,\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(5\,a^4-10\,a^2\,b^2+b^4\right)}^2}-a^7\,d^2-5\,a^3\,b^4\,d^2+10\,a^5\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{2\,d}+\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^6-15\,a^4\,b^2+15\,a^2\,b^4-b^6\right)}{d^2}\right)}{2}-\frac{8\,a^3\,b^3\,\left(3\,a^2-b^2\right)\,{\left(a^2+b^2\right)}^3}{d^3}\right)\,\sqrt{-\frac{a^7\,d^2-\sqrt{-25\,a^{12}\,b^2\,d^4+100\,a^{10}\,b^4\,d^4-110\,a^8\,b^6\,d^4+20\,a^6\,b^8\,d^4-a^4\,b^{10}\,d^4}+5\,a^3\,b^4\,d^2-10\,a^5\,b^2\,d^2}{4\,d^4}}-\frac{2\,b\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}}{5\,d}+\frac{4\,a^2\,b\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d}","Not used",1,"log(((((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - a^7*d^2 - 5*a^3*b^4*d^2 + 10*a^5*b^2*d^2)/d^4)^(1/2)*(((((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - a^7*d^2 - 5*a^3*b^4*d^2 + 10*a^5*b^2*d^2)/d^4)^(1/2)*(64*a^2*b^5 + 64*a^4*b^3 - 32*a*b^2*d*(((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - a^7*d^2 - 5*a^3*b^4*d^2 + 10*a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2 - (8*a^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3)*((20*a^6*b^8*d^4 - a^4*b^10*d^4 - 110*a^8*b^6*d^4 + 100*a^10*b^4*d^4 - 25*a^12*b^2*d^4)^(1/2)/(4*d^4) - a^7/(4*d^2) - (5*a^3*b^4)/(4*d^2) + (5*a^5*b^2)/(2*d^2))^(1/2) - log(((-((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + a^7*d^2 + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/d^4)^(1/2)*(((-((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + a^7*d^2 + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/d^4)^(1/2)*(64*a^2*b^5 + 64*a^4*b^3 + 32*a*b^2*d*(-((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + a^7*d^2 + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2 - (8*a^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3)*(-(a^7*d^2 + (20*a^6*b^8*d^4 - a^4*b^10*d^4 - 110*a^8*b^6*d^4 + 100*a^10*b^4*d^4 - 25*a^12*b^2*d^4)^(1/2) + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/(4*d^4))^(1/2) + log(((-((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + a^7*d^2 + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/d^4)^(1/2)*(((-((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + a^7*d^2 + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/d^4)^(1/2)*(64*a^2*b^5 + 64*a^4*b^3 - 32*a*b^2*d*(-((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + a^7*d^2 + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) - (16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2 - (8*a^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3)*((5*a^5*b^2)/(2*d^2) - a^7/(4*d^2) - (5*a^3*b^4)/(4*d^2) - (20*a^6*b^8*d^4 - a^4*b^10*d^4 - 110*a^8*b^6*d^4 + 100*a^10*b^4*d^4 - 25*a^12*b^2*d^4)^(1/2)/(4*d^4))^(1/2) - ((4*a^2*b)/d - (2*b*(a^2 + b^2))/d)*(a + b*cot(c + d*x))^(1/2) - log(((((((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/d^4)^(1/2)*(32*b^7 - 32*a^4*b^3 + 32*a*b^2*d*(((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*(a + b*cot(c + d*x))^(1/2)*(b^10 - 15*a^2*b^8 + 15*a^4*b^6 - a^6*b^4))/d^2)*(((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/d^4)^(1/2))/2 + (8*a*b^5*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3)*(((20*a^2*b^12*d^4 - b^14*d^4 - 110*a^4*b^10*d^4 + 100*a^6*b^8*d^4 - 25*a^8*b^6*d^4)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/(4*d^4))^(1/2) + log((8*a*b^5*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3 - ((((((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/d^4)^(1/2)*(32*a^4*b^3 - 32*b^7 + 32*a*b^2*d*(((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*(a + b*cot(c + d*x))^(1/2)*(b^10 - 15*a^2*b^8 + 15*a^4*b^6 - a^6*b^4))/d^2)*(((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) + 5*a*b^6*d^2 - 10*a^3*b^4*d^2 + a^5*b^2*d^2)/d^4)^(1/2))/2)*((20*a^2*b^12*d^4 - b^14*d^4 - 110*a^4*b^10*d^4 + 100*a^6*b^8*d^4 - 25*a^8*b^6*d^4)^(1/2)/(4*d^4) + (5*a*b^6)/(4*d^2) - (5*a^3*b^4)/(2*d^2) + (a^5*b^2)/(4*d^2))^(1/2) - log(((((-((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/d^4)^(1/2)*(32*b^7 - 32*a^4*b^3 + 32*a*b^2*d*(-((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*(a + b*cot(c + d*x))^(1/2)*(b^10 - 15*a^2*b^8 + 15*a^4*b^6 - a^6*b^4))/d^2)*(-((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/d^4)^(1/2))/2 + (8*a*b^5*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3)*(-((20*a^2*b^12*d^4 - b^14*d^4 - 110*a^4*b^10*d^4 + 100*a^6*b^8*d^4 - 25*a^8*b^6*d^4)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/(4*d^4))^(1/2) + log((8*a*b^5*(a^2 - 3*b^2)*(a^2 + b^2)^3)/d^3 - ((((-((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/d^4)^(1/2)*(32*a^4*b^3 - 32*b^7 + 32*a*b^2*d*(-((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*(a + b*cot(c + d*x))^(1/2)*(b^10 - 15*a^2*b^8 + 15*a^4*b^6 - a^6*b^4))/d^2)*(-((-b^6*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - 5*a*b^6*d^2 + 10*a^3*b^4*d^2 - a^5*b^2*d^2)/d^4)^(1/2))/2)*((5*a*b^6)/(4*d^2) - (20*a^2*b^12*d^4 - b^14*d^4 - 110*a^4*b^10*d^4 + 100*a^6*b^8*d^4 - 25*a^8*b^6*d^4)^(1/2)/(4*d^4) - (5*a^3*b^4)/(2*d^2) + (a^5*b^2)/(4*d^2))^(1/2) - log(((((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - a^7*d^2 - 5*a^3*b^4*d^2 + 10*a^5*b^2*d^2)/d^4)^(1/2)*(((((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - a^7*d^2 - 5*a^3*b^4*d^2 + 10*a^5*b^2*d^2)/d^4)^(1/2)*(64*a^2*b^5 + 64*a^4*b^3 + 32*a*b^2*d*(((-a^4*b^2*d^4*(5*a^4 + b^4 - 10*a^2*b^2)^2)^(1/2) - a^7*d^2 - 5*a^3*b^4*d^2 + 10*a^5*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/(2*d) + (16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^6 - b^6 + 15*a^2*b^4 - 15*a^4*b^2))/d^2))/2 - (8*a^3*b^3*(3*a^2 - b^2)*(a^2 + b^2)^3)/d^3)*(-(a^7*d^2 - (20*a^6*b^8*d^4 - a^4*b^10*d^4 - 110*a^8*b^6*d^4 + 100*a^10*b^4*d^4 - 25*a^12*b^2*d^4)^(1/2) + 5*a^3*b^4*d^2 - 10*a^5*b^2*d^2)/(4*d^4))^(1/2) - (2*b*(a + b*cot(c + d*x))^(5/2))/(5*d) + (4*a^2*b*(a + b*cot(c + d*x))^(1/2))/d","B"
99,1,2529,408,11.956430,"\text{Not used}","int(-(a + b*cot(c + d*x))^(3/2)*(a - b*cot(c + d*x)),x)","\ln\left(\frac{\left(\frac{16\,b^4\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}-\frac{16\,a\,b^2\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3+d\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{d^4}}}{2}+\frac{8\,b^5\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{\sqrt{-9\,a^4\,b^6\,d^4+6\,a^2\,b^8\,d^4-b^{10}\,d^4}}{4\,d^4}-\frac{3\,a\,b^4}{4\,d^2}+\frac{a^3\,b^2}{4\,d^2}}-\ln\left(\frac{8\,b^5\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,b^4\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}+\frac{16\,a\,b^2\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3-d\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{-\frac{\sqrt{-9\,a^4\,b^6\,d^4+6\,a^2\,b^8\,d^4-b^{10}\,d^4}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{4\,d^4}}-\ln\left(\frac{8\,b^5\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}-\frac{\left(\frac{16\,b^4\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}+\frac{16\,a\,b^2\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3-d\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{d^4}}}{2}\right)\,\sqrt{\frac{\sqrt{-9\,a^4\,b^6\,d^4+6\,a^2\,b^8\,d^4-b^{10}\,d^4}-3\,a\,b^4\,d^2+a^3\,b^2\,d^2}{4\,d^4}}+\ln\left(\frac{\left(\frac{16\,b^4\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}-\frac{16\,a\,b^2\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3+d\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)\,\sqrt{-\frac{\sqrt{-b^6\,d^4\,{\left(3\,a^2-b^2\right)}^2}+3\,a\,b^4\,d^2-a^3\,b^2\,d^2}{d^4}}}{2}+\frac{8\,b^5\,\left(a^2-b^2\right)\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{a^3\,b^2}{4\,d^2}-\frac{3\,a\,b^4}{4\,d^2}-\frac{\sqrt{-9\,a^4\,b^6\,d^4+6\,a^2\,b^8\,d^4-b^{10}\,d^4}}{4\,d^4}}-\ln\left(\frac{\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+a^5\,d^2-3\,a^3\,b^2\,d^2}{d^4}}\,\left(\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}+\frac{16\,a\,b^2\,\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+a^5\,d^2-3\,a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3+d\,\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+a^5\,d^2-3\,a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)}{2}-\frac{16\,a^4\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{-\frac{\sqrt{-9\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4-a^4\,b^6\,d^4}+a^5\,d^2-3\,a^3\,b^2\,d^2}{4\,d^4}}-\ln\left(\frac{\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-a^5\,d^2+3\,a^3\,b^2\,d^2}{d^4}}\,\left(\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}+\frac{16\,a\,b^2\,\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-a^5\,d^2+3\,a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3+d\,\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-a^5\,d^2+3\,a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)}{2}-\frac{16\,a^4\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{\sqrt{-9\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4-a^4\,b^6\,d^4}-a^5\,d^2+3\,a^3\,b^2\,d^2}{4\,d^4}}+\ln\left(-\frac{\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-a^5\,d^2+3\,a^3\,b^2\,d^2}{d^4}}\,\left(\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}-\frac{16\,a\,b^2\,\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-a^5\,d^2+3\,a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3-d\,\sqrt{\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}-a^5\,d^2+3\,a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)}{2}-\frac{16\,a^4\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{\sqrt{-9\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4-a^4\,b^6\,d^4}}{4\,d^4}-\frac{a^5}{4\,d^2}+\frac{3\,a^3\,b^2}{4\,d^2}}+\ln\left(-\frac{\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+a^5\,d^2-3\,a^3\,b^2\,d^2}{d^4}}\,\left(\frac{16\,a^2\,b^2\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a^4-6\,a^2\,b^2+b^4\right)}{d^2}-\frac{16\,a\,b^2\,\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+a^5\,d^2-3\,a^3\,b^2\,d^2}{d^4}}\,\left(a^2\,b+b^3-d\,\sqrt{-\frac{\sqrt{-a^4\,b^2\,d^4\,{\left(3\,a^2-b^2\right)}^2}+a^5\,d^2-3\,a^3\,b^2\,d^2}{d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\right)}{d}\right)}{2}-\frac{16\,a^4\,b^3\,{\left(a^2+b^2\right)}^2}{d^3}\right)\,\sqrt{\frac{3\,a^3\,b^2}{4\,d^2}-\frac{a^5}{4\,d^2}-\frac{\sqrt{-9\,a^8\,b^2\,d^4+6\,a^6\,b^4\,d^4-a^4\,b^6\,d^4}}{4\,d^4}}-\frac{2\,b\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{3\,d}","Not