1,1,225,102,10.282041,"\text{Not used}","int(sin(e + f*x)^3*(a + a*sin(e + f*x))^2,x)","\frac{3\,a^2\,x}{4}-\frac{\frac{3\,a^2\,\left(e+f\,x\right)}{4}+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{2}-\frac{a^2\,\left(15\,e+15\,f\,x-48\right)}{20}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{15\,a^2\,\left(e+f\,x\right)}{2}-\frac{a^2\,\left(150\,e+150\,f\,x-80\right)}{20}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{15\,a^2\,\left(e+f\,x\right)}{4}-\frac{a^2\,\left(75\,e+75\,f\,x-240\right)}{20}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{15\,a^2\,\left(e+f\,x\right)}{2}-\frac{a^2\,\left(150\,e+150\,f\,x-400\right)}{20}\right)+\frac{3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a^2*x)/4 - ((3*a^2*(e + f*x))/4 + 7*a^2*tan(e/2 + (f*x)/2)^3 - 7*a^2*tan(e/2 + (f*x)/2)^7 - (3*a^2*tan(e/2 + (f*x)/2)^9)/2 - (a^2*(15*e + 15*f*x - 48))/20 + tan(e/2 + (f*x)/2)^6*((15*a^2*(e + f*x))/2 - (a^2*(150*e + 150*f*x - 80))/20) + tan(e/2 + (f*x)/2)^2*((15*a^2*(e + f*x))/4 - (a^2*(75*e + 75*f*x - 240))/20) + tan(e/2 + (f*x)/2)^4*((15*a^2*(e + f*x))/2 - (a^2*(150*e + 150*f*x - 400))/20) + (3*a^2*tan(e/2 + (f*x)/2))/2)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
2,1,294,129,10.326386,"\text{Not used}","int(sin(e + f*x)^3*(a + a*sin(e + f*x))^3,x)","\frac{23\,a^3\,x}{16}-\frac{\frac{23\,a^3\,\left(e+f\,x\right)}{16}+\frac{391\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24}+\frac{75\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{4}-\frac{75\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{4}-\frac{391\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{24}-\frac{23\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}}{8}-\frac{a^3\,\left(345\,e+345\,f\,x-1088\right)}{240}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{69\,a^3\,\left(e+f\,x\right)}{8}-\frac{a^3\,\left(2070\,e+2070\,f\,x-6528\right)}{240}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{345\,a^3\,\left(e+f\,x\right)}{16}-\frac{a^3\,\left(5175\,e+5175\,f\,x-960\right)}{240}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{115\,a^3\,\left(e+f\,x\right)}{4}-\frac{a^3\,\left(6900\,e+6900\,f\,x-10880\right)}{240}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{345\,a^3\,\left(e+f\,x\right)}{16}-\frac{a^3\,\left(5175\,e+5175\,f\,x-15360\right)}{240}\right)+\frac{23\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(23*a^3*x)/16 - ((23*a^3*(e + f*x))/16 + (391*a^3*tan(e/2 + (f*x)/2)^3)/24 + (75*a^3*tan(e/2 + (f*x)/2)^5)/4 - (75*a^3*tan(e/2 + (f*x)/2)^7)/4 - (391*a^3*tan(e/2 + (f*x)/2)^9)/24 - (23*a^3*tan(e/2 + (f*x)/2)^11)/8 - (a^3*(345*e + 345*f*x - 1088))/240 + tan(e/2 + (f*x)/2)^2*((69*a^3*(e + f*x))/8 - (a^3*(2070*e + 2070*f*x - 6528))/240) + tan(e/2 + (f*x)/2)^8*((345*a^3*(e + f*x))/16 - (a^3*(5175*e + 5175*f*x - 960))/240) + tan(e/2 + (f*x)/2)^6*((115*a^3*(e + f*x))/4 - (a^3*(6900*e + 6900*f*x - 10880))/240) + tan(e/2 + (f*x)/2)^4*((345*a^3*(e + f*x))/16 - (a^3*(5175*e + 5175*f*x - 15360))/240) + (23*a^3*tan(e/2 + (f*x)/2))/8)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^6)","B"
3,1,78,53,6.818291,"\text{Not used}","int(sin(x)^4/(a + a*sin(x)),x)","-\frac{3\,x}{2\,a}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+13\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{7\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{16}{3}}{a\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^3\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"- (3*x)/(2*a) - ((7*tan(x/2))/3 + 13*tan(x/2)^2 + 8*tan(x/2)^3 + 8*tan(x/2)^4 + 3*tan(x/2)^5 + 3*tan(x/2)^6 + 16/3)/(a*(tan(x/2)^2 + 1)^3*(tan(x/2) + 1))","B"
4,1,59,42,6.910507,"\text{Not used}","int(sin(x)^3/(a + a*sin(x)),x)","\frac{3\,x}{2\,a}+\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\mathrm{tan}\left(\frac{x}{2}\right)+4}{a\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^2\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"(3*x)/(2*a) + (tan(x/2) + 5*tan(x/2)^2 + 3*tan(x/2)^3 + 3*tan(x/2)^4 + 4)/(a*(tan(x/2)^2 + 1)^2*(tan(x/2) + 1))","B"
5,1,46,27,6.769776,"\text{Not used}","int(sin(x)^2/(a + a*sin(x)),x)","-\frac{x}{a}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{x}{2}\right)+4}{a\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"- x/a - (2*tan(x/2) + 2*tan(x/2)^2 + 4)/(a*(tan(x/2)^2 + 1)*(tan(x/2) + 1))","B"
6,1,19,17,6.538680,"\text{Not used}","int(sin(x)/(a + a*sin(x)),x)","\frac{2}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}+\frac{x}{a}","Not used",1,"2/(a*(tan(x/2) + 1)) + x/a","B"
7,1,13,12,0.021238,"\text{Not used}","int(1/(a + a*sin(x)),x)","-\frac{2}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}","Not used",1,"-2/(a*(tan(x/2) + 1))","B"
8,1,23,20,6.423297,"\text{Not used}","int(1/(sin(x)*(a + a*sin(x))),x)","\frac{2}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"2/(a*(tan(x/2) + 1)) + log(tan(x/2))/a","B"
9,1,49,26,6.713885,"\text{Not used}","int(1/(sin(x)^2*(a + a*sin(x))),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a}-\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)+1}{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"tan(x/2)/(2*a) - (5*tan(x/2) + 1)/(2*a*tan(x/2) + 2*a*tan(x/2)^2) - log(tan(x/2))/a","B"
10,1,69,42,6.598051,"\text{Not used}","int(1/(sin(x)^3*(a + a*sin(x))),x)","\frac{10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{3\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}-\frac{1}{2}}{4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a}","Not used",1,"((3*tan(x/2))/2 + 10*tan(x/2)^2 - 1/2)/(4*a*tan(x/2)^2 + 4*a*tan(x/2)^3) - tan(x/2)/(2*a) + tan(x/2)^2/(8*a) + (3*log(tan(x/2)))/(2*a)","B"
11,1,89,55,6.496975,"\text{Not used}","int(1/(sin(x)^4*(a + a*sin(x))),x)","\frac{7\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a}-\frac{23\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{1}{3}}{8\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+8\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,a}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a}","Not used",1,"(7*tan(x/2))/(8*a) - (6*tan(x/2)^2 - (2*tan(x/2))/3 + 23*tan(x/2)^3 + 1/3)/(8*a*tan(x/2)^3 + 8*a*tan(x/2)^4) - tan(x/2)^2/(8*a) + tan(x/2)^3/(24*a) - (3*log(tan(x/2)))/(2*a)","B"
12,1,77,66,6.813475,"\text{Not used}","int(sin(x)^4/(a + a*sin(x))^2,x)","\frac{7\,x}{2\,a^2}+\frac{7\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\frac{98\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{3}+42\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\frac{97\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3}+25\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{32}{3}}{a^2\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"(7*x)/(2*a^2) + (25*tan(x/2) + (97*tan(x/2)^2)/3 + 42*tan(x/2)^3 + (98*tan(x/2)^4)/3 + 21*tan(x/2)^5 + 7*tan(x/2)^6 + 32/3)/(a^2*(tan(x/2)^2 + 1)^2*(tan(x/2) + 1)^3)","B"
13,1,62,47,6.464817,"\text{Not used}","int(sin(x)^3/(a + a*sin(x))^2,x)","-\frac{2\,x}{a^2}-\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+12\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\frac{44\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3}+16\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{20}{3}}{a^2\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"- (2*x)/a^2 - (16*tan(x/2) + (44*tan(x/2)^2)/3 + 12*tan(x/2)^3 + 4*tan(x/2)^4 + 20/3)/(a^2*(tan(x/2)^2 + 1)*(tan(x/2) + 1)^3)","B"
14,1,34,35,6.481788,"\text{Not used}","int(sin(x)^2/(a + a*sin(x))^2,x)","\frac{x}{a^2}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+6\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8}{3}}{a^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"x/a^2 + (6*tan(x/2) + 2*tan(x/2)^2 + 8/3)/(a^2*(tan(x/2) + 1)^3)","B"
15,1,21,33,6.298552,"\text{Not used}","int(sin(x)/(a + a*sin(x))^2,x)","-\frac{2\,\left(3\,\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{3\,a^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(3*tan(x/2) + 1))/(3*a^2*(tan(x/2) + 1)^3)","B"
16,1,29,33,6.305750,"\text{Not used}","int(1/(a + a*sin(x))^2,x)","-\frac{2\,\left(3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+3\,\mathrm{tan}\left(\frac{x}{2}\right)+2\right)}{3\,a^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(3*tan(x/2) + 3*tan(x/2)^2 + 2))/(3*a^2*(tan(x/2) + 1)^3)","B"
17,1,38,38,6.482209,"\text{Not used}","int(1/(sin(x)*(a + a*sin(x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^2}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+6\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{10}{3}}{a^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"log(tan(x/2))/a^2 + (6*tan(x/2) + 4*tan(x/2)^2 + 10/3)/(a^2*(tan(x/2) + 1)^3)","B"
18,1,91,45,6.539829,"\text{Not used}","int(1/(sin(x)^2*(a + a*sin(x))^2),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^2}-\frac{13\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+23\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{41\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+1}{2\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+6\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+6\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^2}","Not used",1,"tan(x/2)/(2*a^2) - ((41*tan(x/2))/3 + 23*tan(x/2)^2 + 13*tan(x/2)^3 + 1)/(2*a^2*tan(x/2) + 6*a^2*tan(x/2)^2 + 6*a^2*tan(x/2)^3 + 2*a^2*tan(x/2)^4) - (2*log(tan(x/2)))/a^2","B"
19,1,111,64,6.398984,"\text{Not used}","int(1/(sin(x)^3*(a + a*sin(x))^2),x)","\frac{36\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+\frac{135\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{2}+\frac{239\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{6}+\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}-\frac{1}{2}}{4\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+12\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+12\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^2}+\frac{7\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a^2}","Not used",1,"((5*tan(x/2))/2 + (239*tan(x/2)^2)/6 + (135*tan(x/2)^3)/2 + 36*tan(x/2)^4 - 1/2)/(4*a^2*tan(x/2)^2 + 12*a^2*tan(x/2)^3 + 12*a^2*tan(x/2)^4 + 4*a^2*tan(x/2)^5) - tan(x/2)/a^2 + tan(x/2)^2/(8*a^2) + (7*log(tan(x/2)))/(2*a^2)","B"
20,1,101,65,6.395901,"\text{Not used}","int(1/(sin(x)^4*(a + a*sin(x))^2),x)","\frac{15\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4\,a^2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,a^2}-\frac{5\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^2}-\frac{\frac{95\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{8}+\frac{187\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{8}+\frac{57\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{4}+\frac{5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{8}+\frac{1}{24}}{a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"(15*tan(x/2))/(8*a^2) - tan(x/2)^2/(4*a^2) + tan(x/2)^3/(24*a^2) - (5*log(tan(x/2)))/a^2 - ((5*tan(x/2)^2)/4 - tan(x/2)/8 + (57*tan(x/2)^3)/4 + (187*tan(x/2)^4)/8 + (95*tan(x/2)^5)/8 + 1/24)/(a^2*tan(x/2)^3*(tan(x/2) + 1)^3)","B"
21,1,110,101,7.022103,"\text{Not used}","int(sin(x)^6/(a + a*sin(x))^3,x)","-\frac{23\,x}{2\,a^3}-\frac{23\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{10}+115\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9+\frac{874\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8}{3}+\frac{1610\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7}{3}+\frac{11684\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{15}+\frac{2668\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{3}+\frac{12622\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{15}+\frac{1846\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3}+\frac{5347\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{15}+\frac{475\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{544}{15}}{a^3\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"- (23*x)/(2*a^3) - ((475*tan(x/2))/3 + (5347*tan(x/2)^2)/15 + (1846*tan(x/2)^3)/3 + (12622*tan(x/2)^4)/15 + (2668*tan(x/2)^5)/3 + (11684*tan(x/2)^6)/15 + (1610*tan(x/2)^7)/3 + (874*tan(x/2)^8)/3 + 115*tan(x/2)^9 + 23*tan(x/2)^10 + 544/15)/(a^3*(tan(x/2)^2 + 1)^3*(tan(x/2) + 1)^5)","B"
22,1,93,90,6.670179,"\text{Not used}","int(sin(x)^5/(a + a*sin(x))^3,x)","\frac{13\,x}{2\,a^3}+\frac{13\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+65\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7+\frac{455\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{3}+\frac{715\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{3}+\frac{1443\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{5}+\frac{761\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3}+\frac{891\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+\frac{265\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{304}{15}}{a^3\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"(13*x)/(2*a^3) + ((265*tan(x/2))/3 + (891*tan(x/2)^2)/5 + (761*tan(x/2)^3)/3 + (1443*tan(x/2)^4)/5 + (715*tan(x/2)^5)/3 + (455*tan(x/2)^6)/3 + 65*tan(x/2)^7 + 13*tan(x/2)^8 + 304/15)/(a^3*(tan(x/2)^2 + 1)^2*(tan(x/2) + 1)^5)","B"
23,1,78,71,6.890939,"\text{Not used}","int(sin(x)^4/(a + a*sin(x))^3,x)","-\frac{3\,x}{a^3}-\frac{6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+30\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+64\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+80\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\frac{378\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{5}+42\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{48}{5}}{a^3\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"- (3*x)/a^3 - (42*tan(x/2) + (378*tan(x/2)^2)/5 + 80*tan(x/2)^3 + 64*tan(x/2)^4 + 30*tan(x/2)^5 + 6*tan(x/2)^6 + 48/5)/(a^3*(tan(x/2)^2 + 1)*(tan(x/2) + 1)^5)","B"
24,1,50,59,6.740393,"\text{Not used}","int(sin(x)^3/(a + a*sin(x))^3,x)","\frac{x}{a^3}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\frac{58\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3}+\frac{38\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{44}{15}}{a^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"x/a^3 + ((38*tan(x/2))/3 + (58*tan(x/2)^2)/3 + 10*tan(x/2)^3 + 2*tan(x/2)^4 + 44/15)/(a^3*(tan(x/2) + 1)^5)","B"
25,1,29,50,6.637321,"\text{Not used}","int(sin(x)^2/(a + a*sin(x))^3,x)","-\frac{4\,\left(10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+5\,\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{15\,a^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"-(4*(5*tan(x/2) + 10*tan(x/2)^2 + 1))/(15*a^3*(tan(x/2) + 1)^5)","B"
26,1,37,50,6.845136,"\text{Not used}","int(sin(x)/(a + a*sin(x))^3,x)","-\frac{2\,\left(5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+5\,\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{5\,a^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(5*tan(x/2) + 5*tan(x/2)^2 + 5*tan(x/2)^3 + 1))/(5*a^3*(tan(x/2) + 1)^5)","B"
27,1,45,50,6.633446,"\text{Not used}","int(1/(a + a*sin(x))^3,x)","-\frac{2\,\left(15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+30\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+40\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+20\,\mathrm{tan}\left(\frac{x}{2}\right)+7\right)}{15\,a^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(20*tan(x/2) + 40*tan(x/2)^2 + 30*tan(x/2)^3 + 15*tan(x/2)^4 + 7))/(15*a^3*(tan(x/2) + 1)^5)","B"
28,1,54,58,6.650586,"\text{Not used}","int(1/(sin(x)*(a + a*sin(x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}+\frac{6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+18\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\frac{74\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{3}+\frac{46\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{64}{15}}{a^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"log(tan(x/2))/a^3 + ((46*tan(x/2))/3 + (74*tan(x/2)^2)/3 + 18*tan(x/2)^3 + 6*tan(x/2)^4 + 64/15)/(a^3*(tan(x/2) + 1)^5)","B"
29,1,129,65,6.724886,"\text{Not used}","int(1/(sin(x)^2*(a + a*sin(x))^3),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^3}-\frac{25\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+85\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+122\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+82\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{121\,\mathrm{tan}\left(\frac{x}{2}\right)}{5}+1}{2\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+10\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+20\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+20\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}","Not used",1,"tan(x/2)/(2*a^3) - ((121*tan(x/2))/5 + 82*tan(x/2)^2 + 122*tan(x/2)^3 + 85*tan(x/2)^4 + 25*tan(x/2)^5 + 1)/(2*a^3*tan(x/2) + 10*a^3*tan(x/2)^2 + 20*a^3*tan(x/2)^3 + 20*a^3*tan(x/2)^4 + 10*a^3*tan(x/2)^5 + 2*a^3*tan(x/2)^6) - (3*log(tan(x/2)))/a^3","B"