used",1,"log((((16*b^4*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 - (16*a*b^2*(((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 + d*(((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/d^4)^(1/2))/2 + (8*b^5*(a^2 - b^2)*(a^2 + b^2)^2)/d^3)*((6*a^2*b^8*d^4 - b^10*d^4 - 9*a^4*b^6*d^4)^(1/2)/(4*d^4) - (3*a*b^4)/(4*d^2) + (a^3*b^2)/(4*d^2))^(1/2) - log((8*b^5*(a^2 - b^2)*(a^2 + b^2)^2)/d^3 - (((16*b^4*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 + (16*a*b^2*(-((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 - d*(-((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(-((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/d^4)^(1/2))/2)*(-((6*a^2*b^8*d^4 - b^10*d^4 - 9*a^4*b^6*d^4)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/(4*d^4))^(1/2) - log((8*b^5*(a^2 - b^2)*(a^2 + b^2)^2)/d^3 - (((16*b^4*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 + (16*a*b^2*(((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 - d*(((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/d^4)^(1/2))/2)*(((6*a^2*b^8*d^4 - b^10*d^4 - 9*a^4*b^6*d^4)^(1/2) - 3*a*b^4*d^2 + a^3*b^2*d^2)/(4*d^4))^(1/2) + log((((16*b^4*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 - (16*a*b^2*(-((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 + d*(-((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d)*(-((-b^6*d^4*(3*a^2 - b^2)^2)^(1/2) + 3*a*b^4*d^2 - a^3*b^2*d^2)/d^4)^(1/2))/2 + (8*b^5*(a^2 - b^2)*(a^2 + b^2)^2)/d^3)*((a^3*b^2)/(4*d^2) - (3*a*b^4)/(4*d^2) - (6*a^2*b^8*d^4 - b^10*d^4 - 9*a^4*b^6*d^4)^(1/2)/(4*d^4))^(1/2) - log(((-((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/d^4)^(1/2)*((16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 + (16*a*b^2*(-((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 + d*(-((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d))/2 - (16*a^4*b^3*(a^2 + b^2)^2)/d^3)*(-((6*a^6*b^4*d^4 - a^4*b^6*d^4 - 9*a^8*b^2*d^4)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/(4*d^4))^(1/2) - log(((((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/d^4)^(1/2)*((16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 + (16*a*b^2*(((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 + d*(((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d))/2 - (16*a^4*b^3*(a^2 + b^2)^2)/d^3)*(((6*a^6*b^4*d^4 - a^4*b^6*d^4 - 9*a^8*b^2*d^4)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/(4*d^4))^(1/2) + log(- ((((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/d^4)^(1/2)*((16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 - (16*a*b^2*(((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 - d*(((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) - a^5*d^2 + 3*a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d))/2 - (16*a^4*b^3*(a^2 + b^2)^2)/d^3)*((6*a^6*b^4*d^4 - a^4*b^6*d^4 - 9*a^8*b^2*d^4)^(1/2)/(4*d^4) - a^5/(4*d^2) + (3*a^3*b^2)/(4*d^2))^(1/2) + log(- ((-((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/d^4)^(1/2)*((16*a^2*b^2*(a + b*cot(c + d*x))^(1/2)*(a^4 + b^4 - 6*a^2*b^2))/d^2 - (16*a*b^2*(-((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/d^4)^(1/2)*(a^2*b + b^3 - d*(-((-a^4*b^2*d^4*(3*a^2 - b^2)^2)^(1/2) + a^5*d^2 - 3*a^3*b^2*d^2)/d^4)^(1/2)*(a + b*cot(c + d*x))^(1/2)))/d))/2 - (16*a^4*b^3*(a^2 + b^2)^2)/d^3)*((3*a^3*b^2)/(4*d^2) - a^5/(4*d^2) - (6*a^6*b^4*d^4 - a^4*b^6*d^4 - 9*a^8*b^2*d^4)^(1/2)/(4*d^4))^(1/2) - (2*b*(a + b*cot(c + d*x))^(3/2))/(3*d)","B"
100,1,583,422,2.571340,"\text{Not used}","int(-(a + b*cot(c + d*x))^(1/2)*(a - b*cot(c + d*x)),x)","-\mathrm{atanh}\left(\frac{d^3\,\left(\frac{16\,\left(a^2\,b^4-a^4\,b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^2}+\frac{16\,a\,b^2\,\left(a^3+1{}\mathrm{i}\,b\,a^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^2}\right)\,\sqrt{-\frac{a^3+1{}\mathrm{i}\,b\,a^2}{d^2}}}{16\,\left(a^5\,b^3+a^3\,b^5\right)}\right)\,\sqrt{-\frac{a^3+1{}\mathrm{i}\,b\,a^2}{d^2}}-\mathrm{atanh}\left(\frac{d^3\,\sqrt{\frac{-a^3+a^2\,b\,1{}\mathrm{i}}{d^2}}\,\left(\frac{16\,\left(a^2\,b^4-a^4\,b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^2}-\frac{16\,a\,b^2\,\left(-a^3+a^2\,b\,1{}\mathrm{i}\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d^2}\right)}{16\,\left(a^5\,b^3+a^3\,b^5\right)}\right)\,\sqrt{\frac{-a^3+a^2\,b\,1{}\mathrm{i}}{d^2}}-\frac{2\,b\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{d}+\mathrm{atan}\left(\frac{b^6\,\sqrt{\frac{a\,b^2}{4\,d^2}-\frac{b^3\,1{}\mathrm{i}}{4\,d^2}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,32{}\mathrm{i}}{\frac{b^8\,16{}\mathrm{i}}{d}+\frac{a^2\,b^6\,16{}\mathrm{i}}{d}}+\frac{32\,a\,b^5\,\sqrt{\frac{a\,b^2}{4\,d^2}-\frac{b^3\,1{}\mathrm{i}}{4\,d^2}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{b^8\,16{}\mathrm{i}}{d}+\frac{a^2\,b^6\,16{}\mathrm{i}}{d}}\right)\,\sqrt{\frac{a\,b^2-b^3\,1{}\mathrm{i}}{4\,d^2}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{b^6\,\sqrt{\frac{a\,b^2}{4\,d^2}+\frac{b^3\,1{}\mathrm{i}}{4\,d^2}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,32{}\mathrm{i}}{\frac{b^8\,16{}\mathrm{i}}{d}+\frac{a^2\,b^6\,16{}\mathrm{i}}{d}}-\frac{32\,a\,b^5\,\sqrt{\frac{a\,b^2}{4\,d^2}+\frac{b^3\,1{}\mathrm{i}}{4\,d^2}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{b^8\,16{}\mathrm{i}}{d}+\frac{a^2\,b^6\,16{}\mathrm{i}}{d}}\right)\,\sqrt{\frac{b^3\,1{}\mathrm{i}+a\,b^2}{4\,d^2}}\,2{}\mathrm{i}","Not used",1,"atan((b^6*((a*b^2)/(4*d^2) - (b^3*1i)/(4*d^2))^(1/2)*(a + b*cot(c + d*x))^(1/2)*32i)/((b^8*16i)/d + (a^2*b^6*16i)/d) + (32*a*b^5*((a*b^2)/(4*d^2) - (b^3*1i)/(4*d^2))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((b^8*16i)/d + (a^2*b^6*16i)/d))*((a*b^2 - b^3*1i)/(4*d^2))^(1/2)*2i - atan((b^6*((b^3*1i)/(4*d^2) + (a*b^2)/(4*d^2))^(1/2)*(a + b*cot(c + d*x))^(1/2)*32i)/((b^8*16i)/d + (a^2*b^6*16i)/d) - (32*a*b^5*((b^3*1i)/(4*d^2) + (a*b^2)/(4*d^2))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((b^8*16i)/d + (a^2*b^6*16i)/d))*((a*b^2 + b^3*1i)/(4*d^2))^(1/2)*2i - atanh((d^3*((16*(a^2*b^4 - a^4*b^2)*(a + b*cot(c + d*x))^(1/2))/d^2 + (16*a*b^2*(a^2*b*1i + a^3)*(a + b*cot(c + d*x))^(1/2))/d^2)*(-(a^2*b*1i + a^3)/d^2)^(1/2))/(16*(a^3*b^5 + a^5*b^3)))*(-(a^2*b*1i + a^3)/d^2)^(1/2) - atanh((d^3*((a^2*b*1i - a^3)/d^2)^(1/2)*((16*(a^2*b^4 - a^4*b^2)*(a + b*cot(c + d*x))^(1/2))/d^2 - (16*a*b^2*(a^2*b*1i - a^3)*(a + b*cot(c + d*x))^(1/2))/d^2))/(16*(a^3*b^5 + a^5*b^3)))*((a^2*b*1i - a^3)/d^2)^(1/2) - (2*b*(a + b*cot(c + d*x))^(1/2))/d","B"
101,1,2909,102,2.289969,"\text{Not used}","int((A + B*cot(c + d*x))/(a + b*cot(c + d*x))^(1/2),x)","2\,\mathrm{atanh}\left(\frac{32\,B^2\,b^2\,\sqrt{\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,B^3\,b^2}{d}-\frac{16\,B^3\,a^2\,b^2\,d^3}{a^2\,d^4+b^2\,d^4}+\frac{4\,B\,a\,b^2\,d^2\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{8\,a\,b^2\,\sqrt{\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,B^4\,b^2\,d^4}}{16\,B^3\,b^4\,d+16\,B^3\,a^2\,b^2\,d-\frac{16\,B^3\,a^2\,b^4\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{16\,B^3\,a^4\,b^2\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,B\,a^3\,b^2\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,B\,a\,b^4\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,B^2\,a^2\,b^2\,d^2\,\sqrt{\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{16\,B^3\,b^4\,d+16\,B^3\,a^2\,b^2\,d-\frac{16\,B^3\,a^2\,b^4\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{16\,B^3\,a^4\,b^2\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,B\,a^3\,b^2\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,B\,a\,b^4\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}+2\,\mathrm{atanh}\left(\frac{8\,a\,b^2\,\sqrt{\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,B^4\,b^2\,d^4}}{\frac{16\,B^3\,a^2\,b^4\,d^5}{a^2\,d^4+b^2\,d^4}-16\,B^3\,a^2\,b^2\,d-16\,B^3\,b^4\,d+\frac{16\,B^3\,a^4\,b^2\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,B\,a^3\,b^2\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,B\,a\,b^4\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,B^2\,b^2\,\sqrt{\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,B^3\,a^2\,b^2\,d^3}{a^2\,d^4+b^2\,d^4}-\frac{16\,B^3\,b^2}{d}+\frac{4\,B\,a\,b^2\,d^2\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{32\,B^2\,a^2\,b^2\,d^2\,\sqrt{\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,B^3\,a^2\,b^4\,d^5}{a^2\,d^4+b^2\,d^4}-16\,B^3\,a^2\,b^2\,d-16\,B^3\,b^4\,d+\frac{16\,B^3\,a^4\,b^2\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,B\,a^3\,b^2\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,B\,a\,b^4\,d^4\,\sqrt{-16\,B^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{\frac{\sqrt{-16\,B^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{B^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}+2\,\mathrm{atanh}\left(\frac{32\,A^2\,b^2\,\sqrt{\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,A^3\,a\,b^3\,d^3}{a^2\,d^4+b^2\,d^4}-\frac{4\,A\,b^3\,d^2\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{8\,a\,b^2\,\sqrt{\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,A^4\,b^2\,d^4}}{\frac{16\,A^3\,a\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{4\,A\,b^5\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{16\,A^3\,a^3\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{4\,A\,a^2\,b^3\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,A^2\,a^2\,b^2\,d^2\,\sqrt{\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,A^3\,a\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{4\,A\,b^5\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{16\,A^3\,a^3\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{4\,A\,a^2\,b^3\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}-2\,\mathrm{atanh}\left(\frac{8\,a\,b^2\,\sqrt{-\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,A^4\,b^2\,d^4}}{\frac{16\,A^3\,a\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,A\,b^5\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{16\,A^3\,a^3\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,A\,a^2\,b^3\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,A^2\,b^2\,\sqrt{-\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,A^3\,a\,b^3\,d^3}{a^2\,d^4+b^2\,d^4}+\frac{4\,A\,b^3\,d^2\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{32\,A^2\,a^2\,b^2\,d^2\,\sqrt{-\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,A^3\,a\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,A\,b^5\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{16\,A^3\,a^3\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,A\,a^2\,b^3\,d^4\,\sqrt{-16\,A^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{-\frac{\sqrt{-16\,A^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{A^2\,a\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}","Not used",1,"2*atanh((32*B^2*b^2*((B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*B^3*b^2)/d - (16*B^3*a^2*b^2*d^3)/(a^2*d^4 + b^2*d^4) + (4*B*a*b^2*d^2*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (8*a*b^2*((B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*B^4*b^2*d^4)^(1/2))/(16*B^3*b^4*d + 16*B^3*a^2*b^2*d - (16*B^3*a^2*b^4*d^5)/(a^2*d^4 + b^2*d^4) - (16*B^3*a^4*b^2*d^5)/(a^2*d^4 + b^2*d^4) + (4*B*a^3*b^2*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*B*a*b^4*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*B^2*a^2*b^2*d^2*((B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/(16*B^3*b^4*d + 16*B^3*a^2*b^2*d - (16*B^3*a^2*b^4*d^5)/(a^2*d^4 + b^2*d^4) - (16*B^3*a^4*b^2*d^5)/(a^2*d^4 + b^2*d^4) + (4*B*a^3*b^2*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*B*a*b^4*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*((B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2) + 2*atanh((8*a*b^2*((-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*B^4*b^2*d^4)^(1/2))/((16*B^3*a^2*b^4*d^5)/(a^2*d^4 + b^2*d^4) - 16*B^3*a^2*b^2*d - 16*B^3*b^4*d + (16*B^3*a^4*b^2*d^5)/(a^2*d^4 + b^2*d^4) + (4*B*a^3*b^2*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*B*a*b^4*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*B^2*b^2*((-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*B^3*a^2*b^2*d^3)/(a^2*d^4 + b^2*d^4) - (16*B^3*b^2)/d + (4*B*a*b^2*d^2*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (32*B^2*a^2*b^2*d^2*((-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*B^3*a^2*b^4*d^5)/(a^2*d^4 + b^2*d^4) - 16*B^3*a^2*b^2*d - 16*B^3*b^4*d + (16*B^3*a^4*b^2*d^5)/(a^2*d^4 + b^2*d^4) + (4*B*a^3*b^2*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*B*a*b^4*d^4*(-16*B^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*((-16*B^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (B^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2) + 2*atanh((32*A^2*b^2*((-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*A^3*a*b^3*d^3)/(a^2*d^4 + b^2*d^4) - (4*A*b^3*d^2*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (8*a*b^2*((-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*A^4*b^2*d^4)^(1/2))/((16*A^3*a*b^5*d^5)/(a^2*d^4 + b^2*d^4) - (4*A*b^5*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (16*A^3*a^3*b^3*d^5)/(a^2*d^4 + b^2*d^4) - (4*A*a^2*b^3*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*A^2*a^2*b^2*d^2*((-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*A^3*a*b^5*d^5)/(a^2*d^4 + b^2*d^4) - (4*A*b^5*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (16*A^3*a^3*b^3*d^5)/(a^2*d^4 + b^2*d^4) - (4*A*a^2*b^3*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*((-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2) - 2*atanh((8*a*b^2*(- (-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*A^4*b^2*d^4)^(1/2))/((16*A^3*a*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (4*A*b^5*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (16*A^3*a^3*b^3*d^5)/(a^2*d^4 + b^2*d^4) + (4*A*a^2*b^3*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*A^2*b^2*(- (-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*A^3*a*b^3*d^3)/(a^2*d^4 + b^2*d^4) + (4*A*b^3*d^2*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (32*A^2*a^2*b^2*d^2*(- (-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*A^3*a*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (4*A*b^5*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (16*A^3*a^3*b^3*d^5)/(a^2*d^4 + b^2*d^4) + (4*A*a^2*b^3*d^4*(-16*A^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*(- (-16*A^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (A^2*a*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)","B"
102,1,5737,138,6.465784,"\text{Not used}","int((A + B*cot(c + d*x))/(a + b*cot(c + d*x))^(3/2),x)","\frac{\ln\left(\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^8\,b^2\,d^3-32\,A^2\,a^6\,b^4\,d^3+32\,A^2\,a^2\,b^8\,d^3+16\,A^2\,b^{10}\,d^3\right)+\frac{\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(64\,A\,a\,b^{11}\,d^4-\frac{\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)}{4}+256\,A\,a^3\,b^9\,d^4+384\,A\,a^5\,b^7\,d^4+256\,A\,a^7\,b^5\,d^4+64\,A\,a^9\,b^3\,d^4\right)}{4}\right)\,\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}-8\,A^3\,b^9\,d^2-24\,A^3\,a^2\,b^7\,d^2-24\,A^3\,a^4\,b^5\,d^2-8\,A^3\,a^6\,b^3\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}+\frac{\ln\left(\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^8\,b^2\,d^3-32\,A^2\,a^6\,b^4\,d^3+32\,A^2\,a^2\,b^8\,d^3+16\,A^2\,b^{10}\,d^3\right)+\frac{\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(64\,A\,a\,b^{11}\,d^4-\frac{\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)}{4}+256\,A\,a^3\,b^9\,d^4+384\,A\,a^5\,b^7\,d^4+256\,A\,a^7\,b^5\,d^4+64\,A\,a^9\,b^3\,d^4\right)}{4}\right)\,\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}-8\,A^3\,b^9\,d^2-24\,A^3\,a^2\,b^7\,d^2-24\,A^3\,a^4\,b^5\,d^2-8\,A^3\,a^6\,b^3\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}-\ln\left(-\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^8\,b^2\,d^3-32\,A^2\,a^6\,b^4\,d^3+32\,A^2\,a^2\,b^8\,d^3+16\,A^2\,b^{10}\,d^3\right)-\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+64\,A\,a\,b^{11}\,d^4+256\,A\,a^3\,b^9\,d^4+384\,A\,a^5\,b^7\,d^4+256\,A\,a^7\,b^5\,d^4+64\,A\,a^9\,b^3\,d^4\right)\right)\,\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-8\,A^3\,b^9\,d^2-24\,A^3\,a^2\,b^7\,d^2-24\,A^3\,a^4\,b^5\,d^2-8\,A^3\,a^6\,b^3\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}-4\,A^2\,a^3\,d^2+12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-\ln\left(-\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^8\,b^2\,d^3-32\,A^2\,a^6\,b^4\,d^3+32\,A^2\,a^2\,b^8\,d^3+16\,A^2\,b^{10}\,d^3\right)-\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+64\,A\,a\,b^{11}\,d^4+256\,A\,a^3\,b^9\,d^4+384\,A\,a^5\,b^7\,d^4+256\,A\,a^7\,b^5\,d^4+64\,A\,a^9\,b^3\,d^4\right)\right)\,\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-8\,A^3\,b^9\,d^2-24\,A^3\,a^2\,b^7\,d^2-24\,A^3\,a^4\,b^5\,d^2-8\,A^3\,a^6\,b^3\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,A^4\,a^4\,b^2\,d^4+96\,A^4\,a^2\,b^4\,d^4-16\,A^4\,b^6\,d^4}+4\,A^2\,a^3\,d^2-12\,A^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}+\frac{\ln\left(24\,B^3\,a^3\,b^6\,d^2-\frac{\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)}{4}-32\,B\,b^{12}\,d^4-96\,B\,a^2\,b^{10}\,d^4-64\,B\,a^4\,b^8\,d^4+64\,B\,a^6\,b^6\,d^4+96\,B\,a^8\,b^4\,d^4+32\,B\,a^{10}\,b^2\,d^4\right)}{4}+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^8\,b^2\,d^3-32\,B^2\,a^6\,b^4\,d^3+32\,B^2\,a^2\,b^8\,d^3+16\,B^2\,b^{10}\,d^3\right)\right)}{4}+24\,B^3\,a^5\,b^4\,d^2+8\,B^3\,a^7\,b^2\,d^2+8\,B^3\,a\,b^8\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}+\frac{\ln\left(24\,B^3\,a^3\,b^6\,d^2-\frac{\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)}{4}-32\,B\,b^{12}\,d^4-96\,B\,a^2\,b^{10}\,d^4-64\,B\,a^4\,b^8\,d^4+64\,B\,a^6\,b^6\,d^4+96\,B\,a^8\,b^4\,d^4+32\,B\,a^{10}\,b^2\,d^4\right)}{4}+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^8\,b^2\,d^3-32\,B^2\,a^6\,b^4\,d^3+32\,B^2\,a^2\,b^8\,d^3+16\,B^2\,b^{10}\,d^3\right)\right)}{4}+24\,B^3\,a^5\,b^4\,d^2+8\,B^3\,a^7\,b^2\,d^2+8\,B^3\,a\,b^8\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}-\ln\left(\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(32\,B\,b^{12}\,d^4+\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+96\,B\,a^2\,b^{10}\,d^4+64\,B\,a^4\,b^8\,d^4-64\,B\,a^6\,b^6\,d^4-96\,B\,a^8\,b^4\,d^4-32\,B\,a^{10}\,b^2\,d^4\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^8\,b^2\,d^3-32\,B^2\,a^6\,b^4\,d^3+32\,B^2\,a^2\,b^8\,d^3+16\,B^2\,b^{10}\,d^3\right)\right)+24\,B^3\,a^3\,b^6\,d^2+24\,B^3\,a^5\,b^4\,d^2+8\,B^3\,a^7\,b^2\,d^2+8\,B^3\,a\,b^8\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}+4\,B^2\,a^3\,d^2-12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-\ln\left(\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(32\,B\,b^{12}\,d^4+\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+96\,B\,a^2\,b^{10}\,d^4+64\,B\,a^4\,b^8\,d^4-64\,B\,a^6\,b^6\,d^4-96\,B\,a^8\,b^4\,d^4-32\,B\,a^{10}\,b^2\,d^4\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^8\,b^2\,d^3-32\,B^2\,a^6\,b^4\,d^3+32\,B^2\,a^2\,b^8\,d^3+16\,B^2\,b^{10}\,d^3\right)\right)+24\,B^3\,a^3\,b^6\,d^2+24\,B^3\,a^5\,b^4\,d^2+8\,B^3\,a^7\,b^2\,d^2+8\,B^3\,a\,b^8\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,B^4\,a^4\,b^2\,d^4+96\,B^4\,a^2\,b^4\,d^4-16\,B^4\,b^6\,d^4}-4\,B^2\,a^3\,d^2+12\,B^2\,a\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}+\frac{2\,A\,b}{d\,\left(a^2+b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}-\frac{2\,B\,a}{d\,\left(a^2+b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}","Not used",1,"(log((((a + b*cot(c + d*x))^(1/2)*(16*A^2*b^10*d^3 + 32*A^2*a^2*b^8*d^3 - 32*A^2*a^6*b^4*d^3 - 16*A^2*a^8*b^2*d^3) + ((((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(64*A*a*b^11*d^4 - ((((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5))/4 + 256*A*a^3*b^9*d^4 + 384*A*a^5*b^7*d^4 + 256*A*a^7*b^5*d^4 + 64*A*a^9*b^3*d^4))/4)*(((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 - 8*A^3*b^9*d^2 - 24*A^3*a^2*b^7*d^2 - 24*A^3*a^4*b^5*d^2 - 8*A^3*a^6*b^3*d^2)*(((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 + (log((((a + b*cot(c + d*x))^(1/2)*(16*A^2*b^10*d^3 + 32*A^2*a^2*b^8*d^3 - 32*A^2*a^6*b^4*d^3 - 16*A^2*a^8*b^2*d^3) + ((-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(64*A*a*b^11*d^4 - ((-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5))/4 + 256*A*a^3*b^9*d^4 + 