30,1,97,86,6.389511,"\text{Not used}","int(1/(sin(x)^3*(a + a*sin(x))^3),x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^3}-\frac{3\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^3}+\frac{13\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a^3}+\frac{\frac{43\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{2}+\frac{619\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{8}+\frac{2729\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{24}+\frac{941\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{12}+\frac{1391\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{60}+\frac{7\,\mathrm{tan}\left(\frac{x}{2}\right)}{8}-\frac{1}{8}}{a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"tan(x/2)^2/(8*a^3) - (3*tan(x/2))/(2*a^3) + (13*log(tan(x/2)))/(2*a^3) + ((7*tan(x/2))/8 + (1391*tan(x/2)^2)/60 + (941*tan(x/2)^3)/12 + (2729*tan(x/2)^4)/24 + (619*tan(x/2)^5)/8 + (43*tan(x/2)^6)/2 - 1/8)/(a^3*tan(x/2)^2*(tan(x/2) + 1)^5)","B"
31,1,117,103,6.686974,"\text{Not used}","int(1/(sin(x)^4*(a + a*sin(x))^3),x)","\frac{27\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^3}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,a^3}-\frac{23\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a^3}-\frac{\frac{267\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7}{8}+\frac{249\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{2}+\frac{2239\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{12}+\frac{3157\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{24}+\frac{4777\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{120}+\frac{23\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{12}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{6}+\frac{1}{24}}{a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"(27*tan(x/2))/(8*a^3) - (3*tan(x/2)^2)/(8*a^3) + tan(x/2)^3/(24*a^3) - (23*log(tan(x/2)))/(2*a^3) - ((23*tan(x/2)^2)/12 - tan(x/2)/6 + (4777*tan(x/2)^3)/120 + (3157*tan(x/2)^4)/24 + (2239*tan(x/2)^5)/12 + (249*tan(x/2)^6)/2 + (267*tan(x/2)^7)/8 + 1/24)/(a^3*tan(x/2)^3*(tan(x/2) + 1)^5)","B"
32,0,-1,158,0.000000,"\text{Not used}","int(sin(c + d*x)^4*(a + a*sin(c + d*x))^(1/2),x)","\int {\sin\left(c+d\,x\right)}^4\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(sin(c + d*x)^4*(a + a*sin(c + d*x))^(1/2), x)","F"
33,0,-1,122,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2),x)","\int {\sin\left(c+d\,x\right)}^3\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2), x)","F"
34,0,-1,86,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2),x)","\int {\sin\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2), x)","F"
35,0,-1,56,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2),x)","\int \sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2), x)","F"
36,1,33,26,0.211073,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2),x)","-\frac{2\,\cos\left(c+d\,x\right)\,\sqrt{a\,\left(\sin\left(c+d\,x\right)+1\right)}}{d\,\left(\sin\left(c+d\,x\right)+1\right)}","Not used",1,"-(2*cos(c + d*x)*(a*(sin(c + d*x) + 1))^(1/2))/(d*(sin(c + d*x) + 1))","B"
37,0,-1,37,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x),x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x), x)","F"
38,0,-1,64,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x)^2,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x)^2, x)","F"
39,0,-1,102,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x)^3,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x)^3, x)","F"
40,0,-1,138,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x)^4,x)","\int \frac{\sqrt{a+a\,\sin\left(c+d\,x\right)}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(1/2)/sin(c + d*x)^4, x)","F"
41,0,-1,38,0.000000,"\text{Not used}","int((a - a*sin(c + d*x))^(1/2)/sin(c + d*x),x)","\int \frac{\sqrt{a-a\,\sin\left(c+d\,x\right)}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a - a*sin(c + d*x))^(1/2)/sin(c + d*x), x)","F"
42,0,-1,39,0.000000,"\text{Not used}","int((a*sin(c + d*x) - a)^(1/2)/sin(c + d*x),x)","\int \frac{\sqrt{a\,\sin\left(c+d\,x\right)-a}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a*sin(c + d*x) - a)^(1/2)/sin(c + d*x), x)","F"
43,0,-1,40,0.000000,"\text{Not used}","int((- a - a*sin(c + d*x))^(1/2)/sin(c + d*x),x)","\int \frac{\sqrt{-a-a\,\sin\left(c+d\,x\right)}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((- a - a*sin(c + d*x))^(1/2)/sin(c + d*x), x)","F"
44,0,-1,162,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2),x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2), x)","F"
45,0,-1,116,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2),x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2), x)","F"
46,0,-1,86,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2),x)","\int \sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2), x)","F"
47,0,-1,59,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2),x)","\int {\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2), x)","F"
48,0,-1,66,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x), x)","F"
49,0,-1,66,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x)^2, x)","F"
50,0,-1,106,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x)^3,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x)^3, x)","F"
51,0,-1,144,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x)^4,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(3/2)/sin(c + d*x)^4, x)","F"
52,0,-1,203,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(5/2),x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(5/2), x)","F"
53,0,-1,146,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(5/2),x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(5/2), x)","F"
54,0,-1,116,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + a*sin(c + d*x))^(5/2),x)","\int \sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(sin(c + d*x)*(a + a*sin(c + d*x))^(5/2), x)","F"
55,0,-1,89,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2),x)","\int {\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2), x)","F"
56,0,-1,98,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x), x)","F"
57,0,-1,94,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^2, x)","F"
58,0,-1,106,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^3,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^3, x)","F"
59,0,-1,144,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^4,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^4, x)","F"
60,0,-1,182,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^5,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\sin\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(5/2)/sin(c + d*x)^5, x)","F"
61,0,-1,139,0.000000,"\text{Not used}","int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^3}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(1/2), x)","F"
62,0,-1,105,0.000000,"\text{Not used}","int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(1/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^2}{\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(1/2), x)","F"
63,1,99,72,0.745036,"\text{Not used}","int(sin(c + d*x)/(a + a*sin(c + d*x))^(1/2),x)","-\frac{\left(4\,\mathrm{E}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(c+d\,x\right)}}{2}\right)\middle|1\right)-2\,\mathrm{F}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(c+d\,x\right)}}{2}\right)\middle|1\right)\right)\,\sqrt{{\cos\left(c+d\,x\right)}^2}\,\sqrt{\frac{a+a\,\sin\left(c+d\,x\right)}{2\,a}}}{d\,\cos\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}","Not used",1,"-((4*ellipticE(asin((2^(1/2)*(1 - sin(c + d*x))^(1/2))/2), 1) - 2*ellipticF(asin((2^(1/2)*(1 - sin(c + d*x))^(1/2))/2), 1))*(cos(c + d*x)^2)^(1/2)*((a + a*sin(c + d*x))/(2*a))^(1/2))/(d*cos(c + d*x)*(a + a*sin(c + d*x))^(1/2))","B"
64,1,49,47,6.436334,"\text{Not used}","int(1/(a + a*sin(c + d*x))^(1/2),x)","-\frac{\mathrm{F}\left(\frac{\pi }{4}-\frac{c}{2}-\frac{d\,x}{2}\middle|1\right)\,\sqrt{\frac{2\,\left(a+a\,\sin\left(c+d\,x\right)\right)}{a}}}{d\,\sqrt{a+a\,\sin\left(c+d\,x\right)}}","Not used",1,"-(ellipticF(pi/4 - c/2 - (d*x)/2, 1)*((2*(a + a*sin(c + d*x)))/a)^(1/2))/(d*(a + a*sin(c + d*x))^(1/2))","B"
65,0,-1,84,0.000000,"\text{Not used}","int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{\sin\left(c+d\,x\right)\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/2)), x)","F"
66,0,-1,109,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^2\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/2)), x)","F"
67,0,-1,146,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^3\,\sqrt{a+a\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(1/2)), x)","F"
68,0,-1,183,0.000000,"\text{Not used}","int(sin(c + d*x)^4/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^4}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(sin(c + d*x)^4/(a + a*sin(c + d*x))^(3/2), x)","F"
69,0,-1,145,0.000000,"\text{Not used}","int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^3}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(3/2), x)","F"
70,0,-1,105,0.000000,"\text{Not used}","int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^2}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(3/2), x)","F"
71,0,-1,77,0.000000,"\text{Not used}","int(sin(c + d*x)/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(sin(c + d*x)/(a + a*sin(c + d*x))^(3/2), x)","F"
72,0,-1,77,0.000000,"\text{Not used}","int(1/(a + a*sin(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + a*sin(c + d*x))^(3/2), x)","F"
73,0,-1,114,0.000000,"\text{Not used}","int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(3/2)), x)","F"
74,0,-1,144,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)), x)","F"
75,0,-1,186,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(3/2)), x)","F"
76,0,-1,221,0.000000,"\text{Not used}","int(sin(c + d*x)^5/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^5}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(sin(c + d*x)^5/(a + a*sin(c + d*x))^(5/2), x)","F"
77,0,-1,183,0.000000,"\text{Not used}","int(sin(c + d*x)^4/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^4}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(sin(c + d*x)^4/(a + a*sin(c + d*x))^(5/2), x)","F"
78,0,-1,145,0.000000,"\text{Not used}","int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^3}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(5/2), x)","F"
79,0,-1,107,0.000000,"\text{Not used}","int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{{\sin\left(c+d\,x\right)}^2}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(5/2), x)","F"
80,0,-1,107,0.000000,"\text{Not used}","int(sin(c + d*x)/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(sin(c + d*x)/(a + a*sin(c + d*x))^(5/2), x)","F"
81,0,-1,107,0.000000,"\text{Not used}","int(1/(a + a*sin(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + a*sin(c + d*x))^(5/2), x)","F"
82,0,-1,144,0.000000,"\text{Not used}","int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(5/2)), x)","F"
83,0,-1,174,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(5/2)), x)","F"
84,0,-1,224,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(5/2)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(sin(c + d*x)^3*(a + a*sin(c + d*x))^(5/2)), x)","F"
85,0,-1,37,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/sin(e + f*x)^(1/2),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sqrt{\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/sin(e + f*x)^(1/2), x)","F"
86,0,-1,38,0.000000,"\text{Not used}","int((a - a*sin(e + f*x))^(1/2)/(-sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{a-a\,\sin\left(e+f\,x\right)}}{\sqrt{-\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a - a*sin(e + f*x))^(1/2)/(-sin(e + f*x))^(1/2), x)","F"
87,0,-1,17,0.000000,"\text{Not used}","int(1/(sin(x)^(1/2)*(sin(x) + 1)^(1/2)),x)","\int \frac{1}{\sqrt{\sin\left(x\right)}\,\sqrt{\sin\left(x\right)+1}} \,d x","Not used",1,"int(1/(sin(x)^(1/2)*(sin(x) + 1)^(1/2)), x)","F"
88,0,-1,42,0.000000,"\text{Not used}","int(1/(sin(x)^(1/2)*(a + a*sin(x))^(1/2)),x)","\int \frac{1}{\sqrt{\sin\left(x\right)}\,\sqrt{a+a\,\sin\left(x\right)}} \,d x","Not used",1,"int(1/(sin(x)^(1/2)*(a + a*sin(x))^(1/2)), x)","F"
89,0,-1,31,0.000000,"\text{Not used}","int(1/(sin(x)^(1/2)*(1 - sin(x))^(1/2)),x)","\int \frac{1}{\sqrt{\sin\left(x\right)}\,\sqrt{1-\sin\left(x\right)}} \,d x","Not used",1,"int(1/(sin(x)^(1/2)*(1 - sin(x))^(1/2)), x)","F"
90,0,-1,42,0.000000,"\text{Not used}","int(1/(sin(x)^(1/2)*(a - a*sin(x))^(1/2)),x)","\int \frac{1}{\sqrt{\sin\left(x\right)}\,\sqrt{a-a\,\sin\left(x\right)}} \,d x","Not used",1,"int(1/(sin(x)^(1/2)*(a - a*sin(x))^(1/2)), x)","F"
91,0,-1,184,0.000000,"\text{Not used}","int(sin(c + d*x)^(1/3)/(a + a*sin(c + d*x))^2,x)","\int \frac{{\sin\left(c+d\,x\right)}^{1/3}}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(sin(c + d*x)^(1/3)/(a + a*sin(c + d*x))^2, x)","F"
92,0,-1,161,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(2/3),x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(2/3), x)","F"
93,0,-1,126,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(2/3),x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(2/3), x)","F"
94,0,-1,96,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + a*sin(c + d*x))^(2/3),x)","\int \sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int(sin(c + d*x)*(a + a*sin(c + d*x))^(2/3), x)","F"
95,0,-1,66,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(2/3),x)","\int {\left(a+a\,\sin\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(2/3), x)","F"
96,0,-1,77,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(2/3)/sin(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{2/3}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(2/3)/sin(c + d*x), x)","F"
97,0,-1,77,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(2/3)/sin(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{2/3}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(2/3)/sin(c + d*x)^2, x)","F"
98,0,-1,162,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(4/3),x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3} \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a*sin(c + d*x))^(4/3), x)","F"
99,0,-1,127,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(4/3),x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3} \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(4/3), x)","F"
100,0,-1,97,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + a*sin(c + d*x))^(4/3),x)","\int \sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3} \,d x","Not used",1,"int(sin(c + d*x)*(a + a*sin(c + d*x))^(4/3), x)","F"
101,0,-1,67,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(4/3),x)","\int {\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(4/3), x)","F"
102,0,-1,78,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(4/3)/sin(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(4/3)/sin(c + d*x), x)","F"
103,0,-1,78,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^(4/3)/sin(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^(4/3)/sin(c + d*x)^2, x)","F"
104,0,-1,161,0.000000,"\text{Not used}","int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(1/3),x)","\int \frac{{\sin\left(c+d\,x\right)}^3}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(1/3), x)","F"
105,0,-1,126,0.000000,"\text{Not used}","int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(1/3),x)","\int \frac{{\sin\left(c+d\,x\right)}^2}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(1/3), x)","F"
106,0,-1,93,0.000000,"\text{Not used}","int(sin(c + d*x)/(a + a*sin(c + d*x))^(1/3),x)","\int \frac{\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(sin(c + d*x)/(a + a*sin(c + d*x))^(1/3), x)","F"
107,0,-1,66,0.000000,"\text{Not used}","int(1/(a + a*sin(c + d*x))^(1/3),x)","\int \frac{1}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(1/(a + a*sin(c + d*x))^(1/3), x)","F"
108,0,-1,77,0.000000,"\text{Not used}","int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/3)),x)","\int \frac{1}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(1/3)), x)","F"
109,0,-1,77,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/3)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(1/3)), x)","F"
110,0,-1,162,0.000000,"\text{Not used}","int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(4/3),x)","\int \frac{{\sin\left(c+d\,x\right)}^3}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int(sin(c + d*x)^3/(a + a*sin(c + d*x))^(4/3), x)","F"
111,0,-1,129,0.000000,"\text{Not used}","int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(4/3),x)","\int \frac{{\sin\left(c+d\,x\right)}^2}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int(sin(c + d*x)^2/(a + a*sin(c + d*x))^(4/3), x)","F"
112,0,-1,99,0.000000,"\text{Not used}","int(sin(c + d*x)/(a + a*sin(c + d*x))^(4/3),x)","\int \frac{\sin\left(c+d\,x\right)}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int(sin(c + d*x)/(a + a*sin(c + d*x))^(4/3), x)","F"
113,0,-1,69,0.000000,"\text{Not used}","int(1/(a + a*sin(c + d*x))^(4/3),x)","\int \frac{1}{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int(1/(a + a*sin(c + d*x))^(4/3), x)","F"