384*A*a^5*b^7*d^4 + 256*A*a^7*b^5*d^4 + 64*A*a^9*b^3*d^4))/4)*(-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 - 8*A^3*b^9*d^2 - 24*A^3*a^2*b^7*d^2 - 24*A^3*a^4*b^5*d^2 - 8*A^3*a^6*b^3*d^2)*(-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 - log(- ((a + b*cot(c + d*x))^(1/2)*(16*A^2*b^10*d^3 + 32*A^2*a^2*b^8*d^3 - 32*A^2*a^6*b^4*d^3 - 16*A^2*a^8*b^2*d^3) - (((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*((((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 64*A*a*b^11*d^4 + 256*A*a^3*b^9*d^4 + 384*A*a^5*b^7*d^4 + 256*A*a^7*b^5*d^4 + 64*A*a^9*b^3*d^4))*(((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 8*A^3*b^9*d^2 - 24*A^3*a^2*b^7*d^2 - 24*A^3*a^4*b^5*d^2 - 8*A^3*a^6*b^3*d^2)*(((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) - 4*A^2*a^3*d^2 + 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - log(- ((a + b*cot(c + d*x))^(1/2)*(16*A^2*b^10*d^3 + 32*A^2*a^2*b^8*d^3 - 32*A^2*a^6*b^4*d^3 - 16*A^2*a^8*b^2*d^3) - (-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*((-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 64*A*a*b^11*d^4 + 256*A*a^3*b^9*d^4 + 384*A*a^5*b^7*d^4 + 256*A*a^7*b^5*d^4 + 64*A*a^9*b^3*d^4))*(-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 8*A^3*b^9*d^2 - 24*A^3*a^2*b^7*d^2 - 24*A^3*a^4*b^5*d^2 - 8*A^3*a^6*b^3*d^2)*(-((96*A^4*a^2*b^4*d^4 - 16*A^4*b^6*d^4 - 144*A^4*a^4*b^2*d^4)^(1/2) + 4*A^2*a^3*d^2 - 12*A^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + (log(24*B^3*a^3*b^6*d^2 - ((((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(((((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(((((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5))/4 - 32*B*b^12*d^4 - 96*B*a^2*b^10*d^4 - 64*B*a^4*b^8*d^4 + 64*B*a^6*b^6*d^4 + 96*B*a^8*b^4*d^4 + 32*B*a^10*b^2*d^4))/4 + (a + b*cot(c + d*x))^(1/2)*(16*B^2*b^10*d^3 + 32*B^2*a^2*b^8*d^3 - 32*B^2*a^6*b^4*d^3 - 16*B^2*a^8*b^2*d^3)))/4 + 24*B^3*a^5*b^4*d^2 + 8*B^3*a^7*b^2*d^2 + 8*B^3*a*b^8*d^2)*(((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 + (log(24*B^3*a^3*b^6*d^2 - ((-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(((-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(((-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5))/4 - 32*B*b^12*d^4 - 96*B*a^2*b^10*d^4 - 64*B*a^4*b^8*d^4 + 64*B*a^6*b^6*d^4 + 96*B*a^8*b^4*d^4 + 32*B*a^10*b^2*d^4))/4 + (a + b*cot(c + d*x))^(1/2)*(16*B^2*b^10*d^3 + 32*B^2*a^2*b^8*d^3 - 32*B^2*a^6*b^4*d^3 - 16*B^2*a^8*b^2*d^3)))/4 + 24*B^3*a^5*b^4*d^2 + 8*B^3*a^7*b^2*d^2 + 8*B^3*a*b^8*d^2)*(-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 - log((((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*((((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(32*B*b^12*d^4 + (((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 96*B*a^2*b^10*d^4 + 64*B*a^4*b^8*d^4 - 64*B*a^6*b^6*d^4 - 96*B*a^8*b^4*d^4 - 32*B*a^10*b^2*d^4) + (a + b*cot(c + d*x))^(1/2)*(16*B^2*b^10*d^3 + 32*B^2*a^2*b^8*d^3 - 32*B^2*a^6*b^4*d^3 - 16*B^2*a^8*b^2*d^3)) + 24*B^3*a^3*b^6*d^2 + 24*B^3*a^5*b^4*d^2 + 8*B^3*a^7*b^2*d^2 + 8*B^3*a*b^8*d^2)*(((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) + 4*B^2*a^3*d^2 - 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - log((-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*((-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(32*B*b^12*d^4 + (-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 96*B*a^2*b^10*d^4 + 64*B*a^4*b^8*d^4 - 64*B*a^6*b^6*d^4 - 96*B*a^8*b^4*d^4 - 32*B*a^10*b^2*d^4) + (a + b*cot(c + d*x))^(1/2)*(16*B^2*b^10*d^3 + 32*B^2*a^2*b^8*d^3 - 32*B^2*a^6*b^4*d^3 - 16*B^2*a^8*b^2*d^3)) + 24*B^3*a^3*b^6*d^2 + 24*B^3*a^5*b^4*d^2 + 8*B^3*a^7*b^2*d^2 + 8*B^3*a*b^8*d^2)*(-((96*B^4*a^2*b^4*d^4 - 16*B^4*b^6*d^4 - 144*B^4*a^4*b^2*d^4)^(1/2) - 4*B^2*a^3*d^2 + 12*B^2*a*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + (2*A*b)/(d*(a^2 + b^2)*(a + b*cot(c + d*x))^(1/2)) - (2*B*a)/(d*(a^2 + b^2)*(a + b*cot(c + d*x))^(1/2))","B"
103,1,9453,185,17.932833,"\text{Not used}","int((A + B*cot(c + d*x))/(a + b*cot(c + d*x))^(5/2),x)","\frac{\ln\left(\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^{16}\,b^2\,d^3+320\,A^2\,a^{12}\,b^6\,d^3+1024\,A^2\,a^{10}\,b^8\,d^3+1440\,A^2\,a^8\,b^{10}\,d^3+1024\,A^2\,a^6\,b^{12}\,d^3+320\,A^2\,a^4\,b^{14}\,d^3-16\,A^2\,b^{18}\,d^3\right)+\frac{\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(896\,A\,a^6\,b^{15}\,d^4-\frac{\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}-160\,A\,a^2\,b^{19}\,d^4-128\,A\,a^4\,b^{17}\,d^4-32\,A\,b^{21}\,d^4+3136\,A\,a^8\,b^{13}\,d^4+4928\,A\,a^{10}\,b^{11}\,d^4+4480\,A\,a^{12}\,b^9\,d^4+2432\,A\,a^{14}\,b^7\,d^4+736\,A\,a^{16}\,b^5\,d^4+96\,A\,a^{18}\,b^3\,d^4\right)}{4}\right)\,\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-96\,A^3\,a^3\,b^{13}\,d^2-240\,A^3\,a^5\,b^{11}\,d^2-320\,A^3\,a^7\,b^9\,d^2-240\,A^3\,a^9\,b^7\,d^2-96\,A^3\,a^{11}\,b^5\,d^2-16\,A^3\,a^{13}\,b^3\,d^2-16\,A^3\,a\,b^{15}\,d^2\right)\,\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}+\frac{\ln\left(\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^{16}\,b^2\,d^3+320\,A^2\,a^{12}\,b^6\,d^3+1024\,A^2\,a^{10}\,b^8\,d^3+1440\,A^2\,a^8\,b^{10}\,d^3+1024\,A^2\,a^6\,b^{12}\,d^3+320\,A^2\,a^4\,b^{14}\,d^3-16\,A^2\,b^{18}\,d^3\right)+\frac{\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(896\,A\,a^6\,b^{15}\,d^4-\frac{\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}-160\,A\,a^2\,b^{19}\,d^4-128\,A\,a^4\,b^{17}\,d^4-32\,A\,b^{21}\,d^4+3136\,A\,a^8\,b^{13}\,d^4+4928\,A\,a^{10}\,b^{11}\,d^4+4480\,A\,a^{12}\,b^9\,d^4+2432\,A\,a^{14}\,b^7\,d^4+736\,A\,a^{16}\,b^5\,d^4+96\,A\,a^{18}\,b^3\,d^4\right)}{4}\right)\,\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-96\,A^3\,a^3\,b^{13}\,d^2-240\,A^3\,a^5\,b^{11}\,d^2-320\,A^3\,a^7\,b^9\,d^2-240\,A^3\,a^9\,b^7\,d^2-96\,A^3\,a^{11}\,b^5\,d^2-16\,A^3\,a^{13}\,b^3\,d^2-16\,A^3\,a\,b^{15}\,d^2\right)\,\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-\ln\left(-\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^{16}\,b^2\,d^3+320\,A^2\,a^{12}\,b^6\,d^3+1024\,A^2\,a^{10}\,b^8\,d^3+1440\,A^2\,a^8\,b^{10}\,d^3+1024\,A^2\,a^6\,b^{12}\,d^3+320\,A^2\,a^4\,b^{14}\,d^3-16\,A^2\,b^{18}\,d^3\right)-\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)-32\,A\,b^{21}\,d^4-160\,A\,a^2\,b^{19}\,d^4-128\,A\,a^4\,b^{17}\,d^4+896\,A\,a^6\,b^{15}\,d^4+3136\,A\,a^8\,b^{13}\,d^4+4928\,A\,a^{10}\,b^{11}\,d^4+4480\,A\,a^{12}\,b^9\,d^4+2432\,A\,a^{14}\,b^7\,d^4+736\,A\,a^{16}\,b^5\,d^4+96\,A\,a^{18}\,b^3\,d^4\right)\right)\,\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-96\,A^3\,a^3\,b^{13}\,d^2-240\,A^3\,a^5\,b^{11}\,d^2-320\,A^3\,a^7\,b^9\,d^2-240\,A^3\,a^9\,b^7\,d^2-96\,A^3\,a^{11}\,b^5\,d^2-16\,A^3\,a^{13}\,b^3\,d^2-16\,A^3\,a\,b^{15}\,d^2\right)\,\sqrt{\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}-4\,A^2\,a^5\,d^2+40\,A^2\,a^3\,b^2\,d^2-20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-\ln\left(-\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,A^2\,a^{16}\,b^2\,d^3+320\,A^2\,a^{12}\,b^6\,d^3+1024\,A^2\,a^{10}\,b^8\,d^3+1440\,A^2\,a^8\,b^{10}\,d^3+1024\,A^2\,a^6\,b^{12}\,d^3+320\,A^2\,a^4\,b^{14}\,d^3-16\,A^2\,b^{18}\,d^3\right)-\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)-32\,A\,b^{21}\,d^4-160\,A\,a^2\,b^{19}\,d^4-128\,A\,a^4\,b^{17}\,d^4+896\,A\,a^6\,b^{15}\,d^4+3136\,A\,a^8\,b^{13}\,d^4+4928\,A\,a^{10}\,b^{11}\,d^4+4480\,A\,a^{12}\,b^9\,d^4+2432\,A\,a^{14}\,b^7\,d^4+736\,A\,a^{16}\,b^5\,d^4+96\,A\,a^{18}\,b^3\,d^4\right)\right)\,\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-96\,A^3\,a^3\,b^{13}\,d^2-240\,A^3\,a^5\,b^{11}\,d^2-320\,A^3\,a^7\,b^9\,d^2-240\,A^3\,a^9\,b^7\,d^2-96\,A^3\,a^{11}\,b^5\,d^2-16\,A^3\,a^{13}\,b^3\,d^2-16\,A^3\,a\,b^{15}\,d^2\right)\,\sqrt{-\frac{\sqrt{-400\,A^4\,a^8\,b^2\,d^4+1600\,A^4\,a^6\,b^4\,d^4-1760\,A^4\,a^4\,b^6\,d^4+320\,A^4\,a^2\,b^8\,d^4-16\,A^4\,b^{10}\,d^4}+4\,A^2\,a^5\,d^2-40\,A^2\,a^3\,b^2\,d^2+20\,A^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}+\frac{\ln\left(40\,B^3\,a^8\,b^8\,d^2-8\,B^3\,b^{16}\,d^2-40\,B^3\,a^2\,b^{14}\,d^2-72\,B^3\,a^4\,b^{12}\,d^2-40\,B^3\,a^6\,b^{10}\,d^2-\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^{16}\,b^2\,d^3+320\,B^2\,a^{12}\,b^6\,d^3+1024\,B^2\,a^{10}\,b^8\,d^3+1440\,B^2\,a^8\,b^{10}\,d^3+1024\,B^2\,a^6\,b^{12}\,d^3+320\,B^2\,a^4\,b^{14}\,d^3-16\,B^2\,b^{18}\,d^3\right)-\frac{\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(96\,B\,a\,b^{20}\,d^4-\frac{\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}+736\,B\,a^3\,b^{18}\,d^4+2432\,B\,a^5\,b^{16}\,d^4+4480\,B\,a^7\,b^{14}\,d^4+4928\,B\,a^9\,b^{12}\,d^4+3136\,B\,a^{11}\,b^{10}\,d^4+896\,B\,a^{13}\,b^8\,d^4-128\,B\,a^{15}\,b^6\,d^4-160\,B\,a^{17}\,b^4\,d^4-32\,B\,a^{19}\,b^2\,d^4\right)}{4}\right)\,\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}+72\,B^3\,a^{10}\,b^6\,d^2+40\,B^3\,a^{12}\,b^4\,d^2+8\,B^3\,a^{14}\,b^2\,d^2\right)\,\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}+\frac{\ln\left(40\,B^3\,a^8\,b^8\,d^2-8\,B^3\,b^{16}\,d^2-40\,B^3\,a^2\,b^{14}\,d^2-72\,B^3\,a^4\,b^{12}\,d^2-40\,B^3\,a^6\,b^{10}\,d^2-\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^{16}\,b^2\,d^3+320\,B^2\,a^{12}\,b^6\,d^3+1024\,B^2\,a^{10}\,b^8\,d^3+1440\,B^2\,a^8\,b^{10}\,d^3+1024\,B^2\,a^6\,b^{12}\,d^3+320\,B^2\,a^4\,b^{14}\,d^3-16\,B^2\,b^{18}\,d^3\right)-\frac{\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(96\,B\,a\,b^{20}\,d^4-\frac{\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}+736\,B\,a^3\,b^{18}\,d^4+2432\,B\,a^5\,b^{16}\,d^4+4480\,B\,a^7\,b^{14}\,d^4+4928\,B\,a^9\,b^{12}\,d^4+3136\,B\,a^{11}\,b^{10}\,d^4+896\,B\,a^{13}\,b^8\,d^4-128\,B\,a^{15}\,b^6\,d^4-160\,B\,a^{17}\,b^4\,d^4-32\,B\,a^{19}\,b^2\,d^4\right)}{4}\right)\,\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}+72\,B^3\,a^{10}\,b^6\,d^2+40\,B^3\,a^{12}\,b^4\,d^2+8\,B^3\,a^{14}\,b^2\,d^2\right)\,\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-\ln\left(\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^{16}\,b^2\,d^3+320\,B^2\,a^{12}\,b^6\,d^3+1024\,B^2\,a^{10}\,b^8\,d^3+1440\,B^2\,a^8\,b^{10}\,d^3+1024\,B^2\,a^6\,b^{12}\,d^3+320\,B^2\,a^4\,b^{14}\,d^3-16\,B^2\,b^{18}\,d^3\right)+\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)+96\,B\,a\,b^{20}\,d^4+736\,B\,a^3\,b^{18}\,d^4+2432\,B\,a^5\,b^{16}\,d^4+4480\,B\,a^7\,b^{14}\,d^4+4928\,B\,a^9\,b^{12}\,d^4+3136\,B\,a^{11}\,b^{10}\,d^4+896\,B\,a^{13}\,b^8\,d^4-128\,B\,a^{15}\,b^6\,d^4-160\,B\,a^{17}\,b^4\,d^4-32\,B\,a^{19}\,b^2\,d^4\right)\right)\,\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-8\,B^3\,b^{16}\,d^2-40\,B^3\,a^2\,b^{14}\,d^2-72\,B^3\,a^4\,b^{12}\,d^2-40\,B^3\,a^6\,b^{10}\,d^2+40\,B^3\,a^8\,b^8\,d^2+72\,B^3\,a^{10}\,b^6\,d^2+40\,B^3\,a^{12}\,b^4\,d^2+8\,B^3\,a^{14}\,b^2\,d^2\right)\,\sqrt{\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}+4\,B^2\,a^5\,d^2-40\,B^2\,a^3\,b^2\,d^2+20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-\ln\left(\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,B^2\,a^{16}\,b^2\,d^3+320\,B^2\,a^{12}\,b^6\,d^3+1024\,B^2\,a^{10}\,b^8\,d^3+1440\,B^2\,a^8\,b^{10}\,d^3+1024\,B^2\,a^6\,b^{12}\,d^3+320\,B^2\,a^4\,b^{14}\,d^3-16\,B^2\,b^{18}\,d^3\right)+\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)+96\,B\,a\,b^{20}\,d^4+736\,B\,a^3\,b^{18}\,d^4+2432\,B\,a^5\,b^{16}\,d^4+4480\,B\,a^7\,b^{14}\,d^4+4928\,B\,a^9\,b^{12}\,d^4+3136\,B\,a^{11}\,b^{10}\,d^4+896\,B\,a^{13}\,b^8\,d^4-128\,B\,a^{15}\,b^6\,d^4-160\,B\,a^{17}\,b^4\,d^4-32\,B\,a^{19}\,b^2\,d^4\right)\right)\,\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-8\,B^3\,b^{16}\,d^2-40\,B^3\,a^2\,b^{14}\,d^2-72\,B^3\,a^4\,b^{12}\,d^2-40\,B^3\,a^6\,b^{10}\,d^2+40\,B^3\,a^8\,b^8\,d^2+72\,B^3\,a^{10}\,b^6\,d^2+40\,B^3\,a^{12}\,b^4\,d^2+8\,B^3\,a^{14}\,b^2\,d^2\right)\,\sqrt{-\frac{\sqrt{-400\,B^4\,a^8\,b^2\,d^4+1600\,B^4\,a^6\,b^4\,d^4-1760\,B^4\,a^4\,b^6\,d^4+320\,B^4\,a^2\,b^8\,d^4-16\,B^4\,b^{10}\,d^4}-4\,B^2\,a^5\,d^2+40\,B^2\,a^3\,b^2\,d^2-20\,B^2\,a\,b^4\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-\frac{\frac{2\,B\,a}{3\,\left(a^2+b^2\right)}+\frac{2\,B\,\left(a^2-b^2\right)\,\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{{\left(a^2+b^2\right)}^2}}{d\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}+\frac{\frac{2\,A\,b}{3\,\left(a^2+b^2\right)}+\frac{4\,A\,a\,b\,\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{{\left(a^2+b^2\right)}^2}}{d\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}","Not used",1,"(log((((a + b*cot(c + d*x))^(1/2)*(320*A^2*a^4*b^14*d^3 - 16*A^2*b^18*d^3 + 1024*A^2*a^6*b^12*d^3 + 1440*A^2*a^8*b^10*d^3 + 1024*A^2*a^10*b^8*d^3 + 320*A^2*a^12*b^6*d^3 - 16*A^2*a^16*b^2*d^3) + ((((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(896*A*a^6*b^15*d^4 - ((((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4 - 160*A*a^2*b^19*d^4 - 128*A*a^4*b^17*d^4 - 32*A*b^21*d^4 + 3136*A*a^8*b^13*d^4 + 4928*A*a^10*b^11*d^4 + 4480*A*a^12*b^9*d^4 + 2432*A*a^14*b^7*d^4 + 736*A*a^16*b^5*d^4 + 96*A*a^18*b^3*d^4))/4)*(((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - 96*A^3*a^3*b^13*d^2 - 240*A^3*a^5*b^11*d^2 - 320*A^3*a^7*b^9*d^2 - 240*A^3*a^9*b^7*d^2 - 96*A^3*a^11*b^5*d^2 - 16*A^3*a^13*b^3*d^2 - 16*A^3*a*b^15*d^2)*(((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 + (log((((a + b*cot(c + d*x))^(1/2)*(320*A^2*a^4*b^14*d^3 - 16*A^2*b^18*d^3 + 1024*A^2*a^6*b^12*d^3 + 1440*A^2*a^8*b^10*d^3 + 1024*A^2*a^10*b^8*d^3 + 320*A^2*a^12*b^6*d^3 - 16*A^2*a^16*b^2*d^3) + ((-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(896*A*a^6*b^15*d^4 - ((-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4 - 160*A*a^2*b^19*d^4 - 128*A*a^4*b^17*d^4 - 32*A*b^21*d^4 + 3136*A*a^8*b^13*d^4 + 4928*A*a^10*b^11*d^4 + 4480*A*a^12*b^9*d^4 + 2432*A*a^14*b^7*d^4 + 736*A*a^16*b^5*d^4 + 96*A*a^18*b^3*d^4))/4)*(-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - 96*A^3*a^3*b^13*d^2 - 240*A^3*a^5*b^11*d^2 - 320*A^3*a^7*b^9*d^2 - 240*A^3*a^9*b^7*d^2 - 96*A^3*a^11*b^5*d^2 - 16*A^3*a^13*b^3*d^2 - 16*A^3*a*b^15*d^2)*(-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - log(- ((a + b*cot(c + d*x))^(1/2)*(320*A^2*a^4*b^14*d^3 - 16*A^2*b^18*d^3 + 1024*A^2*a^6*b^12*d^3 + 1440*A^2*a^8*b^10*d^3 + 1024*A^2*a^10*b^8*d^3 + 320*A^2*a^12*b^6*d^3 - 16*A^2*a^16*b^2*d^3) - (((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5) - 32*A*b^21*d^4 - 160*A*a^2*b^19*d^4 - 128*A*a^4*b^17*d^4 + 896*A*a^6*b^15*d^4 + 3136*A*a^8*b^13*d^4 + 4928*A*a^10*b^11*d^4 + 4480*A*a^12*b^9*d^4 + 2432*A*a^14*b^7*d^4 + 736*A*a^16*b^5*d^4 + 96*A*a^18*b^3*d^4))*(((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 96*A^3*a^3*b^13*d^2 - 240*A^3*a^5*b^11*d^2 - 320*A^3*a^7*b^9*d^2 - 240*A^3*a^9*b^7*d^2 - 96*A^3*a^11*b^5*d^2 - 16*A^3*a^13*b^3*d^2 - 16*A^3*a*b^15*d^2)*(((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) - 4*A^2*a^5*d^2 + 40*A^2*a^3*b^2*d^2 - 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - log(- ((a + b*cot(c + d*x))^(1/2)*(320*A^2*a^4*b^14*d^3 - 16*A^2*b^18*d^3 + 1024*A^2*a^6*b^12*d^3 + 1440*A^2*a^8*b^10*d^3 + 1024*A^2*a^10*b^8*d^3 + 320*A^2*a^12*b^6*d^3 - 16*A^2*a^16*b^2*d^3) - (-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5) - 32*A*b^21*d^4 - 160*A*a^2*b^19*d^4 - 128*A*a^4*b^17*d^4 + 896*A*a^6*b^15*d^4 + 3136*A*a^8*b^13*d^4 + 4928*A*a^10*b^11*d^4 + 4480*A*a^12*b^9*d^4 + 2432*A*a^14*b^7*d^4 + 736*A*a^16*b^5*d^4 + 96*A*a^18*b^3*d^4))*(-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 96*A^3*a^3*b^13*d^2 - 240*A^3*a^5*b^11*d^2 - 320*A^3*a^7*b^9*d^2 - 240*A^3*a^9*b^7*d^2 - 96*A^3*a^11*b^5*d^2 - 16*A^3*a^13*b^3*d^2 - 16*A^3*a*b^15*d^2)*(-((320*A^4*a^2*b^8*d^4 - 16*A^4*b^10*d^4 - 1760*A^4*a^4*b^6*d^4 + 1600*A^4*a^6*b^4*d^4 - 400*A^4*a^8*b^2*d^4)^(1/2) + 4*A^2*a^5*d^2 - 40*A^2*a^3*b^2*d^2 + 20*A^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + (log(40*B^3*a^8*b^8*d^2 - 8*B^3*b^16*d^2 - 40*B^3*a^2*b^14*d^2 - 72*B^3*a^4*b^12*d^2 - 40*B^3*a^6*b^10*d^2 - (((a + b*cot(c + d*x))^(1/2)*(320*B^2*a^4*b^14*d^3 - 16*B^2*b^18*d^3 + 1024*B^2*a^6*b^12*d^3 + 1440*B^2*a^8*b^10*d^3 + 1024*B^2*a^10*b^8*d^3 + 320*B^2*a^12*b^6*d^3 - 16*B^2*a^16*b^2*d^3) - ((((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(96*B*a*b^20*d^4 - ((a + b*cot(c + d*x))^(1/2)*(((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4 + 736*B*a^3*b^18*d^4 + 2432*B*a^5*b^16*d^4 + 4480*B*a^7*b^14*d^4 + 4928*B*a^9*b^12*d^4 + 3136*B*a^11*b^10*d^4 + 896*B*a^13*b^8*d^4 - 128*B*a^15*b^6*d^4 - 160*B*a^17*b^4*d^4 - 32*B*a^19*b^2*d^4))/4)*(((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 + 72*B^3*a^10*b^6*d^2 + 40*B^3*a^12*b^4*d^2 + 8*B^3*a^14*b^2*d^2)*(((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 + (log(40*B^3*a^8*b^8*d^2 - 8*B^3*b^16*d^2 - 40*B^3*a^2*b^14*d^2 - 72*B^3*a^4*b^12*d^2 - 40*B^3*a^6*b^10*d^2 - (((a + b*cot(c + d*x))^(1/2)*(320*B^2*a^4*b^14*d^3 - 16*B^2*b^18*d^3 + 1024*B^2*a^6*b^12*d^3 + 1440*B^2*a^8*b^10*d^3 + 1024*B^2*a^10*b^8*d^3 + 320*B^2*a^12*b^6*d^3 - 16*B^2*a^16*b^2*d^3) - ((-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(96*B*a*b^20*d^4 - ((a + b*cot(c + d*x))^(1/2)*(-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4 + 736*B*a^3*b^18*d^4 + 2432*B*a^5*b^16*d^4 + 4480*B*a^7*b^14*d^4 + 4928*B*a^9*b^12*d^4 + 3136*B*a^11*b^10*d^4 + 896*B*a^13*b^8*d^4 - 128*B*a^15*b^6*d^4 - 160*B*a^17*b^4*d^4 - 32*B*a^19*b^2*d^4))/4)*(-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 + 72*B^3*a^10*b^6*d^2 + 40*B^3*a^12*b^4*d^2 + 8*B^3*a^14*b^2*d^2)*(-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - log(((a + b*cot(c + d*x))^(1/2)*(320*B^2*a^4*b^14*d^3 - 16*B^2*b^18*d^3 + 1024*B^2*a^6*b^12*d^3 + 1440*B^2*a^8*b^10*d^3 + 1024*B^2*a^10*b^8*d^3 + 320*B^2*a^12*b^6*d^3 - 16*B^2*a^16*b^2*d^3) + (((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((a + b*cot(c + d*x))^(1/2)*(((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5) + 96*B*a*b^20*d^4 + 736*B*a^3*b^18*d^4 + 2432*B*a^5*b^16*d^4 + 4480*B*a^7*b^14*d^4 + 4928*B*a^9*b^12*d^4 + 3136*B*a^11*b^10*d^4 + 896*B*a^13*b^8*d^4 - 128*B*a^15*b^6*d^4 - 160*B*a^17*b^4*d^4 - 32*B*a^19*b^2*d^4))*(((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 8*B^3*b^16*d^2 - 40*B^3*a^2*b^14*d^2 - 72*B^3*a^4*b^12*d^2 - 40*B^3*a^6*b^10*d^2 + 40*B^3*a^8*b^8*d^2 + 72*B^3*a^10*b^6*d^2 + 40*B^3*a^12*b^4*d^2 + 8*B^3*a^14*b^2*d^2)*(((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) + 4*B^2*a^5*d^2 - 40*B^2*a^3*b^2*d^2 + 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - log(((a + b*cot(c + d*x))^(1/2)*(320*B^2*a^4*b^14*d^3 - 16*B^2*b^18*d^3 + 1024*B^2*a^6*b^12*d^3 + 1440*B^2*a^8*b^10*d^3 + 1024*B^2*a^10*b^8*d^3 + 320*B^2*a^12*b^6*d^3 - 16*B^2*a^16*b^2*d^3) + (-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((a + b*cot(c + d*x))^(1/2)*(-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5) + 96*B*a*b^20*d^4 + 736*B*a^3*b^18*d^4 + 2432*B*a^5*b^16*d^4 + 4480*B*a^7*b^14*d^4 + 4928*B*a^9*b^12*d^4 + 3136*B*a^11*b^10*d^4 + 896*B*a^13*b^8*d^4 - 128*B*a^15*b^6*d^4 - 160*B*a^17*b^4*d^4 - 32*B*a^19*b^2*d^4))*(-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - 8*B^3*b^16*d^2 - 40*B^3*a^2*b^14*d^2 - 72*B^3*a^4*b^12*d^2 - 40*B^3*a^6*b^10*d^2 + 40*B^3*a^8*b^8*d^2 + 72*B^3*a^10*b^6*d^2 + 40*B^3*a^12*b^4*d^2 + 8*B^3*a^14*b^2*d^2)*(-((320*B^4*a^2*b^8*d^4 - 16*B^4*b^10*d^4 - 1760*B^4*a^4*b^6*d^4 + 1600*B^4*a^6*b^4*d^4 - 400*B^4*a^8*b^2*d^4)^(1/2) - 4*B^2*a^5*d^2 + 40*B^2*a^3*b^2*d^2 - 20*B^2*a*b^4*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - ((2*B*a)/(3*(a^2 + b^2)) + (2*B*(a^2 - b^2)*(a + b*cot(c + d*x)))/(a^2 + b^2)^2)/(d*(a + b*cot(c + d*x))^(3/2)) + ((2*A*b)/(3*(a^2 + b^2)) + (4*A*a*b*(a + b*cot(c + d*x)))/(a^2 + b^2)^2)/(d*(a + b*cot(c + d*x))^(3/2))","B"