114,0,-1,80,0.000000,"\text{Not used}","int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(4/3)),x)","\int \frac{1}{\sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int(1/(sin(c + d*x)*(a + a*sin(c + d*x))^(4/3)), x)","F"
115,0,-1,80,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(4/3)),x)","\int \frac{1}{{\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int(1/(sin(c + d*x)^2*(a + a*sin(c + d*x))^(4/3)), x)","F"
116,0,-1,96,0.000000,"\text{Not used}","int(sin(e + f*x)^n*(sin(e + f*x) + 1)^(3/2),x)","\int {\sin\left(e+f\,x\right)}^n\,{\left(\sin\left(e+f\,x\right)+1\right)}^{3/2} \,d x","Not used",1,"int(sin(e + f*x)^n*(sin(e + f*x) + 1)^(3/2), x)","F"
117,0,-1,43,0.000000,"\text{Not used}","int(sin(e + f*x)^n*(sin(e + f*x) + 1)^(1/2),x)","\int {\sin\left(e+f\,x\right)}^n\,\sqrt{\sin\left(e+f\,x\right)+1} \,d x","Not used",1,"int(sin(e + f*x)^n*(sin(e + f*x) + 1)^(1/2), x)","F"
118,0,-1,58,0.000000,"\text{Not used}","int(sin(e + f*x)^n/(sin(e + f*x) + 1)^(1/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^n}{\sqrt{\sin\left(e+f\,x\right)+1}} \,d x","Not used",1,"int(sin(e + f*x)^n/(sin(e + f*x) + 1)^(1/2), x)","F"
119,0,-1,60,0.000000,"\text{Not used}","int(sin(e + f*x)^n/(sin(e + f*x) + 1)^(3/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^n}{{\left(\sin\left(e+f\,x\right)+1\right)}^{3/2}} \,d x","Not used",1,"int(sin(e + f*x)^n/(sin(e + f*x) + 1)^(3/2), x)","F"
120,0,-1,106,0.000000,"\text{Not used}","int(sin(e + f*x)^n*(a + a*sin(e + f*x))^(3/2),x)","\int {\sin\left(e+f\,x\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(sin(e + f*x)^n*(a + a*sin(e + f*x))^(3/2), x)","F"
121,0,-1,46,0.000000,"\text{Not used}","int(sin(e + f*x)^n*(a + a*sin(e + f*x))^(1/2),x)","\int {\sin\left(e+f\,x\right)}^n\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(sin(e + f*x)^n*(a + a*sin(e + f*x))^(1/2), x)","F"
122,0,-1,60,0.000000,"\text{Not used}","int(sin(e + f*x)^n/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^n}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(sin(e + f*x)^n/(a + a*sin(e + f*x))^(1/2), x)","F"
123,0,-1,65,0.000000,"\text{Not used}","int(sin(e + f*x)^n/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\sin\left(e+f\,x\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(sin(e + f*x)^n/(a + a*sin(e + f*x))^(3/2), x)","F"
124,0,-1,130,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(sin(e + f*x) + 1)^(3/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(\sin\left(e+f\,x\right)+1\right)}^{3/2} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(sin(e + f*x) + 1)^(3/2), x)","F"
125,0,-1,72,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(sin(e + f*x) + 1)^(1/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\sqrt{\sin\left(e+f\,x\right)+1} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(sin(e + f*x) + 1)^(1/2), x)","F"
126,0,-1,78,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n/(sin(e + f*x) + 1)^(1/2),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n}{\sqrt{\sin\left(e+f\,x\right)+1}} \,d x","Not used",1,"int((d*sin(e + f*x))^n/(sin(e + f*x) + 1)^(1/2), x)","F"
127,0,-1,80,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n/(sin(e + f*x) + 1)^(3/2),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(\sin\left(e+f\,x\right)+1\right)}^{3/2}} \,d x","Not used",1,"int((d*sin(e + f*x))^n/(sin(e + f*x) + 1)^(3/2), x)","F"
128,0,-1,131,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^(3/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^(3/2), x)","F"
129,0,-1,66,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^(1/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^(1/2), x)","F"
130,0,-1,80,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(1/2), x)","F"
131,0,-1,85,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(3/2), x)","F"
132,0,-1,71,0.000000,"\text{Not used}","int(sin(e + f*x)^n*(sin(e + f*x) + 1)^m,x)","\int {\sin\left(e+f\,x\right)}^n\,{\left(\sin\left(e+f\,x\right)+1\right)}^m \,d x","Not used",1,"int(sin(e + f*x)^n*(sin(e + f*x) + 1)^m, x)","F"
133,0,-1,68,0.000000,"\text{Not used}","int((-sin(e + f*x))^n*(1 - sin(e + f*x))^m,x)","\int {\left(-\sin\left(e+f\,x\right)\right)}^n\,{\left(1-\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((-sin(e + f*x))^n*(1 - sin(e + f*x))^m, x)","F"
134,0,-1,91,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(sin(e + f*x) + 1)^m,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(\sin\left(e+f\,x\right)+1\right)}^m \,d x","Not used",1,"int((d*sin(e + f*x))^n*(sin(e + f*x) + 1)^m, x)","F"
135,0,-1,90,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(1 - sin(e + f*x))^m,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(1-\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((d*sin(e + f*x))^n*(1 - sin(e + f*x))^m, x)","F"
136,0,-1,87,0.000000,"\text{Not used}","int(sin(e + f*x)^n*(a + a*sin(e + f*x))^m,x)","\int {\sin\left(e+f\,x\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(sin(e + f*x)^n*(a + a*sin(e + f*x))^m, x)","F"
137,0,-1,85,0.000000,"\text{Not used}","int((-sin(e + f*x))^n*(a - a*sin(e + f*x))^m,x)","\int {\left(-\sin\left(e+f\,x\right)\right)}^n\,{\left(a-a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((-sin(e + f*x))^n*(a - a*sin(e + f*x))^m, x)","F"
138,0,-1,107,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^m,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^m, x)","F"
139,0,-1,107,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(a - a*sin(e + f*x))^m,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(a-a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((d*sin(e + f*x))^n*(a - a*sin(e + f*x))^m, x)","F"
140,0,-1,294,0.000000,"\text{Not used}","int(sin(c + d*x)^4*(a + a*sin(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^4\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^4*(a + a*sin(c + d*x))^n, x)","F"
141,0,-1,215,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a*sin(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a*sin(c + d*x))^n, x)","F"
142,0,-1,156,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^n, x)","F"
143,0,-1,109,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + a*sin(c + d*x))^n,x)","\int \sin\left(c+d\,x\right)\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)*(a + a*sin(c + d*x))^n, x)","F"
144,0,-1,74,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^n,x)","\int {\left(a+a\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(c + d*x))^n, x)","F"
145,0,-1,85,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^n/sin(c + d*x),x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^n}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*sin(c + d*x))^n/sin(c + d*x), x)","F"
146,0,-1,85,0.000000,"\text{Not used}","int((a + a*sin(c + d*x))^n/sin(c + d*x)^2,x)","\int \frac{{\left(a+a\,\sin\left(c+d\,x\right)\right)}^n}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*sin(c + d*x))^n/sin(c + d*x)^2, x)","F"
147,0,-1,58,0.000000,"\text{Not used}","int((sin(c + d*x) + 1)^n,x)","\int {\left(\sin\left(c+d\,x\right)+1\right)}^n \,d x","Not used",1,"int((sin(c + d*x) + 1)^n, x)","F"
148,0,-1,57,0.000000,"\text{Not used}","int((1 - sin(c + d*x))^n,x)","\int {\left(1-\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((1 - sin(c + d*x))^n, x)","F"
149,1,111,77,10.285033,"\text{Not used}","int(sin(e + f*x)^3*(a + b*sin(e + f*x)),x)","\frac{3\,b\,x}{8}-\frac{-\frac{3\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{4}-\frac{11\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{4}+4\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+\frac{11\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{4}+\frac{16\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{3}+\frac{3\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}+\frac{4\,a}{3}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(3*b*x)/8 - ((4*a)/3 + (3*b*tan(e/2 + (f*x)/2))/4 + (16*a*tan(e/2 + (f*x)/2)^2)/3 + 4*a*tan(e/2 + (f*x)/2)^4 + (11*b*tan(e/2 + (f*x)/2)^3)/4 - (11*b*tan(e/2 + (f*x)/2)^5)/4 - (3*b*tan(e/2 + (f*x)/2)^7)/4)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^4)","B"
150,1,68,55,8.574663,"\text{Not used}","int(sin(e + f*x)^2*(a + b*sin(e + f*x)),x)","\frac{a\,x}{2}-\frac{-a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+4\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{4\,b}{3}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(a*x)/2 - ((4*b)/3 + a*tan(e/2 + (f*x)/2) - a*tan(e/2 + (f*x)/2)^5 + 4*b*tan(e/2 + (f*x)/2)^2)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^3)","B"
151,1,68,39,7.190932,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x)),x)","\frac{b\,x}{2}-\frac{-b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,a}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(b*x)/2 - (2*a + b*tan(e/2 + (f*x)/2) + 2*a*tan(e/2 + (f*x)/2)^2 - b*tan(e/2 + (f*x)/2)^3)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^2)","B"
152,1,25,16,6.511354,"\text{Not used}","int(a + b*sin(e + f*x),x)","a\,x-\frac{2\,b}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x - (2*b)/(f*(tan(e/2 + (f*x)/2)^2 + 1))","B"
153,1,85,17,6.796744,"\text{Not used}","int((a + b*sin(e + f*x))/sin(e + f*x),x)","\frac{a\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}+\frac{2\,b\,\mathrm{atan}\left(\frac{b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-b\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}","Not used",1,"(a*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/f + (2*b*atan((b*cos(e/2 + (f*x)/2) + a*sin(e/2 + (f*x)/2))/(a*cos(e/2 + (f*x)/2) - b*sin(e/2 + (f*x)/2))))/f","B"
154,1,28,26,6.758884,"\text{Not used}","int((a + b*sin(e + f*x))/sin(e + f*x)^2,x)","\frac{b\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{f}-\frac{a\,\mathrm{cot}\left(e+f\,x\right)}{f}","Not used",1,"(b*log(tan(e/2 + (f*x)/2)))/f - (a*cot(e + f*x))/f","B"
155,1,81,48,6.723417,"\text{Not used}","int((a + b*sin(e + f*x))/sin(e + f*x)^3,x)","\frac{b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a}{2}+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{4\,f}+\frac{a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{2\,f}","Not used",1,"(b*tan(e/2 + (f*x)/2))/(2*f) - (cot(e/2 + (f*x)/2)^2*(a/2 + 2*b*tan(e/2 + (f*x)/2)))/(4*f) + (a*tan(e/2 + (f*x)/2)^2)/(8*f) + (a*log(tan(e/2 + (f*x)/2)))/(2*f)","B"
156,1,111,64,6.741431,"\text{Not used}","int((a + b*sin(e + f*x))/sin(e + f*x)^4,x)","\frac{3\,a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8\,f}+\frac{a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24\,f}+\frac{b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{2\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{a}{3}\right)}{8\,f}","Not used",1,"(3*a*tan(e/2 + (f*x)/2))/(8*f) + (a*tan(e/2 + (f*x)/2)^3)/(24*f) + (b*tan(e/2 + (f*x)/2)^2)/(8*f) + (b*log(tan(e/2 + (f*x)/2)))/(2*f) - (cot(e/2 + (f*x)/2)^3*(a/3 + b*tan(e/2 + (f*x)/2) + 3*a*tan(e/2 + (f*x)/2)^2))/(8*f)","B"
157,1,157,112,10.365621,"\text{Not used}","int(sin(e + f*x)^3*(a + b*sin(e + f*x))^2,x)","\frac{3\,a\,b\,x}{4}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{20\,a^2}{3}+\frac{16\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{28\,a^2}{3}+\frac{32\,b^2}{3}\right)+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+\frac{4\,a^2}{3}+\frac{16\,b^2}{15}+7\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-7\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7-\frac{3\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{2}+\frac{3\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a*b*x)/4 - (tan(e/2 + (f*x)/2)^2*((20*a^2)/3 + (16*b^2)/3) + tan(e/2 + (f*x)/2)^4*((28*a^2)/3 + (32*b^2)/3) + 4*a^2*tan(e/2 + (f*x)/2)^6 + (4*a^2)/3 + (16*b^2)/15 + 7*a*b*tan(e/2 + (f*x)/2)^3 - 7*a*b*tan(e/2 + (f*x)/2)^7 - (3*a*b*tan(e/2 + (f*x)/2)^9)/2 + (3*a*b*tan(e/2 + (f*x)/2))/2)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
158,1,85,101,6.927150,"\text{Not used}","int(sin(e + f*x)^2*(a + b*sin(e + f*x))^2,x)","\frac{\frac{3\,b^2\,\sin\left(4\,e+4\,f\,x\right)}{4}-6\,b^2\,\sin\left(2\,e+2\,f\,x\right)-6\,a^2\,\sin\left(2\,e+2\,f\,x\right)-36\,a\,b\,\cos\left(e+f\,x\right)+4\,a\,b\,\cos\left(3\,e+3\,f\,x\right)+12\,a^2\,f\,x+9\,b^2\,f\,x}{24\,f}","Not used",1,"((3*b^2*sin(4*e + 4*f*x))/4 - 6*b^2*sin(2*e + 2*f*x) - 6*a^2*sin(2*e + 2*f*x) - 36*a*b*cos(e + f*x) + 4*a*b*cos(3*e + 3*f*x) + 12*a^2*f*x + 9*b^2*f*x)/(24*f)","B"
159,1,103,71,8.992790,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x))^2,x)","a\,b\,x-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+2\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,a^2+\frac{4\,b^2}{3}-2\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+2\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"a*b*x - (tan(e/2 + (f*x)/2)^2*(4*a^2 + 4*b^2) + 2*a^2*tan(e/2 + (f*x)/2)^4 + 2*a^2 + (4*b^2)/3 - 2*a*b*tan(e/2 + (f*x)/2)^5 + 2*a*b*tan(e/2 + (f*x)/2))/(f*(tan(e/2 + (f*x)/2)^2 + 1)^3)","B"
160,1,44,50,6.790440,"\text{Not used}","int((a + b*sin(e + f*x))^2,x)","-\frac{\frac{b^2\,\sin\left(2\,e+2\,f\,x\right)}{2}+4\,a\,b\,\cos\left(e+f\,x\right)-2\,a^2\,f\,x-b^2\,f\,x}{2\,f}","Not used",1,"-((b^2*sin(2*e + 2*f*x))/2 + 4*a*b*cos(e + f*x) - 2*a^2*f*x - b^2*f*x)/(2*f)","B"
161,1,125,35,6.479735,"\text{Not used}","int((a + b*sin(e + f*x))^2/sin(e + f*x),x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{f}-\frac{2\,b^2}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{4\,a\,b\,\mathrm{atan}\left(\frac{16\,a^2\,b^2}{8\,a^3\,b-16\,a^2\,b^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}+\frac{8\,a^3\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8\,a^3\,b-16\,a^2\,b^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}","Not used",1,"(a^2*log(tan(e/2 + (f*x)/2)))/f - (2*b^2)/(f*(tan(e/2 + (f*x)/2)^2 + 1)) + (4*a*b*atan((16*a^2*b^2)/(8*a^3*b - 16*a^2*b^2*tan(e/2 + (f*x)/2)) + (8*a^3*b*tan(e/2 + (f*x)/2))/(8*a^3*b - 16*a^2*b^2*tan(e/2 + (f*x)/2))))/f","B"
162,1,105,34,6.833768,"\text{Not used}","int((a + b*sin(e + f*x))^2/sin(e + f*x)^2,x)","\frac{2\,b^2\,\mathrm{atan}\left(\frac{b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-b\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}-\frac{a^2\,\mathrm{cot}\left(e+f\,x\right)}{f}+\frac{2\,a\,b\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}","Not used",1,"(2*b^2*atan((b*cos(e/2 + (f*x)/2) + 2*a*sin(e/2 + (f*x)/2))/(2*a*cos(e/2 + (f*x)/2) - b*sin(e/2 + (f*x)/2))))/f - (a^2*cot(e + f*x))/f + (2*a*b*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/f","B"
163,1,92,59,6.494438,"\text{Not used}","int((a + b*sin(e + f*x))^2/sin(e + f*x)^3,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}+\frac{\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)\,\left(\frac{a^2}{2}+b^2\right)}{f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^2}{8}+b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a\right)}{f}+\frac{a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f}","Not used",1,"(a^2*tan(e/2 + (f*x)/2)^2)/(8*f) + (log(tan(e/2 + (f*x)/2))*(a^2/2 + b^2))/f - (cot(e/2 + (f*x)/2)^2*(a^2/8 + a*b*tan(e/2 + (f*x)/2)))/f + (a*b*tan(e/2 + (f*x)/2))/f","B"
164,1,136,82,6.782737,"\text{Not used}","int((a + b*sin(e + f*x))^2/sin(e + f*x)^4,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24\,f}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{3\,a^2}{8}+\frac{b^2}{2}\right)}{f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,a^2+4\,b^2\right)+\frac{a^2}{3}+2\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{8\,f}+\frac{a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{4\,f}+\frac{a\,b\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{f}","Not used",1,"(a^2*tan(e/2 + (f*x)/2)^3)/(24*f) + (tan(e/2 + (f*x)/2)*((3*a^2)/8 + b^2/2))/f - (cot(e/2 + (f*x)/2)^3*(tan(e/2 + (f*x)/2)^2*(3*a^2 + 4*b^2) + a^2/3 + 2*a*b*tan(e/2 + (f*x)/2)))/(8*f) + (a*b*tan(e/2 + (f*x)/2)^2)/(4*f) + (a*b*log(tan(e/2 + (f*x)/2)))/f","B"
165,1,178,110,6.875837,"\text{Not used}","int((a + b*sin(e + f*x))^2/sin(e + f*x)^5,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)\,\left(\frac{3\,a^2}{8}+\frac{b^2}{2}\right)}{f}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{64\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2+2\,b^2\right)+\frac{a^2}{4}+12\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\frac{4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{3}\right)}{16\,f}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^2}{8}+\frac{b^2}{8}\right)}{f}+\frac{a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{12\,f}+\frac{3\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(log(tan(e/2 + (f*x)/2))*((3*a^2)/8 + b^2/2))/f + (a^2*tan(e/2 + (f*x)/2)^4)/(64*f) - (cot(e/2 + (f*x)/2)^4*(tan(e/2 + (f*x)/2)^2*(2*a^2 + 2*b^2) + a^2/4 + 12*a*b*tan(e/2 + (f*x)/2)^3 + (4*a*b*tan(e/2 + (f*x)/2))/3))/(16*f) + (tan(e/2 + (f*x)/2)^2*(a^2/8 + b^2/8))/f + (a*b*tan(e/2 + (f*x)/2)^3)/(12*f) + (3*a*b*tan(e/2 + (f*x)/2))/(4*f)","B"