104,1,2731,102,2.201615,"\text{Not used}","int(-(a - b*cot(c + d*x))/(a + b*cot(c + d*x))^(1/2),x)","2\,\mathrm{atanh}\left(\frac{32\,a^4\,b^2\,d^2\,\sqrt{-\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{16\,a^6\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,a^2\,b^2\,\sqrt{-\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,a^4\,b^3\,d^3}{a^2\,d^4+b^2\,d^4}+\frac{4\,a\,b^3\,d^2\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{8\,a\,b^2\,\sqrt{-\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,a^4\,b^2\,d^4}}{\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{16\,a^6\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{-\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}-2\,\mathrm{atanh}\left(\frac{32\,a^2\,b^2\,\sqrt{\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,a^4\,b^3\,d^3}{a^2\,d^4+b^2\,d^4}-\frac{4\,a\,b^3\,d^2\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,a^4\,b^2\,d^2\,\sqrt{\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{16\,a^6\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}-\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{8\,a\,b^2\,\sqrt{\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,a^4\,b^2\,d^4}}{\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{16\,a^6\,b^3\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}-\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,a^4\,b^2\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{\frac{\sqrt{-16\,a^4\,b^2\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{a^3\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}+2\,\mathrm{atanh}\left(\frac{32\,b^4\,\sqrt{\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,b^5}{d}-\frac{16\,a^2\,b^5\,d^3}{a^2\,d^4+b^2\,d^4}+\frac{4\,a\,b^3\,d^2\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{8\,a\,b^2\,\sqrt{\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,b^6\,d^4}}{16\,b^7\,d+16\,a^2\,b^5\,d-\frac{16\,a^2\,b^7\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,a^2\,b^4\,d^2\,\sqrt{\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{16\,b^7\,d+16\,a^2\,b^5\,d-\frac{16\,a^2\,b^7\,d^5}{a^2\,d^4+b^2\,d^4}-\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}-\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}}+2\,\mathrm{atanh}\left(\frac{8\,a\,b^2\,\sqrt{\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-16\,b^6\,d^4}}{\frac{16\,a^2\,b^7\,d^5}{a^2\,d^4+b^2\,d^4}-16\,a^2\,b^5\,d-16\,b^7\,d+\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}}-\frac{32\,b^4\,\sqrt{\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,a^2\,b^5\,d^3}{a^2\,d^4+b^2\,d^4}-\frac{16\,b^5}{d}+\frac{4\,a\,b^3\,d^2\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}}+\frac{32\,a^2\,b^4\,d^2\,\sqrt{\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}{\frac{16\,a^2\,b^7\,d^5}{a^2\,d^4+b^2\,d^4}-16\,a^2\,b^5\,d-16\,b^7\,d+\frac{16\,a^4\,b^5\,d^5}{a^2\,d^4+b^2\,d^4}+\frac{4\,a\,b^5\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}+\frac{4\,a^3\,b^3\,d^4\,\sqrt{-16\,b^6\,d^4}}{a^2\,d^5+b^2\,d^5}}\right)\,\sqrt{\frac{\sqrt{-16\,b^6\,d^4}}{16\,\left(a^2\,d^4+b^2\,d^4\right)}+\frac{a\,b^2\,d^2}{4\,\left(a^2\,d^4+b^2\,d^4\right)}}","Not used",1,"2*atanh((32*a^4*b^2*d^2*(- (-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (16*a^6*b^3*d^5)/(a^2*d^4 + b^2*d^4) + (4*a^3*b^3*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*a*b^5*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*a^2*b^2*(- (-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*a^4*b^3*d^3)/(a^2*d^4 + b^2*d^4) + (4*a*b^3*d^2*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (8*a*b^2*(- (-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*a^4*b^2*d^4)^(1/2))/((16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (16*a^6*b^3*d^5)/(a^2*d^4 + b^2*d^4) + (4*a^3*b^3*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*a*b^5*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*(- (-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2) - 2*atanh((32*a^2*b^2*((-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*a^4*b^3*d^3)/(a^2*d^4 + b^2*d^4) - (4*a*b^3*d^2*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*a^4*b^2*d^2*((-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (16*a^6*b^3*d^5)/(a^2*d^4 + b^2*d^4) - (4*a^3*b^3*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) - (4*a*b^5*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (8*a*b^2*((-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*a^4*b^2*d^4)^(1/2))/((16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (16*a^6*b^3*d^5)/(a^2*d^4 + b^2*d^4) - (4*a^3*b^3*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) - (4*a*b^5*d^4*(-16*a^4*b^2*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*((-16*a^4*b^2*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) - (a^3*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2) + 2*atanh((32*b^4*((a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*b^5)/d - (16*a^2*b^5*d^3)/(a^2*d^4 + b^2*d^4) + (4*a*b^3*d^2*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (8*a*b^2*((a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*b^6*d^4)^(1/2))/(16*b^7*d + 16*a^2*b^5*d - (16*a^2*b^7*d^5)/(a^2*d^4 + b^2*d^4) - (16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (4*a*b^5*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*a^3*b^3*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*a^2*b^4*d^2*((a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/(16*b^7*d + 16*a^2*b^5*d - (16*a^2*b^7*d^5)/(a^2*d^4 + b^2*d^4) - (16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (4*a*b^5*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*a^3*b^3*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*((a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)) - (-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)))^(1/2) + 2*atanh((8*a*b^2*((-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(-16*b^6*d^4)^(1/2))/((16*a^2*b^7*d^5)/(a^2*d^4 + b^2*d^4) - 16*a^2*b^5*d - 16*b^7*d + (16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (4*a*b^5*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*a^3*b^3*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) - (32*b^4*((-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*a^2*b^5*d^3)/(a^2*d^4 + b^2*d^4) - (16*b^5)/d + (4*a*b^3*d^2*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)) + (32*a^2*b^4*d^2*((-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)*(a + b*cot(c + d*x))^(1/2))/((16*a^2*b^7*d^5)/(a^2*d^4 + b^2*d^4) - 16*a^2*b^5*d - 16*b^7*d + (16*a^4*b^5*d^5)/(a^2*d^4 + b^2*d^4) + (4*a*b^5*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5) + (4*a^3*b^3*d^4*(-16*b^6*d^4)^(1/2))/(a^2*d^5 + b^2*d^5)))*((-16*b^6*d^4)^(1/2)/(16*(a^2*d^4 + b^2*d^4)) + (a*b^2*d^2)/(4*(a^2*d^4 + b^2*d^4)))^(1/2)","B"
105,1,5475,132,5.960536,"\text{Not used}","int(-(a - b*cot(c + d*x))/(a + b*cot(c + d*x))^(3/2),x)","\ln\left(8\,a\,b^{11}\,d^2-\left(\sqrt{\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}\,\left(64\,a^6\,b^7\,d^4-96\,a^2\,b^{11}\,d^4-64\,a^4\,b^9\,d^4-32\,b^{13}\,d^4+96\,a^8\,b^5\,d^4+32\,a^{10}\,b^3\,d^4+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^8\,b^4\,d^3-32\,a^6\,b^6\,d^3+32\,a^2\,b^{10}\,d^3+16\,b^{12}\,d^3\right)\right)\,\sqrt{\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}+24\,a^3\,b^9\,d^2+24\,a^5\,b^7\,d^2+8\,a^7\,b^5\,d^2\right)\,\sqrt{\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}+\ln\left(8\,a\,b^{11}\,d^2-\left(\sqrt{-\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}\,\left(64\,a^6\,b^7\,d^4-96\,a^2\,b^{11}\,d^4-64\,a^4\,b^9\,d^4-32\,b^{13}\,d^4+96\,a^8\,b^5\,d^4+32\,a^{10}\,b^3\,d^4+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^8\,b^4\,d^3-32\,a^6\,b^6\,d^3+32\,a^2\,b^{10}\,d^3+16\,b^{12}\,d^3\right)\right)\,\sqrt{-\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}+24\,a^3\,b^9\,d^2+24\,a^5\,b^7\,d^2+8\,a^7\,b^5\,d^2\right)\,\sqrt{-\frac{\sqrt{\frac{{\left(24\,a\,b^4\,d^2-8\,a^3\,b^2\,d^2\right)}^2}{4}-b^4\,\left(16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4\right)}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,\left(a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4\right)}}+\frac{\ln\left(\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{10}\,b^2\,d^3-32\,a^8\,b^4\,d^3+32\,a^4\,b^8\,d^3+16\,a^2\,b^{10}\,d^3\right)-\frac{\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)}{4}+64\,a^2\,b^{11}\,d^4+256\,a^4\,b^9\,d^4+384\,a^6\,b^7\,d^4+256\,a^8\,b^5\,d^4+64\,a^{10}\,b^3\,d^4\right)}{4}\right)\,\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}+8\,a^3\,b^9\,d^2+24\,a^5\,b^7\,d^2+24\,a^7\,b^5\,d^2+8\,a^9\,b^3\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}+\frac{\ln\left(\frac{\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{10}\,b^2\,d^3-32\,a^8\,b^4\,d^3+32\,a^4\,b^8\,d^3+16\,a^2\,b^{10}\,d^3\right)-\frac{\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)}{4}+64\,a^2\,b^{11}\,d^4+256\,a^4\,b^9\,d^4+384\,a^6\,b^7\,d^4+256\,a^8\,b^5\,d^4+64\,a^{10}\,b^3\,d^4\right)}{4}\right)\,\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}+8\,a^3\,b^9\,d^2+24\,a^5\,b^7\,d^2+24\,a^7\,b^5\,d^2+8\,a^9\,b^3\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{a^6\,d^4+3\,a^4\,b^2\,d^4+3\,a^2\,b^4\,d^4+b^6\,d^4}}}{4}-\ln\left(8\,a^3\,b^9\,d^2-\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{10}\,b^2\,d^3-32\,a^8\,b^4\,d^3+32\,a^4\,b^8\,d^3+16\,a^2\,b^{10}\,d^3\right)+\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(64\,a^2\,b^{11}\,d^4-\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+256\,a^4\,b^9\,d^4+384\,a^6\,b^7\,d^4+256\,a^8\,b^5\,d^4+64\,a^{10}\,b^3\,d^4\right)\right)\,\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}+24\,a^5\,b^7\,d^2+24\,a^7\,b^5\,d^2+8\,a^9\,b^3\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}-4\,a^5\,d^2+12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-\ln\left(8\,a^3\,b^9\,d^2-\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{10}\,b^2\,d^3-32\,a^8\,b^4\,d^3+32\,a^4\,b^8\,d^3+16\,a^2\,b^{10}\,d^3\right)+\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(64\,a^2\,b^{11}\,d^4-\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+256\,a^4\,b^9\,d^4+384\,a^6\,b^7\,d^4+256\,a^8\,b^5\,d^4+64\,a^{10}\,b^3\,d^4\right)\right)\,\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}+24\,a^5\,b^7\,d^2+24\,a^7\,b^5\,d^2+8\,a^9\,b^3\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,a^8\,b^2\,d^4+96\,a^6\,b^4\,d^4-16\,a^4\,b^6\,d^4}+4\,a^5\,d^2-12\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-\ln\left(\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^8\,b^4\,d^3-32\,a^6\,b^6\,d^3+32\,a^2\,b^{10}\,d^3+16\,b^{12}\,d^3\right)+\sqrt{\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(32\,b^{13}\,d^4+\sqrt{\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+96\,a^2\,b^{11}\,d^4+64\,a^4\,b^9\,d^4-64\,a^6\,b^7\,d^4-96\,a^8\,b^5\,d^4-32\,a^{10}\,b^3\,d^4\right)\right)\,\sqrt{\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}+8\,a\,b^{11}\,d^2+24\,a^3\,b^9\,d^2+24\,a^5\,b^7\,d^2+8\,a^7\,b^5\,d^2\right)\,\sqrt{\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}-12\,a\,b^4\,d^2+4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-\ln\left(\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^8\,b^4\,d^3-32\,a^6\,b^6\,d^3+32\,a^2\,b^{10}\,d^3+16\,b^{12}\,d^3\right)+\sqrt{-\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\left(32\,b^{13}\,d^4+\sqrt{-\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{11}\,b^2\,d^5+320\,a^9\,b^4\,d^5+640\,a^7\,b^6\,d^5+640\,a^5\,b^8\,d^5+320\,a^3\,b^{10}\,d^5+64\,a\,b^{12}\,d^5\right)+96\,a^2\,b^{11}\,d^4+64\,a^4\,b^9\,d^4-64\,a^6\,b^7\,d^4-96\,a^8\,b^5\,d^4-32\,a^{10}\,b^3\,d^4\right)\right)\,\sqrt{-\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}+8\,a\,b^{11}\,d^2+24\,a^3\,b^9\,d^2+24\,a^5\,b^7\,d^2+8\,a^7\,b^5\,d^2\right)\,\sqrt{-\frac{\sqrt{-144\,a^4\,b^6\,d^4+96\,a^2\,b^8\,d^4-16\,b^{10}\,d^4}+12\,a\,b^4\,d^2-4\,a^3\,b^2\,d^2}{16\,a^6\,d^4+48\,a^4\,b^2\,d^4+48\,a^2\,b^4\,d^4+16\,b^6\,d^4}}-\frac{4\,a\,b}{d\,\left(a^2+b^2\right)\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}}","Not