166,1,417,171,8.401471,"\text{Not used}","int(sin(e + f*x)^3*(a + b*sin(e + f*x))^3,x)","\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(18\,a^2+5\,b^2\right)}{8\,\left(\frac{9\,a^2\,b}{4}+\frac{5\,b^3}{8}\right)}\right)\,\left(18\,a^2+5\,b^2\right)}{8\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{9\,a^2\,b}{4}+\frac{5\,b^3}{8}\right)+4\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+\frac{16\,a\,b^2}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(16\,a^3+48\,a\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{40\,a^3}{3}+32\,a\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(8\,a^3+\frac{96\,a\,b^2}{5}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{9\,a^2\,b}{4}+\frac{5\,b^3}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{21\,a^2\,b}{2}+\frac{33\,b^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{21\,a^2\,b}{2}+\frac{33\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{51\,a^2\,b}{4}+\frac{85\,b^3}{24}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{51\,a^2\,b}{4}+\frac{85\,b^3}{24}\right)+\frac{4\,a^3}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{b\,\left(18\,a^2+5\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{8\,f}","Not used",1,"(b*atan((b*tan(e/2 + (f*x)/2)*(18*a^2 + 5*b^2))/(8*((9*a^2*b)/4 + (5*b^3)/8)))*(18*a^2 + 5*b^2))/(8*f) - (tan(e/2 + (f*x)/2)*((9*a^2*b)/4 + (5*b^3)/8) + 4*a^3*tan(e/2 + (f*x)/2)^8 + (16*a*b^2)/5 + tan(e/2 + (f*x)/2)^4*(48*a*b^2 + 16*a^3) + tan(e/2 + (f*x)/2)^6*(32*a*b^2 + (40*a^3)/3) + tan(e/2 + (f*x)/2)^2*((96*a*b^2)/5 + 8*a^3) - tan(e/2 + (f*x)/2)^11*((9*a^2*b)/4 + (5*b^3)/8) + tan(e/2 + (f*x)/2)^5*((21*a^2*b)/2 + (33*b^3)/4) - tan(e/2 + (f*x)/2)^7*((21*a^2*b)/2 + (33*b^3)/4) + tan(e/2 + (f*x)/2)^3*((51*a^2*b)/4 + (85*b^3)/24) - tan(e/2 + (f*x)/2)^9*((51*a^2*b)/4 + (85*b^3)/24) + (4*a^3)/3)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1)) - (b*(18*a^2 + 5*b^2)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(8*f)","B"
167,1,328,160,8.170818,"\text{Not used}","int(sin(e + f*x)^2*(a + b*sin(e + f*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^2+9\,b^2\right)}{4\,\left(a^3+\frac{9\,a\,b^2}{4}\right)}\right)\,\left(4\,a^2+9\,b^2\right)}{4\,f}-\frac{4\,a^2\,b-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(a^3+\frac{9\,a\,b^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,a^3+\frac{21\,a\,b^2}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,a^3+\frac{21\,a\,b^2}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(20\,a^2\,b+\frac{16\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(28\,a^2\,b+\frac{32\,b^3}{3}\right)+\frac{16\,b^3}{15}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^3+\frac{9\,a\,b^2}{4}\right)+12\,a^2\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(4\,a^2+9\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(a*atan((a*tan(e/2 + (f*x)/2)*(4*a^2 + 9*b^2))/(4*((9*a*b^2)/4 + a^3)))*(4*a^2 + 9*b^2))/(4*f) - (4*a^2*b - tan(e/2 + (f*x)/2)^9*((9*a*b^2)/4 + a^3) + tan(e/2 + (f*x)/2)^3*((21*a*b^2)/2 + 2*a^3) - tan(e/2 + (f*x)/2)^7*((21*a*b^2)/2 + 2*a^3) + tan(e/2 + (f*x)/2)^2*(20*a^2*b + (16*b^3)/3) + tan(e/2 + (f*x)/2)^4*(28*a^2*b + (32*b^3)/3) + (16*b^3)/15 + tan(e/2 + (f*x)/2)*((9*a*b^2)/4 + a^3) + 12*a^2*b*tan(e/2 + (f*x)/2)^6)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1)) - (a*(4*a^2 + 9*b^2)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
168,1,313,121,8.084544,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x))^3,x)","\frac{3\,b\,\mathrm{atan}\left(\frac{3\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^2+b^2\right)}{4\,\left(3\,a^2\,b+\frac{3\,b^3}{4}\right)}\right)\,\left(4\,a^2+b^2\right)}{4\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^2\,b+\frac{3\,b^3}{4}\right)+2\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+4\,a\,b^2+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,a^3+16\,a\,b^2\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(3\,a^2\,b+\frac{3\,b^3}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,a^2\,b+\frac{11\,b^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(3\,a^2\,b+\frac{11\,b^3}{4}\right)+2\,a^3}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{3\,b\,\left(4\,a^2+b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(3*b*atan((3*b*tan(e/2 + (f*x)/2)*(4*a^2 + b^2))/(4*(3*a^2*b + (3*b^3)/4)))*(4*a^2 + b^2))/(4*f) - (tan(e/2 + (f*x)/2)*(3*a^2*b + (3*b^3)/4) + 2*a^3*tan(e/2 + (f*x)/2)^6 + 4*a*b^2 + tan(e/2 + (f*x)/2)^4*(12*a*b^2 + 6*a^3) + tan(e/2 + (f*x)/2)^2*(16*a*b^2 + 6*a^3) - tan(e/2 + (f*x)/2)^7*(3*a^2*b + (3*b^3)/4) + tan(e/2 + (f*x)/2)^3*(3*a^2*b + (11*b^3)/4) - tan(e/2 + (f*x)/2)^5*(3*a^2*b + (11*b^3)/4) + 2*a^3)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1)) - (3*b*(4*a^2 + b^2)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
169,1,127,90,6.738364,"\text{Not used}","int((a + b*sin(e + f*x))^3,x)","a^3\,x-\frac{4\,b^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{f}+\frac{8\,b^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6}{3\,f}+\frac{3\,a\,b^2\,x}{2}-\frac{6\,a^2\,b\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{f}-\frac{6\,a\,b^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f}+\frac{3\,a\,b^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f}","Not used",1,"a^3*x - (4*b^3*cos(e/2 + (f*x)/2)^4)/f + (8*b^3*cos(e/2 + (f*x)/2)^6)/(3*f) + (3*a*b^2*x)/2 - (6*a^2*b*cos(e/2 + (f*x)/2)^2)/f - (6*a*b^2*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2))/f + (3*a*b^2*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2))/f","B"
170,1,259,74,6.791034,"\text{Not used}","int((a + b*sin(e + f*x))^3/sin(e + f*x),x)","\frac{a^3\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}-\frac{b^3\,\mathrm{atan}\left(\frac{2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^3+6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^3}{-2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^3+6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^3}\right)}{f}-\frac{b^3\,\sin\left(2\,e+2\,f\,x\right)}{4\,f}-\frac{6\,a^2\,b\,\mathrm{atan}\left(\frac{2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^3+6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^3}{-2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^3+6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^3}\right)}{f}-\frac{3\,a\,b^2\,\cos\left(e+f\,x\right)}{f}","Not used",1,"(a^3*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/f - (b^3*atan((b^3*cos(e/2 + (f*x)/2) + 2*a^3*sin(e/2 + (f*x)/2) + 6*a^2*b*cos(e/2 + (f*x)/2))/(b^3*sin(e/2 + (f*x)/2) - 2*a^3*cos(e/2 + (f*x)/2) + 6*a^2*b*sin(e/2 + (f*x)/2))))/f - (b^3*sin(2*e + 2*f*x))/(4*f) - (6*a^2*b*atan((b^3*cos(e/2 + (f*x)/2) + 2*a^3*sin(e/2 + (f*x)/2) + 6*a^2*b*cos(e/2 + (f*x)/2))/(b^3*sin(e/2 + (f*x)/2) - 2*a^3*cos(e/2 + (f*x)/2) + 6*a^2*b*sin(e/2 + (f*x)/2))))/f - (3*a*b^2*cos(e + f*x))/f","B"
171,1,194,68,6.720368,"\text{Not used}","int((a + b*sin(e + f*x))^3/sin(e + f*x)^2,x)","\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,f}-\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a^3+4\,b^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f\,\left(2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}+\frac{6\,a\,b^2\,\mathrm{atan}\left(\frac{36\,a^2\,b^4}{36\,a^3\,b^3-36\,a^2\,b^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}+\frac{36\,a^3\,b^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{36\,a^3\,b^3-36\,a^2\,b^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}+\frac{3\,a^2\,b\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{f}","Not used",1,"(a^3*tan(e/2 + (f*x)/2))/(2*f) - (a^3*tan(e/2 + (f*x)/2)^2 + a^3 + 4*b^3*tan(e/2 + (f*x)/2))/(f*(2*tan(e/2 + (f*x)/2) + 2*tan(e/2 + (f*x)/2)^3)) + (6*a*b^2*atan((36*a^2*b^4)/(36*a^3*b^3 - 36*a^2*b^4*tan(e/2 + (f*x)/2)) + (36*a^3*b^3*tan(e/2 + (f*x)/2))/(36*a^3*b^3 - 36*a^2*b^4*tan(e/2 + (f*x)/2))))/f + (3*a^2*b*log(tan(e/2 + (f*x)/2)))/f","B"
172,1,234,79,6.962882,"\text{Not used}","int((a + b*sin(e + f*x))^3/sin(e + f*x)^3,x)","\frac{2\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^3+6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a\,b^2+2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^3}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^3+6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a\,b^2-2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^3}\right)}{f}-\frac{a^3\,{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}+\frac{a^3\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{2\,f}-\frac{3\,a^2\,b\,\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,f}+\frac{3\,a\,b^2\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}+\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,f}","Not used",1,"(2*b^3*atan((2*b^3*cos(e/2 + (f*x)/2) + a^3*sin(e/2 + (f*x)/2) + 6*a*b^2*sin(e/2 + (f*x)/2))/(a^3*cos(e/2 + (f*x)/2) - 2*b^3*sin(e/2 + (f*x)/2) + 6*a*b^2*cos(e/2 + (f*x)/2))))/f - (a^3*cot(e/2 + (f*x)/2)^2)/(8*f) + (a^3*tan(e/2 + (f*x)/2)^2)/(8*f) + (a^3*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(2*f) - (3*a^2*b*cot(e/2 + (f*x)/2))/(2*f) + (3*a*b^2*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/f + (3*a^2*b*tan(e/2 + (f*x)/2))/(2*f)","B"
173,1,150,109,6.784847,"\text{Not used}","int((a + b*sin(e + f*x))^3/sin(e + f*x)^4,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)\,\left(\frac{3\,a^2\,b}{2}+b^3\right)}{f}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,a^3+12\,a\,b^2\right)+\frac{a^3}{3}+3\,a^2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{8\,f}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{3\,a^3}{8}+\frac{3\,a\,b^2}{2}\right)}{f}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}","Not used",1,"(log(tan(e/2 + (f*x)/2))*((3*a^2*b)/2 + b^3))/f + (a^3*tan(e/2 + (f*x)/2)^3)/(24*f) - (cot(e/2 + (f*x)/2)^3*(tan(e/2 + (f*x)/2)^2*(12*a*b^2 + 3*a^3) + a^3/3 + 3*a^2*b*tan(e/2 + (f*x)/2)))/(8*f) + (tan(e/2 + (f*x)/2)*((3*a*b^2)/2 + (3*a^3)/8))/f + (3*a^2*b*tan(e/2 + (f*x)/2)^2)/(8*f)","B"
174,1,203,134,6.857635,"\text{Not used}","int((a + b*sin(e + f*x))^3/sin(e + f*x)^5,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{64\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^3+6\,a\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(18\,a^2\,b+8\,b^3\right)+\frac{a^3}{4}+2\,a^2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{16\,f}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^3}{8}+\frac{3\,a\,b^2}{8}\right)}{f}+\frac{\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)\,\left(\frac{3\,a^3}{8}+\frac{3\,a\,b^2}{2}\right)}{f}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{9\,a^2\,b}{8}+\frac{b^3}{2}\right)}{f}+\frac{a^2\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{8\,f}","Not used",1,"(a^3*tan(e/2 + (f*x)/2)^4)/(64*f) - (cot(e/2 + (f*x)/2)^4*(tan(e/2 + (f*x)/2)^2*(6*a*b^2 + 2*a^3) + tan(e/2 + (f*x)/2)^3*(18*a^2*b + 8*b^3) + a^3/4 + 2*a^2*b*tan(e/2 + (f*x)/2)))/(16*f) + (tan(e/2 + (f*x)/2)^2*((3*a*b^2)/8 + a^3/8))/f + (log(tan(e/2 + (f*x)/2))*((3*a*b^2)/2 + (3*a^3)/8))/f + (tan(e/2 + (f*x)/2)*((9*a^2*b)/8 + b^3/2))/f + (a^2*b*tan(e/2 + (f*x)/2)^3)/(8*f)","B"
175,1,114,137,6.951904,"\text{Not used}","int((a + b*sin(e + f*x))^4,x)","\frac{\frac{3\,b^4\,\sin\left(4\,e+4\,f\,x\right)}{4}-6\,b^4\,\sin\left(2\,e+2\,f\,x\right)+8\,a\,b^3\,\cos\left(3\,e+3\,f\,x\right)-36\,a^2\,b^2\,\sin\left(2\,e+2\,f\,x\right)-72\,a\,b^3\,\cos\left(e+f\,x\right)-96\,a^3\,b\,\cos\left(e+f\,x\right)+24\,a^4\,f\,x+9\,b^4\,f\,x+72\,a^2\,b^2\,f\,x}{24\,f}","Not used",1,"((3*b^4*sin(4*e + 4*f*x))/4 - 6*b^4*sin(2*e + 2*f*x) + 8*a*b^3*cos(3*e + 3*f*x) - 36*a^2*b^2*sin(2*e + 2*f*x) - 72*a*b^3*cos(e + f*x) - 96*a^3*b*cos(e + f*x) + 24*a^4*f*x + 9*b^4*f*x + 72*a^2*b^2*f*x)/(24*f)","B"
176,1,1075,110,7.221027,"\text{Not used}","int(sin(x)^4/(a + b*sin(x)),x)","-\frac{\frac{2\,\left(3\,a^2+2\,b^2\right)}{3\,b^3}+\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{b^2}+\frac{2\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2+b^2\right)}{b^3}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{a\,\mathrm{atan}\left(\frac{8\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^4+\frac{40\,a^6}{b^2}+\frac{48\,a^8}{b^4}}+\frac{40\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{40\,a^6+8\,a^4\,b^2+\frac{48\,a^8}{b^2}}+\frac{48\,a^8\,\mathrm{tan}\left(\frac{x}{2}\right)}{48\,a^8+40\,a^6\,b^2+8\,a^4\,b^4}\right)\,\left(2\,a^2+b^2\right)}{b^4}-\frac{a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(\frac{8\,\left(4\,a^8\,b^3+4\,a^6\,b^5+a^4\,b^7\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^3+4\,a^7\,b^5+7\,a^5\,b^7+2\,a^3\,b^9\right)}{b^9}+\frac{a^4\,\left(\frac{8\,\left(2\,a^4\,b^8+2\,a^2\,b^{10}\right)}{b^8}+\frac{64\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{a^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^4\,\sqrt{b^2-a^2}}\right)}{b^4\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^4\,\sqrt{b^2-a^2}}+\frac{a^4\,\left(\frac{8\,\left(4\,a^8\,b^3+4\,a^6\,b^5+a^4\,b^7\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^3+4\,a^7\,b^5+7\,a^5\,b^7+2\,a^3\,b^9\right)}{b^9}-\frac{a^4\,\left(\frac{8\,\left(2\,a^4\,b^8+2\,a^2\,b^{10}\right)}{b^8}+\frac{64\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}-\frac{a^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^4\,\sqrt{b^2-a^2}}\right)}{b^4\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^4\,\sqrt{b^2-a^2}}}{\frac{16\,\left(2\,a^{10}+a^8\,b^2\right)}{b^8}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{11}+8\,a^9\,b^2+2\,a^7\,b^4\right)}{b^9}+\frac{a^4\,\left(\frac{8\,\left(4\,a^8\,b^3+4\,a^6\,b^5+a^4\,b^7\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^3+4\,a^7\,b^5+7\,a^5\,b^7+2\,a^3\,b^9\right)}{b^9}+\frac{a^4\,\left(\frac{8\,\left(2\,a^4\,b^8+2\,a^2\,b^{10}\right)}{b^8}+\frac{64\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{a^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^4\,\sqrt{b^2-a^2}}\right)}{b^4\,\sqrt{b^2-a^2}}\right)}{b^4\,\sqrt{b^2-a^2}}-\frac{a^4\,\left(\frac{8\,\left(4\,a^8\,b^3+4\,a^6\,b^5+a^4\,b^7\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^3+4\,a^7\,b^5+7\,a^5\,b^7+2\,a^3\,b^9\right)}{b^9}-\frac{a^4\,\left(\frac{8\,\left(2\,a^4\,b^8+2\,a^2\,b^{10}\right)}{b^8}+\frac{64\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}-\frac{a^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^4\,\sqrt{b^2-a^2}}\right)}{b^4\,\sqrt{b^2-a^2}}\right)}{b^4\,\sqrt{b^2-a^2}}}\right)\,2{}\mathrm{i}}{b^4\,\sqrt{b^2-a^2}}","Not used",1,"- ((2*(3*a^2 + 2*b^2))/(3*b^3) + (a*tan(x/2)^5)/b^2 + (2*a^2*tan(x/2)^4)/b^3 + (4*tan(x/2)^2*(a^2 + b^2))/b^3 - (a*tan(x/2))/b^2)/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1) - (a*atan((8*a^4*tan(x/2))/(8*a^4 + (40*a^6)/b^2 + (48*a^8)/b^4) + (40*a^6*tan(x/2))/(40*a^6 + 8*a^4*b^2 + (48*a^8)/b^2) + (48*a^8*tan(x/2))/(48*a^8 + 8*a^4*b^4 + 40*a^6*b^2))*(2*a^2 + b^2))/b^4 - (a^4*atan(((a^4*((8*(a^4*b^7 + 4*a^6*b^5 + 4*a^8*b^3))/b^8 + (8*tan(x/2)*(2*a^3*b^9 + 7*a^5*b^7 + 4*a^7*b^5 - 8*a^9*b^3))/b^9 + (a^4*((8*(2*a^2*b^10 + 2*a^4*b^8))/b^8 + (64*a^5*tan(x/2))/b + (a^4*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^4*(b^2 - a^2)^(1/2))))/(b^4*(b^2 - a^2)^(1/2)))*1i)/(b^4*(b^2 - a^2)^(1/2)) + (a^4*((8*(a^4*b^7 + 4*a^6*b^5 + 4*a^8*b^3))/b^8 + (8*tan(x/2)*(2*a^3*b^9 + 7*a^5*b^7 + 4*a^7*b^5 - 8*a^9*b^3))/b^9 - (a^4*((8*(2*a^2*b^10 + 2*a^4*b^8))/b^8 + (64*a^5*tan(x/2))/b - (a^4*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^4*(b^2 - a^2)^(1/2))))/(b^4*(b^2 - a^2)^(1/2)))*1i)/(b^4*(b^2 - a^2)^(1/2)))/((16*(2*a^10 + a^8*b^2))/b^8 + (16*tan(x/2)*(8*a^11 + 2*a^7*b^4 + 8*a^9*b^2))/b^9 + (a^4*((8*(a^4*b^7 + 4*a^6*b^5 + 4*a^8*b^3))/b^8 + (8*tan(x/2)*(2*a^3*b^9 + 7*a^5*b^7 + 4*a^7*b^5 - 8*a^9*b^3))/b^9 + (a^4*((8*(2*a^2*b^10 + 2*a^4*b^8))/b^8 + (64*a^5*tan(x/2))/b + (a^4*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^4*(b^2 - a^2)^(1/2))))/(b^4*(b^2 - a^2)^(1/2))))/(b^4*(b^2 - a^2)^(1/2)) - (a^4*((8*(a^4*b^7 + 4*a^6*b^5 + 4*a^8*b^3))/b^8 + (8*tan(x/2)*(2*a^3*b^9 + 7*a^5*b^7 + 4*a^7*b^5 - 8*a^9*b^3))/b^9 - (a^4*((8*(2*a^2*b^10 + 2*a^4*b^8))/b^8 + (64*a^5*tan(x/2))/b - (a^4*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^4*(b^2 - a^2)^(1/2))))/(b^4*(b^2 - a^2)^(1/2))))/(b^4*(b^2 - a^2)^(1/2))))*2i)/(b^4*(b^2 - a^2)^(1/2))","B"