used",1,"log(8*a*b^11*d^2 - (((((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(64*a^6*b^7*d^4 - 96*a^2*b^11*d^4 - 64*a^4*b^9*d^4 - 32*b^13*d^4 + 96*a^8*b^5*d^4 + 32*a^10*b^3*d^4 + (a + b*cot(c + d*x))^(1/2)*((((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5)) + (a + b*cot(c + d*x))^(1/2)*(16*b^12*d^3 + 32*a^2*b^10*d^3 - 32*a^6*b^6*d^3 - 16*a^8*b^4*d^3))*((((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 24*a^3*b^9*d^2 + 24*a^5*b^7*d^2 + 8*a^7*b^5*d^2)*((((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + log(8*a*b^11*d^2 - ((-(((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(64*a^6*b^7*d^4 - 96*a^2*b^11*d^4 - 64*a^4*b^9*d^4 - 32*b^13*d^4 + 96*a^8*b^5*d^4 + 32*a^10*b^3*d^4 + (a + b*cot(c + d*x))^(1/2)*(-(((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5)) + (a + b*cot(c + d*x))^(1/2)*(16*b^12*d^3 + 32*a^2*b^10*d^3 - 32*a^6*b^6*d^3 - 16*a^8*b^4*d^3))*(-(((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + 24*a^3*b^9*d^2 + 24*a^5*b^7*d^2 + 8*a^7*b^5*d^2)*(-(((24*a*b^4*d^2 - 8*a^3*b^2*d^2)^2/4 - b^4*(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4)))^(1/2) + (log((((a + b*cot(c + d*x))^(1/2)*(16*a^2*b^10*d^3 + 32*a^4*b^8*d^3 - 32*a^8*b^4*d^3 - 16*a^10*b^2*d^3) - ((((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(((((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5))/4 + 64*a^2*b^11*d^4 + 256*a^4*b^9*d^4 + 384*a^6*b^7*d^4 + 256*a^8*b^5*d^4 + 64*a^10*b^3*d^4))/4)*(((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 + 8*a^3*b^9*d^2 + 24*a^5*b^7*d^2 + 24*a^7*b^5*d^2 + 8*a^9*b^3*d^2)*(((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 + (log((((a + b*cot(c + d*x))^(1/2)*(16*a^2*b^10*d^3 + 32*a^4*b^8*d^3 - 32*a^8*b^4*d^3 - 16*a^10*b^2*d^3) - ((-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(((-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5))/4 + 64*a^2*b^11*d^4 + 256*a^4*b^9*d^4 + 384*a^6*b^7*d^4 + 256*a^8*b^5*d^4 + 64*a^10*b^3*d^4))/4)*(-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 + 8*a^3*b^9*d^2 + 24*a^5*b^7*d^2 + 24*a^7*b^5*d^2 + 8*a^9*b^3*d^2)*(-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(a^6*d^4 + b^6*d^4 + 3*a^2*b^4*d^4 + 3*a^4*b^2*d^4))^(1/2))/4 - log(8*a^3*b^9*d^2 - ((a + b*cot(c + d*x))^(1/2)*(16*a^2*b^10*d^3 + 32*a^4*b^8*d^3 - 32*a^8*b^4*d^3 - 16*a^10*b^2*d^3) + (((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(64*a^2*b^11*d^4 - (((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 256*a^4*b^9*d^4 + 384*a^6*b^7*d^4 + 256*a^8*b^5*d^4 + 64*a^10*b^3*d^4))*(((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 24*a^5*b^7*d^2 + 24*a^7*b^5*d^2 + 8*a^9*b^3*d^2)*(((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) - 4*a^5*d^2 + 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - log(8*a^3*b^9*d^2 - ((a + b*cot(c + d*x))^(1/2)*(16*a^2*b^10*d^3 + 32*a^4*b^8*d^3 - 32*a^8*b^4*d^3 - 16*a^10*b^2*d^3) + (-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(64*a^2*b^11*d^4 - (-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 256*a^4*b^9*d^4 + 384*a^6*b^7*d^4 + 256*a^8*b^5*d^4 + 64*a^10*b^3*d^4))*(-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 24*a^5*b^7*d^2 + 24*a^7*b^5*d^2 + 8*a^9*b^3*d^2)*(-((96*a^6*b^4*d^4 - 16*a^4*b^6*d^4 - 144*a^8*b^2*d^4)^(1/2) + 4*a^5*d^2 - 12*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - log(((a + b*cot(c + d*x))^(1/2)*(16*b^12*d^3 + 32*a^2*b^10*d^3 - 32*a^6*b^6*d^3 - 16*a^8*b^4*d^3) + (((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(32*b^13*d^4 + (((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 96*a^2*b^11*d^4 + 64*a^4*b^9*d^4 - 64*a^6*b^7*d^4 - 96*a^8*b^5*d^4 - 32*a^10*b^3*d^4))*(((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 8*a*b^11*d^2 + 24*a^3*b^9*d^2 + 24*a^5*b^7*d^2 + 8*a^7*b^5*d^2)*(((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) - 12*a*b^4*d^2 + 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - log(((a + b*cot(c + d*x))^(1/2)*(16*b^12*d^3 + 32*a^2*b^10*d^3 - 32*a^6*b^6*d^3 - 16*a^8*b^4*d^3) + (-((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(32*b^13*d^4 + (-((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^12*d^5 + 320*a^3*b^10*d^5 + 640*a^5*b^8*d^5 + 640*a^7*b^6*d^5 + 320*a^9*b^4*d^5 + 64*a^11*b^2*d^5) + 96*a^2*b^11*d^4 + 64*a^4*b^9*d^4 - 64*a^6*b^7*d^4 - 96*a^8*b^5*d^4 - 32*a^10*b^3*d^4))*(-((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) + 8*a*b^11*d^2 + 24*a^3*b^9*d^2 + 24*a^5*b^7*d^2 + 8*a^7*b^5*d^2)*(-((96*a^2*b^8*d^4 - 16*b^10*d^4 - 144*a^4*b^6*d^4)^(1/2) + 12*a*b^4*d^2 - 4*a^3*b^2*d^2)/(16*a^6*d^4 + 16*b^6*d^4 + 48*a^2*b^4*d^4 + 48*a^4*b^2*d^4))^(1/2) - (4*a*b)/(d*(a^2 + b^2)*(a + b*cot(c + d*x))^(1/2))","B"
106,1,8438,174,16.173046,"\text{Not used}","int(-(a - b*cot(c + d*x))/(a + b*cot(c + d*x))^(5/2),x)","\frac{\ln\left(\frac{\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{18}\,b^2\,d^3+320\,a^{14}\,b^6\,d^3+1024\,a^{12}\,b^8\,d^3+1440\,a^{10}\,b^{10}\,d^3+1024\,a^8\,b^{12}\,d^3+320\,a^6\,b^{14}\,d^3-16\,a^2\,b^{18}\,d^3\right)-\frac{\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(\frac{\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}-32\,a\,b^{21}\,d^4-160\,a^3\,b^{19}\,d^4-128\,a^5\,b^{17}\,d^4+896\,a^7\,b^{15}\,d^4+3136\,a^9\,b^{13}\,d^4+4928\,a^{11}\,b^{11}\,d^4+4480\,a^{13}\,b^9\,d^4+2432\,a^{15}\,b^7\,d^4+736\,a^{17}\,b^5\,d^4+96\,a^{19}\,b^3\,d^4\right)}{4}\right)}{4}+16\,a^4\,b^{15}\,d^2+96\,a^6\,b^{13}\,d^2+240\,a^8\,b^{11}\,d^2+320\,a^{10}\,b^9\,d^2+240\,a^{12}\,b^7\,d^2+96\,a^{14}\,b^5\,d^2+16\,a^{16}\,b^3\,d^2\right)\,\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-\ln\left(16\,a^4\,b^{15}\,d^2-\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{18}\,b^2\,d^3+320\,a^{14}\,b^6\,d^3+1024\,a^{12}\,b^8\,d^3+1440\,a^{10}\,b^{10}\,d^3+1024\,a^8\,b^{12}\,d^3+320\,a^6\,b^{14}\,d^3-16\,a^2\,b^{18}\,d^3\right)+\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(896\,a^7\,b^{15}\,d^4-\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)-160\,a^3\,b^{19}\,d^4-128\,a^5\,b^{17}\,d^4-32\,a\,b^{21}\,d^4+3136\,a^9\,b^{13}\,d^4+4928\,a^{11}\,b^{11}\,d^4+4480\,a^{13}\,b^9\,d^4+2432\,a^{15}\,b^7\,d^4+736\,a^{17}\,b^5\,d^4+96\,a^{19}\,b^3\,d^4\right)\right)+96\,a^6\,b^{13}\,d^2+240\,a^8\,b^{11}\,d^2+320\,a^{10}\,b^9\,d^2+240\,a^{12}\,b^7\,d^2+96\,a^{14}\,b^5\,d^2+16\,a^{16}\,b^3\,d^2\right)\,\sqrt{-\frac{4\,a^7\,d^2-\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}+\frac{\ln\left(\frac{\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(\frac{\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(96\,a\,b^{21}\,d^4+736\,a^3\,b^{19}\,d^4+2432\,a^5\,b^{17}\,d^4+4480\,a^7\,b^{15}\,d^4+4928\,a^9\,b^{13}\,d^4+3136\,a^{11}\,b^{11}\,d^4+896\,a^{13}\,b^9\,d^4-128\,a^{15}\,b^7\,d^4-160\,a^{17}\,b^5\,d^4-32\,a^{19}\,b^3\,d^4-\frac{\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}\right)}{4}-\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{16}\,b^4\,d^3+320\,a^{12}\,b^8\,d^3+1024\,a^{10}\,b^{10}\,d^3+1440\,a^8\,b^{12}\,d^3+1024\,a^6\,b^{14}\,d^3+320\,a^4\,b^{16}\,d^3-16\,b^{20}\,d^3\right)\right)}{4}-8\,b^{19}\,d^2-40\,a^2\,b^{17}\,d^2-72\,a^4\,b^{15}\,d^2-40\,a^6\,b^{13}\,d^2+40\,a^8\,b^{11}\,d^2+72\,a^{10}\,b^9\,d^2+40\,a^{12}\,b^7\,d^2+8\,a^{14}\,b^5\,d^2\right)\,\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}+\frac{\ln\left(\frac{\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(\frac{\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(96\,a\,b^{21}\,d^4+736\,a^3\,b^{19}\,d^4+2432\,a^5\,b^{17}\,d^4+4480\,a^7\,b^{15}\,d^4+4928\,a^9\,b^{13}\,d^4+3136\,a^{11}\,b^{11}\,d^4+896\,a^{13}\,b^9\,d^4-128\,a^{15}\,b^7\,d^4-160\,a^{17}\,b^5\,d^4-32\,a^{19}\,b^3\,d^4-\frac{\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}\right)}{4}-\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{16}\,b^4\,d^3+320\,a^{12}\,b^8\,d^3+1024\,a^{10}\,b^{10}\,d^3+1440\,a^8\,b^{12}\,d^3+1024\,a^6\,b^{14}\,d^3+320\,a^4\,b^{16}\,d^3-16\,b^{20}\,d^3\right)\right)}{4}-8\,b^{19}\,d^2-40\,a^2\,b^{17}\,d^2-72\,a^4\,b^{15}\,d^2-40\,a^6\,b^{13}\,d^2+40\,a^8\,b^{11}\,d^2+72\,a^{10}\,b^9\,d^2+40\,a^{12}\,b^7\,d^2+8\,a^{14}\,b^5\,d^2\right)\,\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-\ln\left(\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(96\,a\,b^{21}\,d^4+736\,a^3\,b^{19}\,d^4+2432\,a^5\,b^{17}\,d^4+4480\,a^7\,b^{15}\,d^4+4928\,a^9\,b^{13}\,d^4+3136\,a^{11}\,b^{11}\,d^4+896\,a^{13}\,b^9\,d^4-128\,a^{15}\,b^7\,d^4-160\,a^{17}\,b^5\,d^4-32\,a^{19}\,b^3\,d^4+\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{16}\,b^4\,d^3+320\,a^{12}\,b^8\,d^3+1024\,a^{10}\,b^{10}\,d^3+1440\,a^8\,b^{12}\,d^3+1024\,a^6\,b^{14}\,d^3+320\,a^4\,b^{16}\,d^3-16\,b^{20}\,d^3\right)\right)-8\,b^{19}\,d^2-40\,a^2\,b^{17}\,d^2-72\,a^4\,b^{15}\,d^2-40\,a^6\,b^{13}\,d^2+40\,a^8\,b^{11}\,d^2+72\,a^{10}\,b^9\,d^2+40\,a^{12}\,b^7\,d^2+8\,a^{14}\,b^5\,d^2\right)\,\sqrt{\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}+20\,a\,b^6\,d^2-40\,a^3\,b^4\,d^2+4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-\ln\left(\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(96\,a\,b^{21}\,d^4+736\,a^3\,b^{19}\,d^4+2432\,a^5\,b^{17}\,d^4+4480\,a^7\,b^{15}\,d^4+4928\,a^9\,b^{13}\,d^4+3136\,a^{11}\,b^{11}\,d^4+896\,a^{13}\,b^9\,d^4-128\,a^{15}\,b^7\,d^4-160\,a^{17}\,b^5\,d^4-32\,a^{19}\,b^3\,d^4+\