177,1,1004,82,7.079967,"\text{Not used}","int(sin(x)^3/(a + b*sin(x)),x)","\frac{\frac{2\,a}{b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{b}+\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{\mathrm{atan}\left(\frac{40\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a\,b^2+40\,a^3+\frac{48\,a^5}{b^2}}+\frac{48\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{48\,a^5+40\,a^3\,b^2+8\,a\,b^4}+\frac{8\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a\,b+\frac{40\,a^3}{b}+\frac{48\,a^5}{b^3}}\right)\,\left(a^2\,2{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^3}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^2+4\,a^4\,b^4+a^2\,b^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^2+4\,a^5\,b^4+7\,a^3\,b^6+2\,a\,b^8\right)}{b^6}+\frac{a^3\,\left(64\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^3\,b^6+2\,a\,b^8\right)}{b^5}+\frac{a^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^3\,\sqrt{b^2-a^2}}\right)}{b^3\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^3\,\sqrt{b^2-a^2}}+\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^2+4\,a^4\,b^4+a^2\,b^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^2+4\,a^5\,b^4+7\,a^3\,b^6+2\,a\,b^8\right)}{b^6}-\frac{a^3\,\left(64\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^3\,b^6+2\,a\,b^8\right)}{b^5}-\frac{a^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^3\,\sqrt{b^2-a^2}}\right)}{b^3\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^3\,\sqrt{b^2-a^2}}}{\frac{16\,\left(2\,a^7+a^5\,b^2\right)}{b^5}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^8+8\,a^6\,b^2+2\,a^4\,b^4\right)}{b^6}+\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^2+4\,a^4\,b^4+a^2\,b^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^2+4\,a^5\,b^4+7\,a^3\,b^6+2\,a\,b^8\right)}{b^6}+\frac{a^3\,\left(64\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^3\,b^6+2\,a\,b^8\right)}{b^5}+\frac{a^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^3\,\sqrt{b^2-a^2}}\right)}{b^3\,\sqrt{b^2-a^2}}\right)}{b^3\,\sqrt{b^2-a^2}}-\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^2+4\,a^4\,b^4+a^2\,b^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^2+4\,a^5\,b^4+7\,a^3\,b^6+2\,a\,b^8\right)}{b^6}-\frac{a^3\,\left(64\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{8\,\left(2\,a^3\,b^6+2\,a\,b^8\right)}{b^5}-\frac{a^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^3\,\sqrt{b^2-a^2}}\right)}{b^3\,\sqrt{b^2-a^2}}\right)}{b^3\,\sqrt{b^2-a^2}}}\right)\,2{}\mathrm{i}}{b^3\,\sqrt{b^2-a^2}}","Not used",1,"((2*a)/b^2 - tan(x/2)/b + tan(x/2)^3/b + (2*a*tan(x/2)^2)/b^2)/(2*tan(x/2)^2 + tan(x/2)^4 + 1) - (atan((40*a^3*tan(x/2))/(8*a*b^2 + 40*a^3 + (48*a^5)/b^2) + (48*a^5*tan(x/2))/(8*a*b^4 + 48*a^5 + 40*a^3*b^2) + (8*a*b*tan(x/2))/(8*a*b + (40*a^3)/b + (48*a^5)/b^3))*(a^2*2i + b^2*1i)*1i)/b^3 + (a^3*atan(((a^3*((8*(a^2*b^6 + 4*a^4*b^4 + 4*a^6*b^2))/b^5 + (8*tan(x/2)*(2*a*b^8 + 7*a^3*b^6 + 4*a^5*b^4 - 8*a^7*b^2))/b^6 + (a^3*(64*a^4*tan(x/2) + (8*(2*a*b^8 + 2*a^3*b^6))/b^5 + (a^3*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^3*(b^2 - a^2)^(1/2))))/(b^3*(b^2 - a^2)^(1/2)))*1i)/(b^3*(b^2 - a^2)^(1/2)) + (a^3*((8*(a^2*b^6 + 4*a^4*b^4 + 4*a^6*b^2))/b^5 + (8*tan(x/2)*(2*a*b^8 + 7*a^3*b^6 + 4*a^5*b^4 - 8*a^7*b^2))/b^6 - (a^3*(64*a^4*tan(x/2) + (8*(2*a*b^8 + 2*a^3*b^6))/b^5 - (a^3*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^3*(b^2 - a^2)^(1/2))))/(b^3*(b^2 - a^2)^(1/2)))*1i)/(b^3*(b^2 - a^2)^(1/2)))/((16*(2*a^7 + a^5*b^2))/b^5 + (16*tan(x/2)*(8*a^8 + 2*a^4*b^4 + 8*a^6*b^2))/b^6 + (a^3*((8*(a^2*b^6 + 4*a^4*b^4 + 4*a^6*b^2))/b^5 + (8*tan(x/2)*(2*a*b^8 + 7*a^3*b^6 + 4*a^5*b^4 - 8*a^7*b^2))/b^6 + (a^3*(64*a^4*tan(x/2) + (8*(2*a*b^8 + 2*a^3*b^6))/b^5 + (a^3*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^3*(b^2 - a^2)^(1/2))))/(b^3*(b^2 - a^2)^(1/2))))/(b^3*(b^2 - a^2)^(1/2)) - (a^3*((8*(a^2*b^6 + 4*a^4*b^4 + 4*a^6*b^2))/b^5 + (8*tan(x/2)*(2*a*b^8 + 7*a^3*b^6 + 4*a^5*b^4 - 8*a^7*b^2))/b^6 - (a^3*(64*a^4*tan(x/2) + (8*(2*a*b^8 + 2*a^3*b^6))/b^5 - (a^3*(32*a^2*b^3 + (8*tan(x/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^3*(b^2 - a^2)^(1/2))))/(b^3*(b^2 - a^2)^(1/2))))/(b^3*(b^2 - a^2)^(1/2))))*2i)/(b^3*(b^2 - a^2)^(1/2))","B"
178,1,623,61,6.911335,"\text{Not used}","int(sin(x)^2/(a + b*sin(x)),x)","-\frac{2}{b\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}-\frac{a\,x}{b^2}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{32\,a^4}{b}-\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^5\,b-2\,a^3\,b^3\right)}{b^3}+\frac{a^2\,\left(32\,a^2\,b^2+64\,a^3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{a^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^2\,\sqrt{b^2-a^2}}-\frac{a^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^5\,b-2\,a^3\,b^3\right)}{b^3}-\frac{32\,a^4}{b}+\frac{a^2\,\left(32\,a^2\,b^2+64\,a^3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{a^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}}{b^2\,\sqrt{b^2-a^2}}}{\frac{128\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^3}+\frac{a^2\,\left(\frac{32\,a^4}{b}-\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^5\,b-2\,a^3\,b^3\right)}{b^3}+\frac{a^2\,\left(32\,a^2\,b^2+64\,a^3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{a^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}+\frac{a^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^5\,b-2\,a^3\,b^3\right)}{b^3}-\frac{32\,a^4}{b}+\frac{a^2\,\left(32\,a^2\,b^2+64\,a^3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{a^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}\right)}{b^2\,\sqrt{b^2-a^2}}}\right)\,2{}\mathrm{i}}{b^2\,\sqrt{b^2-a^2}}","Not used",1,"- 2/(b*(tan(x/2)^2 + 1)) - (a*x)/b^2 - (a^2*atan(((a^2*((32*a^4)/b - (32*tan(x/2)*(2*a^5*b - 2*a^3*b^3))/b^3 + (a^2*(32*a^2*b^2 + 64*a^3*b*tan(x/2) + (a^2*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2)))*1i)/(b^2*(b^2 - a^2)^(1/2)) - (a^2*((32*tan(x/2)*(2*a^5*b - 2*a^3*b^3))/b^3 - (32*a^4)/b + (a^2*(32*a^2*b^2 + 64*a^3*b*tan(x/2) - (a^2*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2)))*1i)/(b^2*(b^2 - a^2)^(1/2)))/((128*a^5*tan(x/2))/b^3 + (a^2*((32*a^4)/b - (32*tan(x/2)*(2*a^5*b - 2*a^3*b^3))/b^3 + (a^2*(32*a^2*b^2 + 64*a^3*b*tan(x/2) + (a^2*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2)) + (a^2*((32*tan(x/2)*(2*a^5*b - 2*a^3*b^3))/b^3 - (32*a^4)/b + (a^2*(32*a^2*b^2 + 64*a^3*b*tan(x/2) - (a^2*(32*a^2*b^3 + (32*tan(x/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2))))/(b^2*(b^2 - a^2)^(1/2))))*2i)/(b^2*(b^2 - a^2)^(1/2))","B"
179,1,101,50,6.703627,"\text{Not used}","int(sin(x)/(a + b*sin(x)),x)","\frac{x}{b}-\frac{2\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)\,a^4-\cos\left(\frac{x}{2}\right)\,a^3\,b-3\,\sin\left(\frac{x}{2}\right)\,a^2\,b^2+\cos\left(\frac{x}{2}\right)\,a\,b^3+2\,\sin\left(\frac{x}{2}\right)\,b^4}{{\left(b^2-a^2\right)}^{3/2}\,\left(2\,b\,\sin\left(\frac{x}{2}\right)+a\,\cos\left(\frac{x}{2}\right)\right)}\right)}{b\,\sqrt{b^2-a^2}}","Not used",1,"x/b - (2*a*atanh((a^4*sin(x/2) + 2*b^4*sin(x/2) - 3*a^2*b^2*sin(x/2) + a*b^3*cos(x/2) - a^3*b*cos(x/2))/((b^2 - a^2)^(3/2)*(2*b*sin(x/2) + a*cos(x/2)))))/(b*(b^2 - a^2)^(1/2))","B"
180,1,45,40,6.882667,"\text{Not used}","int(1/(a + b*sin(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{b}{\sqrt{a^2-b^2}}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}","Not used",1,"(2*atan(b/(a^2 - b^2)^(1/2) + (a*tan(x/2))/(a^2 - b^2)^(1/2)))/(a^2 - b^2)^(1/2)","B"
181,1,122,53,6.856678,"\text{Not used}","int(1/(sin(x)*(a + b*sin(x))),x)","\frac{\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{a}+\frac{2\,b\,\mathrm{atanh}\left(\frac{\sqrt{b^2-a^2}\,\left(-1{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^2+2{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a\,b+4{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,b^2\right)}{1{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^3+3{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^2\,b-2{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a\,b^2-4{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,b^3}\right)}{a\,\sqrt{b^2-a^2}}","Not used",1,"log(sin(x/2)/cos(x/2))/a + (2*b*atanh(((b^2 - a^2)^(1/2)*(b^2*sin(x/2)*4i - a^2*sin(x/2)*1i + a*b*cos(x/2)*2i))/(a^3*cos(x/2)*1i - b^3*sin(x/2)*4i - a*b^2*cos(x/2)*2i + a^2*b*sin(x/2)*3i)))/(a*(b^2 - a^2)^(1/2))","B"
182,1,179,62,7.006486,"\text{Not used}","int(1/(sin(x)^2*(a + b*sin(x))),x)","\frac{b^3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-a^2\,b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)+b^2\,\mathrm{atan}\left(\frac{-a^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a\,b\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{-a^3-3\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b+2\,a\,b^2+4\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^4-a^2\,b^2}+\frac{a\,b^2-a^3}{a^4\,\mathrm{tan}\left(x\right)-a^2\,b^2\,\mathrm{tan}\left(x\right)}","Not used",1,"(b^3*log(tan(x/2)) - a^2*b*log(tan(x/2)) + b^2*atan((b^2*tan(x/2)*(b^2 - a^2)^(1/2)*4i - a^2*tan(x/2)*(b^2 - a^2)^(1/2)*1i + a*b*(b^2 - a^2)^(1/2)*2i)/(4*b^3*tan(x/2) + 2*a*b^2 - a^3 - 3*a^2*b*tan(x/2)))*(b^2 - a^2)^(1/2)*2i)/(a^4 - a^2*b^2) + (a*b^2 - a^3)/(a^4*tan(x) - a^2*b^2*tan(x))","B"
183,1,531,84,7.387732,"\text{Not used}","int(1/(sin(x)^3*(a + b*sin(x))),x)","\frac{a^4\,\left(\frac{\cos\left(x\right)}{2}-\frac{\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{4}+\frac{\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{4}\right)-a^2\,\left(\frac{b^2\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{4}+\frac{b^2\,\cos\left(x\right)}{2}-\frac{b^2\,\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{4}\right)+\frac{b^4\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{2}-b^3\,\mathrm{atan}\left(\frac{-a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^5+2\,\sin\left(\frac{x}{2}\right)\,a^4\,b+\cos\left(\frac{x}{2}\right)\,a^3\,b^2+4\,\sin\left(\frac{x}{2}\right)\,a^2\,b^3-4\,\cos\left(\frac{x}{2}\right)\,a\,b^4-8\,\sin\left(\frac{x}{2}\right)\,b^5}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-\frac{b^4\,\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{2}+\frac{a\,b^3\,\sin\left(2\,x\right)}{2}-\frac{a^3\,b\,\sin\left(2\,x\right)}{2}+b^3\,\cos\left(2\,x\right)\,\mathrm{atan}\left(\frac{-a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^5+2\,\sin\left(\frac{x}{2}\right)\,a^4\,b+\cos\left(\frac{x}{2}\right)\,a^3\,b^2+4\,\sin\left(\frac{x}{2}\right)\,a^2\,b^3-4\,\cos\left(\frac{x}{2}\right)\,a\,b^4-8\,\sin\left(\frac{x}{2}\right)\,b^5}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\frac{a^5\,\cos\left(2\,x\right)}{2}-\frac{a^5}{2}+\frac{a^3\,b^2}{2}-\frac{a^3\,b^2\,\cos\left(2\,x\right)}{2}}","Not used",1,"(a^4*(cos(x)/2 - log(sin(x/2)/cos(x/2))/4 + (cos(2*x)*log(sin(x/2)/cos(x/2)))/4) - a^2*((b^2*log(sin(x/2)/cos(x/2)))/4 + (b^2*cos(x))/2 - (b^2*cos(2*x)*log(sin(x/2)/cos(x/2)))/4) + (b^4*log(sin(x/2)/cos(x/2)))/2 - b^3*atan((b^4*sin(x/2)*(b^2 - a^2)^(1/2)*8i - a^4*sin(x/2)*(b^2 - a^2)^(1/2)*1i + a*b^3*cos(x/2)*(b^2 - a^2)^(1/2)*4i + a^3*b*cos(x/2)*(b^2 - a^2)^(1/2)*1i)/(a^5*cos(x/2) - 8*b^5*sin(x/2) + a^3*b^2*cos(x/2) + 4*a^2*b^3*sin(x/2) - 4*a*b^4*cos(x/2) + 2*a^4*b*sin(x/2)))*(b^2 - a^2)^(1/2)*1i - (b^4*cos(2*x)*log(sin(x/2)/cos(x/2)))/2 + (a*b^3*sin(2*x))/2 - (a^3*b*sin(2*x))/2 + b^3*cos(2*x)*atan((b^4*sin(x/2)*(b^2 - a^2)^(1/2)*8i - a^4*sin(x/2)*(b^2 - a^2)^(1/2)*1i + a*b^3*cos(x/2)*(b^2 - a^2)^(1/2)*4i + a^3*b*cos(x/2)*(b^2 - a^2)^(1/2)*1i)/(a^5*cos(x/2) - 8*b^5*sin(x/2) + a^3*b^2*cos(x/2) + 4*a^2*b^3*sin(x/2) - 4*a*b^4*cos(x/2) + 2*a^4*b*sin(x/2)))*(b^2 - a^2)^(1/2)*1i)/((a^5*cos(2*x))/2 - a^5/2 + (a^3*b^2)/2 - (a^3*b^2*cos(2*x))/2)","B"
184,1,586,112,7.517476,"\text{Not used}","int(1/(sin(x)^4*(a + b*sin(x))),x)","\frac{a^5\,\left(\frac{\cos\left(3\,x\right)}{12}-\frac{\cos\left(x\right)}{4}\right)-a\,\left(\frac{b^4\,\cos\left(3\,x\right)}{8}-\frac{b^4\,\cos\left(x\right)}{8}\right)+a^4\,\left(\frac{b\,\sin\left(2\,x\right)}{8}-\frac{3\,b\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)}{16}+\frac{b\,\sin\left(3\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{16}\right)-a^2\,\left(\frac{b^3\,\sin\left(2\,x\right)}{8}-\frac{b^3\,\sin\left(3\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{16}+\frac{3\,b^3\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)}{16}\right)+a^3\,\left(\frac{b^2\,\cos\left(3\,x\right)}{24}+\frac{b^2\,\cos\left(x\right)}{8}\right)-\frac{b^5\,\sin\left(3\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{8}+\frac{3\,b^5\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)}{8}+\frac{b^4\,\mathrm{atan}\left(\frac{-a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^5+2\,\sin\left(\frac{x}{2}\right)\,a^4\,b+\cos\left(\frac{x}{2}\right)\,a^3\,b^2+4\,\sin\left(\frac{x}{2}\right)\,a^2\,b^3-4\,\cos\left(\frac{x}{2}\right)\,a\,b^4-8\,\sin\left(\frac{x}{2}\right)\,b^5}\right)\,\sin\left(3\,x\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{4}-\frac{b^4\,\mathrm{atan}\left(\frac{-a^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}+a\,b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^3\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{\cos\left(\frac{x}{2}\right)\,a^5+2\,\sin\left(\frac{x}{2}\right)\,a^4\,b+\cos\left(\frac{x}{2}\right)\,a^3\,b^2+4\,\sin\left(\frac{x}{2}\right)\,a^2\,b^3-4\,\cos\left(\frac{x}{2}\right)\,a\,b^4-8\,\sin\left(\frac{x}{2}\right)\,b^5}\right)\,\sin\left(x\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{4}}{\frac{3\,a^6\,\sin\left(x\right)}{8}-\frac{a^6\,\sin\left(3\,x\right)}{8}+\frac{a^4\,b^2\,\sin\left(3\,x\right)}{8}-\frac{3\,a^4\,b^2\,\sin\left(x\right)}{8}}","Not used",1,"(a^5*(cos(3*x)/12 - cos(x)/4) - a*((b^4*cos(3*x))/8 - (b^4*cos(x))/8) + a^4*((b*sin(2*x))/8 - (3*b*log(sin(x/2)/cos(x/2))*sin(x))/16 + (b*sin(3*x)*log(sin(x/2)/cos(x/2)))/16) - a^2*((b^3*sin(2*x))/8 - (b^3*sin(3*x)*log(sin(x/2)/cos(x/2)))/16 + (3*b^3*log(sin(x/2)/cos(x/2))*sin(x))/16) + a^3*((b^2*cos(3*x))/24 + (b^2*cos(x))/8) - (b^5*sin(3*x)*log(sin(x/2)/cos(x/2)))/8 + (3*b^5*log(sin(x/2)/cos(x/2))*sin(x))/8 + (b^4*atan((b^4*sin(x/2)*(b^2 - a^2)^(1/2)*8i - a^4*sin(x/2)*(b^2 - a^2)^(1/2)*1i + a*b^3*cos(x/2)*(b^2 - a^2)^(1/2)*4i + a^3*b*cos(x/2)*(b^2 - a^2)^(1/2)*1i)/(a^5*cos(x/2) - 8*b^5*sin(x/2) + a^3*b^2*cos(x/2) + 4*a^2*b^3*sin(x/2) - 4*a*b^4*cos(x/2) + 2*a^4*b*sin(x/2)))*sin(3*x)*(b^2 - a^2)^(1/2)*1i)/4 - (b^4*atan((b^4*sin(x/2)*(b^2 - a^2)^(1/2)*8i - a^4*sin(x/2)*(b^2 - a^2)^(1/2)*1i + a*b^3*cos(x/2)*(b^2 - a^2)^(1/2)*4i + a^3*b*cos(x/2)*(b^2 - a^2)^(1/2)*1i)/(a^5*cos(x/2) - 8*b^5*sin(x/2) + a^3*b^2*cos(x/2) + 4*a^2*b^3*sin(x/2) - 4*a*b^4*cos(x/2) + 2*a^4*b*sin(x/2)))*sin(x)*(b^2 - a^2)^(1/2)*3i)/4)/((3*a^6*sin(x))/8 - (a^6*sin(3*x))/8 + (a^4*b^2*sin(3*x))/8 - (3*a^4*b^2*sin(x))/8)","B"
185,1,4368,169,11.883083,"\text{Not used}","int(sin(x)^4/(a + b*sin(x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(7\,a\,b^2-9\,a^3\right)}{b^2\,\left(a^2-b^2\right)}-\frac{2\,\left(3\,a^4-2\,a^2\,b^2\right)}{b^3\,\left(a^2-b^2\right)}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(2\,a\,b^2-3\,a^3\right)}{b^2\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(a\,b^2-3\,a^3\right)}{b^2\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(-3\,a^4+a^2\,b^2+b^4\right)}{b^3\,\left(a^2-b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(6\,a^4-5\,a^2\,b^2+b^4\right)}{b^3\,\left(a^2-b^2\right)}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(54\,a^{11}-81\,a^9\,b^2+9\,a^7\,b^4+4\,a^5\,b^6\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)}{2\,b^4}\right)}{2\,b^4}+\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^4}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)}{2\,b^4}\right)}{2\,b^4}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(216\,a^{12}-432\,a^{10}\,b^2+126\,a^8\,b^4+82\,a^6\,b^6+8\,a^4\,b^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(54\,a^{11}-81\,a^9\,b^2+9\,a^7\,b^4+4\,a^5\,b^6\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(216\,a^{12}-432\,a^{10}\,b^2+126\,a^8\,b^4+82\,a^6\,b^6+8\,a^4\,b^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}-\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3-60\,a^8\,b^5+13\,a^6\,b^7+10\,a^4\,b^9+a^2\,b^{11}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{11}\,b^3+228\,a^9\,b^5-197\,a^7\,b^7+16\,a^5\,b^9+19\,a^3\,b^{11}+2\,a\,b^{13}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8-14\,a^5\,b^{10}+6\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^8\,b^8-56\,a^6\,b^{10}+32\,a^4\,b^{12}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}","Not used",1,"(atan((((a^2*6i + b^2*1i)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) - ((a^2*6i + b^2*1i)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*6i + b^2*1i))/(2*b^4) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9)))/(2*b^4))*1i)/(2*b^4) + ((a^2*6i + b^2*1i)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((a^2*6i + b^2*1i)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*6i + b^2*1i))/(2*b^4) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9)))/(2*b^4))*1i)/(2*b^4))/((16*(54*a^11 + 4*a^5*b^6 + 9*a^7*b^4 - 81*a^9*b^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) - ((a^2*6i + b^2*1i)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) - ((a^2*6i + b^2*1i)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*6i + b^2*1i))/(2*b^4) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9)))/(2*b^4)))/(2*b^4) + ((a^2*6i + b^2*1i)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((a^2*6i + b^2*1i)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*6i + b^2*1i))/(2*b^4) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9)))/(2*b^4)))/(2*b^4) + (16*tan(x/2)*(216*a^12 + 8*a^4*b^8 + 82*a^6*b^6 + 126*a^8*b^4 - 432*a^10*b^2))/(b^13 - 2*a^2*b^11 + a^4*b^9)))*(a^2*6i + b^2*1i)*1i)/b^4 - ((tan(x/2)*(7*a*b^2 - 9*a^3))/(b^2*(a^2 - b^2)) - (2*(3*a^4 - 2*a^2*b^2))/(b^3*(a^2 - b^2)) + (4*tan(x/2)^3*(2*a*b^2 - 3*a^3))/(b^2*(a^2 - b^2)) + (tan(x/2)^5*(a*b^2 - 3*a^3))/(b^2*(a^2 - b^2)) + (2*tan(x/2)^4*(b^4 - 3*a^4 + a^2*b^2))/(b^3*(a^2 - b^2)) - (2*tan(x/2)^2*(6*a^4 + b^4 - 5*a^2*b^2))/(b^3*(a^2 - b^2)))/(a + 2*b*tan(x/2) + 3*a*tan(x/2)^2 + 3*a*tan(x/2)^4 + a*tan(x/2)^6 + 4*b*tan(x/2)^3 + 2*b*tan(x/2)^5) + (a^3*atan(((a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a^3*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a^3*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(54*a^11 + 4*a^5*b^6 + 9*a^7*b^4 - 81*a^9*b^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (16*tan(x/2)*(216*a^12 + 8*a^4*b^8 + 82*a^6*b^6 + 126*a^8*b^4 - 432*a^10*b^2))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (a^3*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) - (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11 + 10*a^4*b^9 + 13*a^6*b^7 - 60*a^8*b^5 + 36*a^10*b^3))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(2*a*b^13 + 19*a^3*b^11 + 16*a^5*b^9 - 197*a^7*b^7 + 228*a^9*b^5 - 72*a^11*b^3))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14 + 6*a^3*b^12 - 14*a^5*b^10 + 6*a^7*b^8))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(32*a^4*b^12 - 56*a^6*b^10 + 24*a^8*b^8))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (a^3*((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(x/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)","B"