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{16}\,b^4\,d^3+320\,a^{12}\,b^8\,d^3+1024\,a^{10}\,b^{10}\,d^3+1440\,a^8\,b^{12}\,d^3+1024\,a^6\,b^{14}\,d^3+320\,a^4\,b^{16}\,d^3-16\,b^{20}\,d^3\right)\right)-8\,b^{19}\,d^2-40\,a^2\,b^{17}\,d^2-72\,a^4\,b^{15}\,d^2-40\,a^6\,b^{13}\,d^2+40\,a^8\,b^{11}\,d^2+72\,a^{10}\,b^9\,d^2+40\,a^{12}\,b^7\,d^2+8\,a^{14}\,b^5\,d^2\right)\,\sqrt{-\frac{\sqrt{-400\,a^8\,b^6\,d^4+1600\,a^6\,b^8\,d^4-1760\,a^4\,b^{10}\,d^4+320\,a^2\,b^{12}\,d^4-16\,b^{14}\,d^4}-20\,a\,b^6\,d^2+40\,a^3\,b^4\,d^2-4\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}+\frac{\ln\left(16\,a^4\,b^{15}\,d^2-\frac{\left(\frac{\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(\frac{\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)}{4}-32\,a\,b^{21}\,d^4-160\,a^3\,b^{19}\,d^4-128\,a^5\,b^{17}\,d^4+896\,a^7\,b^{15}\,d^4+3136\,a^9\,b^{13}\,d^4+4928\,a^{11}\,b^{11}\,d^4+4480\,a^{13}\,b^9\,d^4+2432\,a^{15}\,b^7\,d^4+736\,a^{17}\,b^5\,d^4+96\,a^{19}\,b^3\,d^4\right)}{4}-\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{18}\,b^2\,d^3+320\,a^{14}\,b^6\,d^3+1024\,a^{12}\,b^8\,d^3+1440\,a^{10}\,b^{10}\,d^3+1024\,a^8\,b^{12}\,d^3+320\,a^6\,b^{14}\,d^3-16\,a^2\,b^{18}\,d^3\right)\right)\,\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}+96\,a^6\,b^{13}\,d^2+240\,a^8\,b^{11}\,d^2+320\,a^{10}\,b^9\,d^2+240\,a^{12}\,b^7\,d^2+96\,a^{14}\,b^5\,d^2+16\,a^{16}\,b^3\,d^2\right)\,\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{a^{10}\,d^4+5\,a^8\,b^2\,d^4+10\,a^6\,b^4\,d^4+10\,a^4\,b^6\,d^4+5\,a^2\,b^8\,d^4+b^{10}\,d^4}}}{4}-\ln\left(16\,a^4\,b^{15}\,d^2-\left(\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(896\,a^7\,b^{15}\,d^4-32\,a\,b^{21}\,d^4-160\,a^3\,b^{19}\,d^4-128\,a^5\,b^{17}\,d^4-\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}\,\left(64\,a^{21}\,b^2\,d^5+640\,a^{19}\,b^4\,d^5+2880\,a^{17}\,b^6\,d^5+7680\,a^{15}\,b^8\,d^5+13440\,a^{13}\,b^{10}\,d^5+16128\,a^{11}\,b^{12}\,d^5+13440\,a^9\,b^{14}\,d^5+7680\,a^7\,b^{16}\,d^5+2880\,a^5\,b^{18}\,d^5+640\,a^3\,b^{20}\,d^5+64\,a\,b^{22}\,d^5\right)+3136\,a^9\,b^{13}\,d^4+4928\,a^{11}\,b^{11}\,d^4+4480\,a^{13}\,b^9\,d^4+2432\,a^{15}\,b^7\,d^4+736\,a^{17}\,b^5\,d^4+96\,a^{19}\,b^3\,d^4\right)+\sqrt{a+b\,\mathrm{cot}\left(c+d\,x\right)}\,\left(-16\,a^{18}\,b^2\,d^3+320\,a^{14}\,b^6\,d^3+1024\,a^{12}\,b^8\,d^3+1440\,a^{10}\,b^{10}\,d^3+1024\,a^8\,b^{12}\,d^3+320\,a^6\,b^{14}\,d^3-16\,a^2\,b^{18}\,d^3\right)\right)\,\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}+96\,a^6\,b^{13}\,d^2+240\,a^8\,b^{11}\,d^2+320\,a^{10}\,b^9\,d^2+240\,a^{12}\,b^7\,d^2+96\,a^{14}\,b^5\,d^2+16\,a^{16}\,b^3\,d^2\right)\,\sqrt{-\frac{4\,a^7\,d^2+\sqrt{-400\,a^{12}\,b^2\,d^4+1600\,a^{10}\,b^4\,d^4-1760\,a^8\,b^6\,d^4+320\,a^6\,b^8\,d^4-16\,a^4\,b^{10}\,d^4}+20\,a^3\,b^4\,d^2-40\,a^5\,b^2\,d^2}{16\,a^{10}\,d^4+80\,a^8\,b^2\,d^4+160\,a^6\,b^4\,d^4+160\,a^4\,b^6\,d^4+80\,a^2\,b^8\,d^4+16\,b^{10}\,d^4}}-\frac{\frac{2\,a\,b}{3\,\left(a^2+b^2\right)}+\frac{2\,b\,\left(a^2-b^2\right)\,\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{{\left(a^2+b^2\right)}^2}}{d\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}-\frac{\frac{2\,a\,b}{3\,\left(a^2+b^2\right)}+\frac{4\,a^2\,b\,\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}{{\left(a^2+b^2\right)}^2}}{d\,{\left(a+b\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}","Not used",1,"(log(((-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*((a + b*cot(c + d*x))^(1/2)*(320*a^6*b^14*d^3 - 16*a^2*b^18*d^3 + 1024*a^8*b^12*d^3 + 1440*a^10*b^10*d^3 + 1024*a^12*b^8*d^3 + 320*a^14*b^6*d^3 - 16*a^18*b^2*d^3) - ((-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(((-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4 - 32*a*b^21*d^4 - 160*a^3*b^19*d^4 - 128*a^5*b^17*d^4 + 896*a^7*b^15*d^4 + 3136*a^9*b^13*d^4 + 4928*a^11*b^11*d^4 + 4480*a^13*b^9*d^4 + 2432*a^15*b^7*d^4 + 736*a^17*b^5*d^4 + 96*a^19*b^3*d^4))/4))/4 + 16*a^4*b^15*d^2 + 96*a^6*b^13*d^2 + 240*a^8*b^11*d^2 + 320*a^10*b^9*d^2 + 240*a^12*b^7*d^2 + 96*a^14*b^5*d^2 + 16*a^16*b^3*d^2)*(-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - log(16*a^4*b^15*d^2 - (-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((a + b*cot(c + d*x))^(1/2)*(320*a^6*b^14*d^3 - 16*a^2*b^18*d^3 + 1024*a^8*b^12*d^3 + 1440*a^10*b^10*d^3 + 1024*a^12*b^8*d^3 + 320*a^14*b^6*d^3 - 16*a^18*b^2*d^3) + (-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(896*a^7*b^15*d^4 - (-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5) - 160*a^3*b^19*d^4 - 128*a^5*b^17*d^4 - 32*a*b^21*d^4 + 3136*a^9*b^13*d^4 + 4928*a^11*b^11*d^4 + 4480*a^13*b^9*d^4 + 2432*a^15*b^7*d^4 + 736*a^17*b^5*d^4 + 96*a^19*b^3*d^4)) + 96*a^6*b^13*d^2 + 240*a^8*b^11*d^2 + 320*a^10*b^9*d^2 + 240*a^12*b^7*d^2 + 96*a^14*b^5*d^2 + 16*a^16*b^3*d^2)*(-(4*a^7*d^2 - (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + (log(((((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(((((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(96*a*b^21*d^4 + 736*a^3*b^19*d^4 + 2432*a^5*b^17*d^4 + 4480*a^7*b^15*d^4 + 4928*a^9*b^13*d^4 + 3136*a^11*b^11*d^4 + 896*a^13*b^9*d^4 - 128*a^15*b^7*d^4 - 160*a^17*b^5*d^4 - 32*a^19*b^3*d^4 - ((((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4))/4 - (a + b*cot(c + d*x))^(1/2)*(320*a^4*b^16*d^3 - 16*b^20*d^3 + 1024*a^6*b^14*d^3 + 1440*a^8*b^12*d^3 + 1024*a^10*b^10*d^3 + 320*a^12*b^8*d^3 - 16*a^16*b^4*d^3)))/4 - 8*b^19*d^2 - 40*a^2*b^17*d^2 - 72*a^4*b^15*d^2 - 40*a^6*b^13*d^2 + 40*a^8*b^11*d^2 + 72*a^10*b^9*d^2 + 40*a^12*b^7*d^2 + 8*a^14*b^5*d^2)*(((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 + (log(((-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(((-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(96*a*b^21*d^4 + 736*a^3*b^19*d^4 + 2432*a^5*b^17*d^4 + 4480*a^7*b^15*d^4 + 4928*a^9*b^13*d^4 + 3136*a^11*b^11*d^4 + 896*a^13*b^9*d^4 - 128*a^15*b^7*d^4 - 160*a^17*b^5*d^4 - 32*a^19*b^3*d^4 - ((-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4))/4 - (a + b*cot(c + d*x))^(1/2)*(320*a^4*b^16*d^3 - 16*b^20*d^3 + 1024*a^6*b^14*d^3 + 1440*a^8*b^12*d^3 + 1024*a^10*b^10*d^3 + 320*a^12*b^8*d^3 - 16*a^16*b^4*d^3)))/4 - 8*b^19*d^2 - 40*a^2*b^17*d^2 - 72*a^4*b^15*d^2 - 40*a^6*b^13*d^2 + 40*a^8*b^11*d^2 + 72*a^10*b^9*d^2 + 40*a^12*b^7*d^2 + 8*a^14*b^5*d^2)*(-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - log((((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(96*a*b^21*d^4 + 736*a^3*b^19*d^4 + 2432*a^5*b^17*d^4 + 4480*a^7*b^15*d^4 + 4928*a^9*b^13*d^4 + 3136*a^11*b^11*d^4 + 896*a^13*b^9*d^4 - 128*a^15*b^7*d^4 - 160*a^17*b^5*d^4 - 32*a^19*b^3*d^4 + (((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5)) + (a + b*cot(c + d*x))^(1/2)*(320*a^4*b^16*d^3 - 16*b^20*d^3 + 1024*a^6*b^14*d^3 + 1440*a^8*b^12*d^3 + 1024*a^10*b^10*d^3 + 320*a^12*b^8*d^3 - 16*a^16*b^4*d^3)) - 8*b^19*d^2 - 40*a^2*b^17*d^2 - 72*a^4*b^15*d^2 - 40*a^6*b^13*d^2 + 40*a^8*b^11*d^2 + 72*a^10*b^9*d^2 + 40*a^12*b^7*d^2 + 8*a^14*b^5*d^2)*(((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) + 20*a*b^6*d^2 - 40*a^3*b^4*d^2 + 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - log((-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*((-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(96*a*b^21*d^4 + 736*a^3*b^19*d^4 + 2432*a^5*b^17*d^4 + 4480*a^7*b^15*d^4 + 4928*a^9*b^13*d^4 + 3136*a^11*b^11*d^4 + 896*a^13*b^9*d^4 - 128*a^15*b^7*d^4 - 160*a^17*b^5*d^4 - 32*a^19*b^3*d^4 + (-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(a + b*cot(c + d*x))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5)) + (a + b*cot(c + d*x))^(1/2)*(320*a^4*b^16*d^3 - 16*b^20*d^3 + 1024*a^6*b^14*d^3 + 1440*a^8*b^12*d^3 + 1024*a^10*b^10*d^3 + 320*a^12*b^8*d^3 - 16*a^16*b^4*d^3)) - 8*b^19*d^2 - 40*a^2*b^17*d^2 - 72*a^4*b^15*d^2 - 40*a^6*b^13*d^2 + 40*a^8*b^11*d^2 + 72*a^10*b^9*d^2 + 40*a^12*b^7*d^2 + 8*a^14*b^5*d^2)*(-((320*a^2*b^12*d^4 - 16*b^14*d^4 - 1760*a^4*b^10*d^4 + 1600*a^6*b^8*d^4 - 400*a^8*b^6*d^4)^(1/2) - 20*a*b^6*d^2 + 40*a^3*b^4*d^2 - 4*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + (log(16*a^4*b^15*d^2 - ((((-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(((a + b*cot(c + d*x))^(1/2)*(-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5))/4 - 32*a*b^21*d^4 - 160*a^3*b^19*d^4 - 128*a^5*b^17*d^4 + 896*a^7*b^15*d^4 + 3136*a^9*b^13*d^4 + 4928*a^11*b^11*d^4 + 4480*a^13*b^9*d^4 + 2432*a^15*b^7*d^4 + 736*a^17*b^5*d^4 + 96*a^19*b^3*d^4))/4 - (a + b*cot(c + d*x))^(1/2)*(320*a^6*b^14*d^3 - 16*a^2*b^18*d^3 + 1024*a^8*b^12*d^3 + 1440*a^10*b^10*d^3 + 1024*a^12*b^8*d^3 + 320*a^14*b^6*d^3 - 16*a^18*b^2*d^3))*(-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 + 96*a^6*b^13*d^2 + 240*a^8*b^11*d^2 + 320*a^10*b^9*d^2 + 240*a^12*b^7*d^2 + 96*a^14*b^5*d^2 + 16*a^16*b^3*d^2)*(-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(a^10*d^4 + b^10*d^4 + 5*a^2*b^8*d^4 + 10*a^4*b^6*d^4 + 10*a^6*b^4*d^4 + 5*a^8*b^2*d^4))^(1/2))/4 - log(16*a^4*b^15*d^2 - ((-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(896*a^7*b^15*d^4 - 32*a*b^21*d^4 - 160*a^3*b^19*d^4 - 128*a^5*b^17*d^4 - (a + b*cot(c + d*x))^(1/2)*(-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2)*(64*a*b^22*d^5 + 640*a^3*b^20*d^5 + 2880*a^5*b^18*d^5 + 7680*a^7*b^16*d^5 + 13440*a^9*b^14*d^5 + 16128*a^11*b^12*d^5 + 13440*a^13*b^10*d^5 + 7680*a^15*b^8*d^5 + 2880*a^17*b^6*d^5 + 640*a^19*b^4*d^5 + 64*a^21*b^2*d^5) + 3136*a^9*b^13*d^4 + 4928*a^11*b^11*d^4 + 4480*a^13*b^9*d^4 + 2432*a^15*b^7*d^4 + 736*a^17*b^5*d^4 + 96*a^19*b^3*d^4) + (a + b*cot(c + d*x))^(1/2)*(320*a^6*b^14*d^3 - 16*a^2*b^18*d^3 + 1024*a^8*b^12*d^3 + 1440*a^10*b^10*d^3 + 1024*a^12*b^8*d^3 + 320*a^14*b^6*d^3 - 16*a^18*b^2*d^3))*(-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) + 96*a^6*b^13*d^2 + 240*a^8*b^11*d^2 + 320*a^10*b^9*d^2 + 240*a^12*b^7*d^2 + 96*a^14*b^5*d^2 + 16*a^16*b^3*d^2)*(-(4*a^7*d^2 + (320*a^6*b^8*d^4 - 16*a^4*b^10*d^4 - 1760*a^8*b^6*d^4 + 1600*a^10*b^4*d^4 - 400*a^12*b^2*d^4)^(1/2) + 20*a^3*b^4*d^2 - 40*a^5*b^2*d^2)/(16*a^10*d^4 + 16*b^10*d^4 + 80*a^2*b^8*d^4 + 160*a^4*b^6*d^4 + 160*a^6*b^4*d^4 + 80*a^8*b^2*d^4))^(1/2) - ((2*a*b)/(3*(a^2 + b^2)) + (2*b*(a^2 - b^2)*(a + b*cot(c + d*x)))/(a^2 + b^2)^2)/(d*(a + b*cot(c + d*x))^(3/2)) - ((2*a*b)/(3*(a^2 + b^2)) + (4*a^2*b*(a + b*cot(c + d*x)))/(a^2 + b^2)^2)/(d*(a + b*cot(c + d*x))^(3/2))","B"