186,1,2578,124,9.983088,"\text{Not used}","int(sin(x)^3/(a + b*sin(x))^2,x)","\frac{\frac{2\,\left(a\,b^2-2\,a^3\right)}{b^2\,\left(a^2-b^2\right)}-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{b\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a\,b^2-2\,a^3\right)}{b^2\,\left(a^2-b^2\right)}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2-2\,b^2\right)}{b\,\left(a^2-b^2\right)}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{4\,a\,\mathrm{atan}\left(\frac{512\,a^4\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{512\,a^4\,b^{14}}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{1408\,a^6\,b^{12}}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{1280\,a^8\,b^{10}}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{384\,a^{10}\,b^8}{a^4\,b^5-2\,a^2\,b^7+b^9}}-\frac{384\,a^6\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{512\,a^4\,b^{14}}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{1408\,a^6\,b^{12}}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{1280\,a^8\,b^{10}}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{384\,a^{10}\,b^8}{a^4\,b^5-2\,a^2\,b^7+b^9}}\right)}{b^3}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2-8\,a^6\,b^4+4\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^2+28\,a^7\,b^4-29\,a^5\,b^6+8\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b^6-3\,a^4\,b^8+2\,a^2\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^7\,b^6-10\,a^5\,b^8+6\,a^3\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2-8\,a^6\,b^4+4\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^2+28\,a^7\,b^4-29\,a^5\,b^6+8\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b^6-3\,a^4\,b^8+2\,a^2\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^7\,b^6-10\,a^5\,b^8+6\,a^3\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(4\,a^8-6\,a^6\,b^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(16\,a^9-40\,a^7\,b^2+24\,a^5\,b^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2-8\,a^6\,b^4+4\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^2+28\,a^7\,b^4-29\,a^5\,b^6+8\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b^6-3\,a^4\,b^8+2\,a^2\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^7\,b^6-10\,a^5\,b^8+6\,a^3\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}-\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2-8\,a^6\,b^4+4\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^9\,b^2+28\,a^7\,b^4-29\,a^5\,b^6+8\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b^6-3\,a^4\,b^8+2\,a^2\,b^{10}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^7\,b^6-10\,a^5\,b^8+6\,a^3\,b^{10}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}","Not used",1,"((2*(a*b^2 - 2*a^3))/(b^2*(a^2 - b^2)) - (2*a^2*tan(x/2)^3)/(b*(a^2 - b^2)) + (2*tan(x/2)^2*(a*b^2 - 2*a^3))/(b^2*(a^2 - b^2)) - (2*tan(x/2)*(3*a^2 - 2*b^2))/(b*(a^2 - b^2)))/(a + 2*b*tan(x/2) + 2*a*tan(x/2)^2 + a*tan(x/2)^4 + 2*b*tan(x/2)^3) - (4*a*atan((512*a^4*b^5*tan(x/2))/((512*a^4*b^14)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (1408*a^6*b^12)/(b^9 - 2*a^2*b^7 + a^4*b^5) + (1280*a^8*b^10)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (384*a^10*b^8)/(b^9 - 2*a^2*b^7 + a^4*b^5)) - (384*a^6*b^3*tan(x/2))/((512*a^4*b^14)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (1408*a^6*b^12)/(b^9 - 2*a^2*b^7 + a^4*b^5) + (1280*a^8*b^10)/(b^9 - 2*a^2*b^7 + a^4*b^5) - (384*a^10*b^8)/(b^9 - 2*a^2*b^7 + a^4*b^5))))/b^3 - (a^2*atan(((a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6 - 8*a^6*b^4 + 4*a^8*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(8*a^3*b^8 - 29*a^5*b^6 + 28*a^7*b^4 - 8*a^9*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^2*b^10 - 3*a^4*b^8 + a^6*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(6*a^3*b^10 - 10*a^5*b^8 + 4*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6 - 8*a^6*b^4 + 4*a^8*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(8*a^3*b^8 - 29*a^5*b^6 + 28*a^7*b^4 - 8*a^9*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^2*b^10 - 3*a^4*b^8 + a^6*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(6*a^3*b^10 - 10*a^5*b^8 + 4*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(4*a^8 - 6*a^6*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (64*tan(x/2)*(16*a^9 + 24*a^5*b^4 - 40*a^7*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6 - 8*a^6*b^4 + 4*a^8*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(8*a^3*b^8 - 29*a^5*b^6 + 28*a^7*b^4 - 8*a^9*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^2*b^10 - 3*a^4*b^8 + a^6*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(6*a^3*b^10 - 10*a^5*b^8 + 4*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) - (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6 - 8*a^6*b^4 + 4*a^8*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(8*a^3*b^8 - 29*a^5*b^6 + 28*a^7*b^4 - 8*a^9*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a^2*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^2*b^10 - 3*a^4*b^8 + a^6*b^6))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(6*a^3*b^10 - 10*a^5*b^8 + 4*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(x/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)","B"
187,1,2562,87,9.952855,"\text{Not used}","int(sin(x)^2/(a + b*sin(x))^2,x)","\frac{\frac{2\,a^2}{b\,\left(a^2-b^2\right)}+\frac{2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2-b^2}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{2\,\mathrm{atan}\left(\frac{64\,a^3\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{64\,a^3\,b^9}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{128\,a^5\,b^7}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{192\,a^7\,b^5}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{64\,a^9\,b^3}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{64\,a\,b^{11}}{a^4\,b^2-2\,a^2\,b^4+b^6}}+\frac{64\,a\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{64\,a^3\,b^9}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{128\,a^5\,b^7}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{192\,a^7\,b^5}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{64\,a^9\,b^3}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{64\,a\,b^{11}}{a^4\,b^2-2\,a^2\,b^4+b^6}}-\frac{64\,a^5\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{\frac{64\,a^3\,b^9}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{128\,a^5\,b^7}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{192\,a^7\,b^5}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{64\,a^9\,b^3}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{64\,a\,b^{11}}{a^4\,b^2-2\,a^2\,b^4+b^6}}\right)}{b^2}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b-2\,a^4\,b^3+a^2\,b^5\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+8\,a^5\,b^3-9\,a^3\,b^5+2\,a\,b^7\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a\,b^8-a^3\,b^6\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^6\,b^4-6\,a^4\,b^6+4\,a^2\,b^8\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b-2\,a^4\,b^3+a^2\,b^5\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+8\,a^5\,b^3-9\,a^3\,b^5+2\,a\,b^7\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a\,b^8-a^3\,b^6\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^6\,b^4-6\,a^4\,b^6+4\,a^2\,b^8\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(a^5-2\,a^3\,b^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^6-6\,a^4\,b^2+4\,a^2\,b^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b-2\,a^4\,b^3+a^2\,b^5\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+8\,a^5\,b^3-9\,a^3\,b^5+2\,a\,b^7\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a\,b^8-a^3\,b^6\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^6\,b^4-6\,a^4\,b^6+4\,a^2\,b^8\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}-\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b-2\,a^4\,b^3+a^2\,b^5\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+8\,a^5\,b^3-9\,a^3\,b^5+2\,a\,b^7\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a\,b^8-a^3\,b^6\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^6\,b^4-6\,a^4\,b^6+4\,a^2\,b^8\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}","Not used",1,"((2*a^2)/(b*(a^2 - b^2)) + (2*a*tan(x/2))/(a^2 - b^2))/(a + 2*b*tan(x/2) + a*tan(x/2)^2) - (2*atan((64*a^3*b^3*tan(x/2))/((64*a^3*b^9)/(b^6 - 2*a^2*b^4 + a^4*b^2) + (128*a^5*b^7)/(b^6 - 2*a^2*b^4 + a^4*b^2) - (192*a^7*b^5)/(b^6 - 2*a^2*b^4 + a^4*b^2) + (64*a^9*b^3)/(b^6 - 2*a^2*b^4 + a^4*b^2) - (64*a*b^11)/(b^6 - 2*a^2*b^4 + a^4*b^2)) + (64*a*b^5*tan(x/2))/((64*a^3*b^9)/(b^6 - 2*a^2*b^4 + a^4*b^2) + (128*a^5*b^7)/(b^6 - 2*a^2*b^4 + a^4*b^2) - (192*a^7*b^5)/(b^6 - 2*a^2*b^4 + a^4*b^2) + (64*a^9*b^3)/(b^6 - 2*a^2*b^4 + a^4*b^2) - (64*a*b^11)/(b^6 - 2*a^2*b^4 + a^4*b^2)) - (64*a^5*b*tan(x/2))/((64*a^3*b^9)/(b^6 - 2*a^2*b^4 + a^4*b^2) + (128*a^5*b^7)/(b^6 - 2*a^2*b^4 + a^4*b^2) - (192*a^7*b^5)/(b^6 - 2*a^2*b^4 + a^4*b^2) + (64*a^9*b^3)/(b^6 - 2*a^2*b^4 + a^4*b^2) - (64*a*b^11)/(b^6 - 2*a^2*b^4 + a^4*b^2))))/b^2 + (a*atan(((a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^6*b + a^2*b^5 - 2*a^4*b^3))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(2*a*b^7 - 2*a^7*b - 9*a^3*b^5 + 8*a^5*b^3))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8 - a^3*b^6))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(4*a^2*b^8 - 6*a^4*b^6 + 2*a^6*b^4))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (a*(a^2 - 2*b^2)*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^6*b + a^2*b^5 - 2*a^4*b^3))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(2*a*b^7 - 2*a^7*b - 9*a^3*b^5 + 8*a^5*b^3))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8 - a^3*b^6))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(4*a^2*b^8 - 6*a^4*b^6 + 2*a^6*b^4))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (a*(a^2 - 2*b^2)*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(a^5 - 2*a^3*b^2))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (64*tan(x/2)*(2*a^6 + 4*a^2*b^4 - 6*a^4*b^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^6*b + a^2*b^5 - 2*a^4*b^3))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(2*a*b^7 - 2*a^7*b - 9*a^3*b^5 + 8*a^5*b^3))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8 - a^3*b^6))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(4*a^2*b^8 - 6*a^4*b^6 + 2*a^6*b^4))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (a*(a^2 - 2*b^2)*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) - (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^6*b + a^2*b^5 - 2*a^4*b^3))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(2*a*b^7 - 2*a^7*b - 9*a^3*b^5 + 8*a^5*b^3))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8 - a^3*b^6))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(4*a^2*b^8 - 6*a^4*b^6 + 2*a^6*b^4))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (a*(a^2 - 2*b^2)*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(x/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)","B"
188,1,123,66,6.493663,"\text{Not used}","int(sin(x)/(a + b*sin(x))^2,x)","-\frac{\frac{2\,a}{a^2-b^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2-b^2}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{2\,b\,\mathrm{atan}\left(\frac{\left(a^2-b^2\right)\,\left(\frac{2\,b^2}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}+\frac{2\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}\right)}{2\,b}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"- ((2*a)/(a^2 - b^2) + (2*b*tan(x/2))/(a^2 - b^2))/(a + 2*b*tan(x/2) + a*tan(x/2)^2) - (2*b*atan(((a^2 - b^2)*((2*b^2)/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a*b*tan(x/2))/((a + b)^(3/2)*(a - b)^(3/2))))/(2*b)))/((a + b)^(3/2)*(a - b)^(3/2))","B"
189,1,148,65,6.821425,"\text{Not used}","int(1/(a + b*sin(x))^2,x)","\frac{\frac{2\,b}{a^2-b^2}+\frac{2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{a\,\left(a^2-b^2\right)}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{2\,a\,\mathrm{atan}\left(\frac{\left(a^2-b^2\right)\,\left(\frac{2\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}+\frac{2\,a\,\left(a^2\,b-b^3\right)}{{\left(a+b\right)}^{3/2}\,\left(a^2-b^2\right)\,{\left(a-b\right)}^{3/2}}\right)}{2\,a}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"((2*b)/(a^2 - b^2) + (2*b^2*tan(x/2))/(a*(a^2 - b^2)))/(a + 2*b*tan(x/2) + a*tan(x/2)^2) + (2*a*atan(((a^2 - b^2)*((2*a^2*tan(x/2))/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a*(a^2*b - b^3))/((a + b)^(3/2)*(a^2 - b^2)*(a - b)^(3/2))))/(2*a)))/((a + b)^(3/2)*(a - b)^(3/2))","B"
190,1,1356,93,7.818905,"\text{Not used}","int(1/(sin(x)*(a + b*sin(x))^2),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^2}-\frac{\frac{2\,b^2}{a\,\left(a^2-b^2\right)}+\frac{2\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2\,\left(a^2-b^2\right)}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^6-8\,a^4\,b^2+11\,a^2\,b^4-4\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}-\frac{2\,\left(3\,a^4\,b-2\,a^2\,b^3\right)}{a^4-a^2\,b^2}+\frac{b\,\left(\frac{2\,\left(a^6\,b-a^4\,b^3\right)}{a^4-a^2\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^8-10\,a^6\,b^2+11\,a^4\,b^4-4\,a^2\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}-\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(3\,a^4\,b-2\,a^2\,b^3\right)}{a^4-a^2\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^6-8\,a^4\,b^2+11\,a^2\,b^4-4\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}+\frac{b\,\left(\frac{2\,\left(a^6\,b-a^4\,b^3\right)}{a^4-a^2\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^8-10\,a^6\,b^2+11\,a^4\,b^4-4\,a^2\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{4\,\left(2\,a^2\,b-b^3\right)}{a^4-a^2\,b^2}+\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,b^4-4\,a^2\,b^2\right)}{a^5-2\,a^3\,b^2+a\,b^4}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^6-8\,a^4\,b^2+11\,a^2\,b^4-4\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}-\frac{2\,\left(3\,a^4\,b-2\,a^2\,b^3\right)}{a^4-a^2\,b^2}+\frac{b\,\left(\frac{2\,\left(a^6\,b-a^4\,b^3\right)}{a^4-a^2\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^8-10\,a^6\,b^2+11\,a^4\,b^4-4\,a^2\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(3\,a^4\,b-2\,a^2\,b^3\right)}{a^4-a^2\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^6-8\,a^4\,b^2+11\,a^2\,b^4-4\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}+\frac{b\,\left(\frac{2\,\left(a^6\,b-a^4\,b^3\right)}{a^4-a^2\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^8-10\,a^6\,b^2+11\,a^4\,b^4-4\,a^2\,b^6\right)}{a^5-2\,a^3\,b^2+a\,b^4}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}","Not used",1,"log(tan(x/2))/a^2 - ((2*b^2)/(a*(a^2 - b^2)) + (2*b^3*tan(x/2))/(a^2*(a^2 - b^2)))/(a + 2*b*tan(x/2) + a*tan(x/2)^2) - (b*atan(((b*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*tan(x/2)*(a^6 - 4*b^6 + 11*a^2*b^4 - 8*a^4*b^2))/(a*b^4 + a^5 - 2*a^3*b^2) - (2*(3*a^4*b - 2*a^2*b^3))/(a^4 - a^2*b^2) + (b*((2*(a^6*b - a^4*b^3))/(a^4 - a^2*b^2) - (2*tan(x/2)*(3*a^8 - 4*a^2*b^6 + 11*a^4*b^4 - 10*a^6*b^2))/(a*b^4 + a^5 - 2*a^3*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) - (b*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(3*a^4*b - 2*a^2*b^3))/(a^4 - a^2*b^2) - (2*tan(x/2)*(a^6 - 4*b^6 + 11*a^2*b^4 - 8*a^4*b^2))/(a*b^4 + a^5 - 2*a^3*b^2) + (b*((2*(a^6*b - a^4*b^3))/(a^4 - a^2*b^2) - (2*tan(x/2)*(3*a^8 - 4*a^2*b^6 + 11*a^4*b^4 - 10*a^6*b^2))/(a*b^4 + a^5 - 2*a^3*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((4*(2*a^2*b - b^3))/(a^4 - a^2*b^2) + (4*tan(x/2)*(2*b^4 - 4*a^2*b^2))/(a*b^4 + a^5 - 2*a^3*b^2) + (b*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*tan(x/2)*(a^6 - 4*b^6 + 11*a^2*b^4 - 8*a^4*b^2))/(a*b^4 + a^5 - 2*a^3*b^2) - (2*(3*a^4*b - 2*a^2*b^3))/(a^4 - a^2*b^2) + (b*((2*(a^6*b - a^4*b^3))/(a^4 - a^2*b^2) - (2*tan(x/2)*(3*a^8 - 4*a^2*b^6 + 11*a^4*b^4 - 10*a^6*b^2))/(a*b^4 + a^5 - 2*a^3*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(3*a^4*b - 2*a^2*b^3))/(a^4 - a^2*b^2) - (2*tan(x/2)*(a^6 - 4*b^6 + 11*a^2*b^4 - 8*a^4*b^2))/(a*b^4 + a^5 - 2*a^3*b^2) + (b*((2*(a^6*b - a^4*b^3))/(a^4 - a^2*b^2) - (2*tan(x/2)*(3*a^8 - 4*a^2*b^6 + 11*a^4*b^4 - 10*a^6*b^2))/(a*b^4 + a^5 - 2*a^3*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)","B"
191,1,1471,123,7.633967,"\text{Not used}","int(1/(sin(x)^2*(a + b*sin(x))^2),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^2}-\frac{a-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-a^4+a^2\,b^2+4\,b^4\right)}{a\,\left(a^2-b^2\right)}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-3\,b^2\right)}{a^2-b^2}}{2\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,b\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}-\frac{2\,b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+14\,a^5\,b^3-20\,a^3\,b^5+8\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{2\,\left(4\,a^3\,b^4-5\,a^5\,b^2\right)}{a^6-a^4\,b^2}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(a^8\,b-a^6\,b^3\right)}{a^6-a^4\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^{10}-10\,a^8\,b^2+11\,a^6\,b^4-4\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}-\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(4\,a^3\,b^4-5\,a^5\,b^2\right)}{a^6-a^4\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+14\,a^5\,b^3-20\,a^3\,b^5+8\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(a^8\,b-a^6\,b^3\right)}{a^6-a^4\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^{10}-10\,a^8\,b^2+11\,a^6\,b^4-4\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,b^6-6\,a^2\,b^4\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{4\,\left(4\,b^5-6\,a^2\,b^3\right)}{a^6-a^4\,b^2}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+14\,a^5\,b^3-20\,a^3\,b^5+8\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}-\frac{2\,\left(4\,a^3\,b^4-5\,a^5\,b^2\right)}{a^6-a^4\,b^2}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(a^8\,b-a^6\,b^3\right)}{a^6-a^4\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^{10}-10\,a^8\,b^2+11\,a^6\,b^4-4\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(4\,a^3\,b^4-5\,a^5\,b^2\right)}{a^6-a^4\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^7\,b+14\,a^5\,b^3-20\,a^3\,b^5+8\,a\,b^7\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,\left(a^8\,b-a^6\,b^3\right)}{a^6-a^4\,b^2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^{10}-10\,a^8\,b^2+11\,a^6\,b^4-4\,a^4\,b^6\right)}{a^7-2\,a^5\,b^2+a^3\,b^4}\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}","Not used",1,"tan(x/2)/(2*a^2) - (a - (tan(x/2)^2*(4*b^4 - a^4 + a^2*b^2))/(a*(a^2 - b^2)) + (2*b*tan(x/2)*(a^2 - 3*b^2))/(a^2 - b^2))/(2*a^3*tan(x/2) + 2*a^3*tan(x/2)^3 + 4*a^2*b*tan(x/2)^2) - (2*b*log(tan(x/2)))/a^3 - (b^2*atan(((b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*tan(x/2)*(8*a*b^7 - 2*a^7*b - 20*a^3*b^5 + 14*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (2*(4*a^3*b^4 - 5*a^5*b^2))/(a^6 - a^4*b^2) + (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(a^8*b - a^6*b^3))/(a^6 - a^4*b^2) - (2*tan(x/2)*(3*a^10 - 4*a^4*b^6 + 11*a^6*b^4 - 10*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) - (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(4*a^3*b^4 - 5*a^5*b^2))/(a^6 - a^4*b^2) - (2*tan(x/2)*(8*a*b^7 - 2*a^7*b - 20*a^3*b^5 + 14*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(a^8*b - a^6*b^3))/(a^6 - a^4*b^2) - (2*tan(x/2)*(3*a^10 - 4*a^4*b^6 + 11*a^6*b^4 - 10*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((4*tan(x/2)*(4*b^6 - 6*a^2*b^4))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (4*(4*b^5 - 6*a^2*b^3))/(a^6 - a^4*b^2) + (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*tan(x/2)*(8*a*b^7 - 2*a^7*b - 20*a^3*b^5 + 14*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) - (2*(4*a^3*b^4 - 5*a^5*b^2))/(a^6 - a^4*b^2) + (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(a^8*b - a^6*b^3))/(a^6 - a^4*b^2) - (2*tan(x/2)*(3*a^10 - 4*a^4*b^6 + 11*a^6*b^4 - 10*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(4*a^3*b^4 - 5*a^5*b^2))/(a^6 - a^4*b^2) - (2*tan(x/2)*(8*a*b^7 - 2*a^7*b - 20*a^3*b^5 + 14*a^5*b^3))/(a^7 + a^3*b^4 - 2*a^5*b^2) + (b^2*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*(a^8*b - a^6*b^3))/(a^6 - a^4*b^2) - (2*tan(x/2)*(3*a^10 - 4*a^4*b^6 + 11*a^6*b^4 - 10*a^8*b^2))/(a^7 + a^3*b^4 - 2*a^5*b^2)))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)","B"
192,1,1576,168,7.669004,"\text{Not used}","int(1/(sin(x)^3*(a + b*sin(x))^2),x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^2}-\frac{\frac{a^2}{2}-3\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^4-17\,a^2\,b^2+32\,b^4\right)}{2\,\left(a^2-b^2\right)}+\frac{4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(-a^4+a^2\,b^2+2\,b^4\right)}{a\,\left(a^2-b^2\right)}}{4\,a^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^2+6\,b^2\right)}{2\,a^4}-\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^3}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{a^8\,b+13\,a^6\,b^3-12\,a^4\,b^5}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{10}+2\,a^8\,b^2-35\,a^6\,b^4+56\,a^4\,b^6-24\,a^2\,b^8\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}-\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{10}+2\,a^8\,b^2-35\,a^6\,b^4+56\,a^4\,b^6-24\,a^2\,b^8\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{a^8\,b+13\,a^6\,b^3-12\,a^4\,b^5}{a^8-a^6\,b^2}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{2\,\left(4\,a^4\,b^3+21\,a^2\,b^5-18\,b^7\right)}{a^8-a^6\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^4\,b^4-30\,a^2\,b^6+18\,b^8\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{a^8\,b+13\,a^6\,b^3-12\,a^4\,b^5}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{10}+2\,a^8\,b^2-35\,a^6\,b^4+56\,a^4\,b^6-24\,a^2\,b^8\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{10}+2\,a^8\,b^2-35\,a^6\,b^4+56\,a^4\,b^6-24\,a^2\,b^8\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{a^8\,b+13\,a^6\,b^3-12\,a^4\,b^5}{a^8-a^6\,b^2}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}","Not used",1,"tan(x/2)^2/(8*a^2) - (a^2/2 - 3*a*b*tan(x/2) + (tan(x/2)^2*(a^4 + 32*b^4 - 17*a^2*b^2))/(2*(a^2 - b^2)) + (4*b*tan(x/2)^3*(2*b^4 - a^4 + a^2*b^2))/(a*(a^2 - b^2)))/(4*a^4*tan(x/2)^2 + 4*a^4*tan(x/2)^4 + 8*a^3*b*tan(x/2)^3) + (log(tan(x/2))*(a^2 + 6*b^2))/(2*a^4) - (b*tan(x/2))/a^3 + (b^3*atan(((b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((a^8*b - 12*a^4*b^5 + 13*a^6*b^3)/(a^8 - a^6*b^2) - (tan(x/2)*(a^10 - 24*a^2*b^8 + 56*a^4*b^6 - 35*a^6*b^4 + 2*a^8*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(x/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) - (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(x/2)*(a^10 - 24*a^2*b^8 + 56*a^4*b^6 - 35*a^6*b^4 + 2*a^8*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2) - (a^8*b - 12*a^4*b^5 + 13*a^6*b^3)/(a^8 - a^6*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(x/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((2*(21*a^2*b^5 - 18*b^7 + 4*a^4*b^3))/(a^8 - a^6*b^2) + (2*tan(x/2)*(18*b^8 - 30*a^2*b^6 + 8*a^4*b^4))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((a^8*b - 12*a^4*b^5 + 13*a^6*b^3)/(a^8 - a^6*b^2) - (tan(x/2)*(a^10 - 24*a^2*b^8 + 56*a^4*b^6 - 35*a^6*b^4 + 2*a^8*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(x/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((tan(x/2)*(a^10 - 24*a^2*b^8 + 56*a^4*b^6 - 35*a^6*b^4 + 2*a^8*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2) - (a^8*b - 12*a^4*b^5 + 13*a^6*b^3)/(a^8 - a^6*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(x/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)","B"
193,1,6640,243,15.805988,"\text{Not used}","int(sin(x)^5/(a + b*sin(x))^3,x)","\frac{\frac{3\,\left(4\,a^7-7\,a^5\,b^2+2\,a^3\,b^4\right)}{b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(6\,a^6-10\,a^4\,b^2+a^2\,b^4\right)}{b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(54\,a^6-90\,a^4\,b^2+17\,a^2\,b^4+4\,b^6\right)}{b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(90\,a^6-162\,a^4\,b^2+55\,a^2\,b^4-4\,b^6\right)}{b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(12\,a^7-5\,a^5\,b^2-20\,a^3\,b^4+4\,a\,b^6\right)}{b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(36\,a^7-31\,a^5\,b^2-40\,a^3\,b^4+20\,a\,b^6\right)}{b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(42\,a^6-74\,a^4\,b^2+23\,a^2\,b^4\right)}{b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(3\,a^2+4\,b^2\right)\,\left(4\,a^5-7\,a^3\,b^2+2\,a\,b^4\right)}{b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(6\,a^2+8\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+12\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+12\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,1{}\mathrm{i}}{2\,b^5}+\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(864\,a^{15}-3456\,a^{13}\,b^2+4770\,a^{11}\,b^4-2326\,a^9\,b^6+11\,a^7\,b^8+20\,a^5\,b^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)}{2\,b^5}+\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)}{2\,b^5}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(1728\,a^{16}-7344\,a^{14}\,b^2+11700\,a^{12}\,b^4-7829\,a^{10}\,b^6+1314\,a^8\,b^8+411\,a^6\,b^{10}+20\,a^4\,b^{12}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{a^3\,\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{a^3\,\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}{\frac{8\,\left(864\,a^{15}-3456\,a^{13}\,b^2+4770\,a^{11}\,b^4-2326\,a^9\,b^6+11\,a^7\,b^8+20\,a^5\,b^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(1728\,a^{16}-7344\,a^{14}\,b^2+11700\,a^{12}\,b^4-7829\,a^{10}\,b^6+1314\,a^8\,b^8+411\,a^6\,b^{10}+20\,a^4\,b^{12}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{a^3\,\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4-1104\,a^{12}\,b^6+1538\,a^{10}\,b^8-872\,a^8\,b^{10}+108\,a^6\,b^{12}+40\,a^4\,b^{14}+2\,a^2\,b^{16}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-288\,a^{15}\,b^4+1536\,a^{13}\,b^6-3194\,a^{11}\,b^8+3134\,a^9\,b^{10}-1326\,a^7\,b^{12}+88\,a^5\,b^{14}+39\,a^3\,b^{16}+2\,a\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{a^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}-100\,a^9\,b^{12}+164\,a^7\,b^{14}-120\,a^5\,b^{16}+28\,a^3\,b^{18}+4\,a\,b^{20}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(48\,a^{12}\,b^{10}-212\,a^{10}\,b^{12}+360\,a^8\,b^{14}-276\,a^6\,b^{16}+80\,a^4\,b^{18}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{a^3\,\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}}","Not used",1,"((3*(4*a^7 + 2*a^3*b^4 - 7*a^5*b^2))/(b^4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)^7*(6*a^6 + a^2*b^4 - 10*a^4*b^2))/(b^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)^5*(54*a^6 + 4*b^6 + 17*a^2*b^4 - 90*a^4*b^2))/(b^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)^3*(90*a^6 - 4*b^6 + 55*a^2*b^4 - 162*a^4*b^2))/(b^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)^6*(4*a*b^6 + 12*a^7 - 20*a^3*b^4 - 5*a^5*b^2))/(b^4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)^2*(20*a*b^6 + 36*a^7 - 40*a^3*b^4 - 31*a^5*b^2))/(b^4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)*(42*a^6 + 23*a^2*b^4 - 74*a^4*b^2))/(b^3*(a^4 + b^4 - 2*a^2*b^2)) + (3*tan(x/2)^4*(3*a^2 + 4*b^2)*(2*a*b^4 + 4*a^5 - 7*a^3*b^2))/(b^4*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^2*(4*a^2 + 4*b^2) + tan(x/2)^6*(4*a^2 + 4*b^2) + tan(x/2)^4*(6*a^2 + 8*b^2) + a^2 + a^2*tan(x/2)^8 + 4*a*b*tan(x/2) + 12*a*b*tan(x/2)^3 + 12*a*b*tan(x/2)^5 + 4*a*b*tan(x/2)^7) + (atan((((a^2*12i + b^2*1i)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - ((a^2*12i + b^2*1i)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*12i + b^2*1i))/(2*b^5) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))/(2*b^5) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*1i)/(2*b^5) + ((a^2*12i + b^2*1i)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + ((a^2*12i + b^2*1i)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*12i + b^2*1i))/(2*b^5) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))/(2*b^5) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*1i)/(2*b^5))/((8*(864*a^15 + 20*a^5*b^10 + 11*a^7*b^8 - 2326*a^9*b^6 + 4770*a^11*b^4 - 3456*a^13*b^2))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - ((a^2*12i + b^2*1i)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - ((a^2*12i + b^2*1i)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*12i + b^2*1i))/(2*b^5) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))/(2*b^5) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))/(2*b^5) + ((a^2*12i + b^2*1i)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + ((a^2*12i + b^2*1i)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*12i + b^2*1i))/(2*b^5) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))/(2*b^5) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))/(2*b^5) + (16*tan(x/2)*(1728*a^16 + 20*a^4*b^12 + 411*a^6*b^10 + 1314*a^8*b^8 - 7829*a^10*b^6 + 11700*a^12*b^4 - 7344*a^14*b^2))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12)))*(a^2*12i + b^2*1i)*1i)/b^5 + (a^3*atan(((a^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (a^3*((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4 + 20*b^4 - 29*a^2*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (a^3*((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4 + 20*b^4 - 29*a^2*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(864*a^15 + 20*a^5*b^10 + 11*a^7*b^8 - 2326*a^9*b^6 + 4770*a^11*b^4 - 3456*a^13*b^2))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (16*tan(x/2)*(1728*a^16 + 20*a^4*b^12 + 411*a^6*b^10 + 1314*a^8*b^8 - 7829*a^10*b^6 + 11700*a^12*b^4 - 7344*a^14*b^2))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (a^3*((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16 + 40*a^4*b^14 + 108*a^6*b^12 - 872*a^8*b^10 + 1538*a^10*b^8 - 1104*a^12*b^6 + 288*a^14*b^4))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(2*a*b^18 + 39*a^3*b^16 + 88*a^5*b^14 - 1326*a^7*b^12 + 3134*a^9*b^10 - 3194*a^11*b^8 + 1536*a^13*b^6 - 288*a^15*b^4))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (a^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*((4*(4*a*b^20 + 28*a^3*b^18 - 120*a^5*b^16 + 164*a^7*b^14 - 100*a^9*b^12 + 24*a^11*b^10))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(80*a^4*b^18 - 276*a^6*b^16 + 360*a^8*b^14 - 212*a^10*b^12 + 48*a^12*b^10))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (a^3*((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(x/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*1i)/(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)","B"
194,1,5945,179,14.873968,"\text{Not used}","int(sin(x)^4/(a + b*sin(x))^3,x)","-\frac{\frac{a^2\,\left(6\,a^4-11\,a^2\,b^2+2\,b^4\right)}{b^3\,{\left(a^2-b^2\right)}^2}+\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(a^5-2\,a^3\,b^2\right)}{b^2\,{\left(a^2-b^2\right)}^2}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(-2\,a^6+a^4\,b^2+4\,a^2\,b^4\right)}{b^3\,{\left(a^2-b^2\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(6\,a^6-3\,a^4\,b^2-13\,a^2\,b^4+4\,b^6\right)}{b^3\,{\left(a^2-b^2\right)}^2}+\frac{4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(6\,a^4-11\,a^2\,b^2+2\,b^4\right)}{b^2\,{\left(a^2-b^2\right)}^2}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(21\,a^4-38\,a^2\,b^2+8\,b^4\right)}{b^2\,{\left(a^2-b^2\right)}^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(3\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(3\,a^2+4\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+8\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}-\frac{6\,a\,\mathrm{atan}\left(\frac{\frac{3\,a\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{a\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}+\frac{3\,a\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{a\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{16\,\left(54\,a^{12}-243\,a^{10}\,b^2+378\,a^8\,b^4-216\,a^6\,b^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(216\,a^{13}-972\,a^{11}\,b^2+1728\,a^9\,b^4-1404\,a^7\,b^6+432\,a^5\,b^8\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{a\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{a\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}+\frac{a\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{a\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}}\right)}{b^4}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{3\,a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{3\,a^2\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,3{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{3\,a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{3\,a^2\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,3{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(54\,a^{12}-243\,a^{10}\,b^2+378\,a^8\,b^4-216\,a^6\,b^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(216\,a^{13}-972\,a^{11}\,b^2+1728\,a^9\,b^4-1404\,a^7\,b^6+432\,a^5\,b^8\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{3\,a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{3\,a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{3\,a^2\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{3\,a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(\frac{8\,\left(36\,a^{12}\,b^3-144\,a^{10}\,b^5+216\,a^8\,b^7-144\,a^6\,b^9+36\,a^4\,b^{11}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^{13}\,b^3+396\,a^{11}\,b^5-873\,a^9\,b^7+936\,a^7\,b^9-468\,a^5\,b^{11}+72\,a^3\,b^{13}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{3\,a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8-24\,a^8\,b^{10}+42\,a^6\,b^{12}-36\,a^4\,b^{14}+12\,a^2\,b^{16}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(24\,a^{11}\,b^8-108\,a^9\,b^{10}+192\,a^7\,b^{12}-156\,a^5\,b^{14}+48\,a^3\,b^{16}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{3\,a^2\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,3{}\mathrm{i}}{-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}}","Not used",1,"- ((a^2*(6*a^4 + 2*b^4 - 11*a^2*b^2))/(b^3*(a^2 - b^2)^2) + (3*tan(x/2)^5*(a^5 - 2*a^3*b^2))/(b^2*(a^2 - b^2)^2) - (3*tan(x/2)^4*(4*a^2*b^4 - 2*a^6 + a^4*b^2))/(b^3*(a^2 - b^2)^2) + (2*tan(x/2)^2*(6*a^6 + 4*b^6 - 13*a^2*b^4 - 3*a^4*b^2))/(b^3*(a^2 - b^2)^2) + (4*a*tan(x/2)^3*(6*a^4 + 2*b^4 - 11*a^2*b^2))/(b^2*(a^2 - b^2)^2) + (a*tan(x/2)*(21*a^4 + 8*b^4 - 38*a^2*b^2))/(b^2*(a^2 - b^2)^2))/(tan(x/2)^2*(3*a^2 + 4*b^2) + tan(x/2)^4*(3*a^2 + 4*b^2) + a^2 + a^2*tan(x/2)^6 + 4*a*b*tan(x/2) + 8*a*b*tan(x/2)^3 + 4*a*b*tan(x/2)^5) - (6*a*atan(((3*a*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (a*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) - (a*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4 + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4))/b^4 + (3*a*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (a*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (a*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4 + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4))/b^4)/((16*(54*a^12 - 216*a^6*b^6 + 378*a^8*b^4 - 243*a^10*b^2))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (16*tan(x/2)*(216*a^13 + 432*a^5*b^8 - 1404*a^7*b^6 + 1728*a^9*b^4 - 972*a^11*b^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (a*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (a*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) - (a*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4 + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4)*3i)/b^4 + (a*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (a*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (a*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4 + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*3i)/b^4)*3i)/b^4)))/b^4 - (a^2*atan(((a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (3*a^2*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*3i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (3*a^2*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*3i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(54*a^12 - 216*a^6*b^6 + 378*a^8*b^4 - 243*a^10*b^2))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (16*tan(x/2)*(216*a^13 + 432*a^5*b^8 - 1404*a^7*b^6 + 1728*a^9*b^4 - 972*a^11*b^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (3*a^2*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*((8*(36*a^4*b^11 - 144*a^6*b^9 + 216*a^8*b^7 - 144*a^10*b^5 + 36*a^12*b^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(72*a^3*b^13 - 468*a^5*b^11 + 936*a^7*b^9 - 873*a^9*b^7 + 396*a^11*b^5 - 72*a^13*b^3))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(12*a^2*b^16 - 36*a^4*b^14 + 42*a^6*b^12 - 24*a^8*b^10 + 6*a^10*b^8))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(48*a^3*b^16 - 156*a^5*b^14 + 192*a^7*b^12 - 108*a^9*b^10 + 24*a^11*b^8))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (3*a^2*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(x/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*3i)/(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)","B"
195,1,5756,144,14.902782,"\text{Not used}","int(sin(x)^3/(a + b*sin(x))^3,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}{b^3}+\frac{\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}{b^3}}{\frac{16\,\left(2\,a^9-13\,a^7\,b^2+26\,a^5\,b^4-24\,a^3\,b^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}-36\,a^8\,b^2+72\,a^6\,b^4-68\,a^4\,b^6+24\,a^2\,b^8\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)}{b^3}+\frac{\frac{2\,a^5-5\,a^3\,b^2}{b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(7\,a^4-16\,a^2\,b^2\right)}{b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^4-4\,a^2\,b^2\right)}{b\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(5\,a\,b^2-2\,a^3\right)\,\left(a^2+2\,b^2\right)}{b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(2\,a^9-13\,a^7\,b^2+26\,a^5\,b^4-24\,a^3\,b^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{16\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}-36\,a^8\,b^2+72\,a^6\,b^4-68\,a^4\,b^6+24\,a^2\,b^8\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2-16\,a^8\,b^4+24\,a^6\,b^6-16\,a^4\,b^8+4\,a^2\,b^{10}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^2+44\,a^9\,b^4-105\,a^7\,b^6+124\,a^5\,b^8-72\,a^3\,b^{10}+8\,a\,b^{12}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(2\,a^9\,b^6-4\,a^7\,b^8+6\,a^5\,b^{10}-8\,a^3\,b^{12}+4\,a\,b^{14}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{10}\,b^6-36\,a^8\,b^8+72\,a^6\,b^{10}-68\,a^4\,b^{12}+24\,a^2\,b^{14}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{a\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}}","Not used",1,"(2*atan((((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (((8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))/b^3 + ((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (((((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))/b^3)/((((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (((((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 - (((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (((8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 + (16*(2*a^9 - 24*a^3*b^6 + 26*a^5*b^4 - 13*a^7*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (16*tan(x/2)*(8*a^10 + 24*a^2*b^8 - 68*a^4*b^6 + 72*a^6*b^4 - 36*a^8*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))))/b^3 + ((2*a^5 - 5*a^3*b^2)/(b^2*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)*(7*a^4 - 16*a^2*b^2))/(b*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)^3*(a^4 - 4*a^2*b^2))/(b*(a^4 + b^4 - 2*a^2*b^2)) - (tan(x/2)^2*(5*a*b^2 - 2*a^3)*(a^2 + 2*b^2))/(b^2*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^2*(2*a^2 + 4*b^2) + a^2 + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) + 4*a*b*tan(x/2)^3) + (a*atan(((a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (a*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (a*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(2*a^9 - 24*a^3*b^6 + 26*a^5*b^4 - 13*a^7*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (16*tan(x/2)*(8*a^10 + 24*a^2*b^8 - 68*a^4*b^6 + 72*a^6*b^4 - 36*a^8*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (a*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10 - 16*a^4*b^8 + 24*a^6*b^6 - 16*a^8*b^4 + 4*a^10*b^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(8*a*b^12 - 72*a^3*b^10 + 124*a^5*b^8 - 105*a^7*b^6 + 44*a^9*b^4 - 8*a^11*b^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^14 - 8*a^3*b^12 + 6*a^5*b^10 - 4*a^7*b^8 + 2*a^9*b^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(24*a^2*b^14 - 68*a^4*b^12 + 72*a^6*b^10 - 36*a^8*b^8 + 8*a^10*b^6))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (a*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(x/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*1i)/(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)","B"
196,1,318,118,7.233443,"\text{Not used}","int(sin(x)^2/(a + b*sin(x))^3,x)","\frac{\frac{3\,a^2\,b}{a^4-2\,a^2\,b^2+b^4}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-10\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2+2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(a^2+2\,b^2\right)\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+2\,b^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{a^2+2\,b^2}\right)\,\left(a^2+2\,b^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((3*a^2*b)/(a^4 + b^4 - 2*a^2*b^2) - (a*tan(x/2)*(a^2 - 10*b^2))/(a^4 + b^4 - 2*a^2*b^2) + (a*tan(x/2)^3*(a^2 + 2*b^2))/(a^4 + b^4 - 2*a^2*b^2) + (3*b*tan(x/2)^2*(a^2 + 2*b^2))/(a^4 + b^4 - 2*a^2*b^2))/(tan(x/2)^2*(2*a^2 + 4*b^2) + a^2 + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) + 4*a*b*tan(x/2)^3) + (atan(((((a^2 + 2*b^2)*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/(2*(a + b)^(5/2)*(a - b)^(5/2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(x/2)*(a^2 + 2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))*(a^4 + b^4 - 2*a^2*b^2))/(a^2 + 2*b^2))*(a^2 + 2*b^2))/((a + b)^(5/2)*(a - b)^(5/2))","B"
197,1,310,103,7.509265,"\text{Not used}","int(sin(x)/(a + b*sin(x))^3,x)","-\frac{\frac{2\,a^3+a\,b^2}{a^4-2\,a^2\,b^2+b^4}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^4-2\,a^2\,b^2+b^4}+\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(5\,a^2+4\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+b^2\right)\,\left(a^2+2\,b^2\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}-\frac{3\,a\,b\,\mathrm{atan}\left(\frac{\left(\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}+\frac{3\,a\,b^2\,\left(2\,a^4-4\,a^2\,b^2+2\,b^4\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}\,\left(a^4-2\,a^2\,b^2+b^4\right)}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{3\,a\,b}\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"- ((a*b^2 + 2*a^3)/(a^4 + b^4 - 2*a^2*b^2) + (3*a^2*b*tan(x/2)^3)/(a^4 + b^4 - 2*a^2*b^2) + (b*tan(x/2)*(5*a^2 + 4*b^2))/(a^4 + b^4 - 2*a^2*b^2) + (tan(x/2)^2*(2*a^2 + b^2)*(a^2 + 2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^2*(2*a^2 + 4*b^2) + a^2 + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) + 4*a*b*tan(x/2)^3) - (3*a*b*atan((((3*a^2*b*tan(x/2))/((a + b)^(5/2)*(a - b)^(5/2)) + (3*a*b^2*(2*a^4 + 2*b^4 - 4*a^2*b^2))/(2*(a + b)^(5/2)*(a - b)^(5/2)*(a^4 + b^4 - 2*a^2*b^2)))*(a^4 + b^4 - 2*a^2*b^2))/(3*a*b)))/((a + b)^(5/2)*(a - b)^(5/2))","B"
198,1,349,102,7.323159,"\text{Not used}","int(1/(a + b*sin(x))^3,x)","\frac{\frac{4\,a^2\,b-b^3}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(4\,a^2\,b-b^3\right)\,\left(a^2+2\,b^2\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(5\,a^2\,b-2\,b^3\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(11\,a^2\,b-2\,b^3\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,a^2+b^2\right)\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2+b^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{2\,a^2+b^2}\right)\,\left(2\,a^2+b^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((4*a^2*b - b^3)/(a^4 + b^4 - 2*a^2*b^2) + (tan(x/2)^2*(4*a^2*b - b^3)*(a^2 + 2*b^2))/(a^2*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(x/2)^3*(5*a^2*b - 2*b^3))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(x/2)*(11*a^2*b - 2*b^3))/(a*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^2*(2*a^2 + 4*b^2) + a^2 + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) + 4*a*b*tan(x/2)^3) + (atan(((((2*a^2 + b^2)*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/(2*(a + b)^(5/2)*(a - b)^(5/2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(x/2)*(2*a^2 + b^2))/((a + b)^(5/2)*(a - b)^(5/2)))*(a^4 + b^4 - 2*a^2*b^2))/(2*a^2 + b^2))*(2*a^2 + b^2))/((a + b)^(5/2)*(a - b)^(5/2))","B"
199,1,2191,145,11.385310,"\text{Not used}","int(1/(sin(x)*(a + b*sin(x))^3),x)","\frac{\frac{3\,\left(b^4-2\,a^2\,b^2\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^4\,b^2+3\,a^2\,b^4-2\,b^6\right)}{a^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,b^5-17\,a^2\,b^3\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,b^4-7\,a^2\,b^2\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^7\,b-9\,a^5\,b^3+4\,a^3\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^{11}+24\,a^9\,b^2-62\,a^7\,b^4+68\,a^5\,b^6-36\,a^3\,b^8+8\,a\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}-\frac{b\,\left(\frac{2\,a^{10}\,b-4\,a^8\,b^3+2\,a^6\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{14}-32\,a^{12}\,b^2+68\,a^{10}\,b^4-72\,a^8\,b^6+38\,a^6\,b^8-8\,a^4\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^7\,b-9\,a^5\,b^3+4\,a^3\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^{11}+24\,a^9\,b^2-62\,a^7\,b^4+68\,a^5\,b^6-36\,a^3\,b^8+8\,a\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\frac{b\,\left(\frac{2\,a^{10}\,b-4\,a^8\,b^3+2\,a^6\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{14}-32\,a^{12}\,b^2+68\,a^{10}\,b^4-72\,a^8\,b^6+38\,a^6\,b^8-8\,a^4\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{2\,\left(6\,a^4\,b-5\,a^2\,b^3+2\,b^5\right)}{a^8-2\,a^6\,b^2+a^4\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-24\,a^6\,b^2+26\,a^4\,b^4-13\,a^2\,b^6+2\,b^8\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^7\,b-9\,a^5\,b^3+4\,a^3\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^{11}+24\,a^9\,b^2-62\,a^7\,b^4+68\,a^5\,b^6-36\,a^3\,b^8+8\,a\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}-\frac{b\,\left(\frac{2\,a^{10}\,b-4\,a^8\,b^3+2\,a^6\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{14}-32\,a^{12}\,b^2+68\,a^{10}\,b^4-72\,a^8\,b^6+38\,a^6\,b^8-8\,a^4\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^7\,b-9\,a^5\,b^3+4\,a^3\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^{11}+24\,a^9\,b^2-62\,a^7\,b^4+68\,a^5\,b^6-36\,a^3\,b^8+8\,a\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}+\frac{b\,\left(\frac{2\,a^{10}\,b-4\,a^8\,b^3+2\,a^6\,b^5}{a^8-2\,a^6\,b^2+a^4\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{14}-32\,a^{12}\,b^2+68\,a^{10}\,b^4-72\,a^8\,b^6+38\,a^6\,b^8-8\,a^4\,b^{10}\right)}{a^{11}-4\,a^9\,b^2+6\,a^7\,b^4-4\,a^5\,b^6+a^3\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\mathrm{i}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}","Not used",1,"((3*(b^4 - 2*a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) - (3*tan(x/2)^2*(3*a^2*b^4 - 2*b^6 + 2*a^4*b^2))/(a^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(x/2)*(8*b^5 - 17*a^2*b^3))/(a^2*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(x/2)^3*(4*b^4 - 7*a^2*b^2))/(a^2*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^2*(2*a^2 + 4*b^2) + a^2 + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) + 4*a*b*tan(x/2)^3) + log(tan(x/2))/a^3 + (b*atan(((b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*a^7*b + 4*a^3*b^5 - 9*a^5*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) + (tan(x/2)*(8*a*b^10 - 2*a^11 - 36*a^3*b^8 + 68*a^5*b^6 - 62*a^7*b^4 + 24*a^9*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) - (b*((2*a^10*b + 2*a^6*b^5 - 4*a^8*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) - (tan(x/2)*(6*a^14 - 8*a^4*b^10 + 38*a^6*b^8 - 72*a^8*b^6 + 68*a^10*b^4 - 32*a^12*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*a^7*b + 4*a^3*b^5 - 9*a^5*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) + (tan(x/2)*(8*a*b^10 - 2*a^11 - 36*a^3*b^8 + 68*a^5*b^6 - 62*a^7*b^4 + 24*a^9*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) + (b*((2*a^10*b + 2*a^6*b^5 - 4*a^8*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) - (tan(x/2)*(6*a^14 - 8*a^4*b^10 + 38*a^6*b^8 - 72*a^8*b^6 + 68*a^10*b^4 - 32*a^12*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((2*(6*a^4*b + 2*b^5 - 5*a^2*b^3))/(a^8 + a^4*b^4 - 2*a^6*b^2) + (2*tan(x/2)*(2*b^8 - 13*a^2*b^6 + 26*a^4*b^4 - 24*a^6*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*a^7*b + 4*a^3*b^5 - 9*a^5*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) + (tan(x/2)*(8*a*b^10 - 2*a^11 - 36*a^3*b^8 + 68*a^5*b^6 - 62*a^7*b^4 + 24*a^9*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) - (b*((2*a^10*b + 2*a^6*b^5 - 4*a^8*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) - (tan(x/2)*(6*a^14 - 8*a^4*b^10 + 38*a^6*b^8 - 72*a^8*b^6 + 68*a^10*b^4 - 32*a^12*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*a^7*b + 4*a^3*b^5 - 9*a^5*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) + (tan(x/2)*(8*a*b^10 - 2*a^11 - 36*a^3*b^8 + 68*a^5*b^6 - 62*a^7*b^4 + 24*a^9*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2) + (b*((2*a^10*b + 2*a^6*b^5 - 4*a^8*b^3)/(a^8 + a^4*b^4 - 2*a^6*b^2) - (tan(x/2)*(6*a^14 - 8*a^4*b^10 + 38*a^6*b^8 - 72*a^8*b^6 + 68*a^10*b^4 - 32*a^12*b^2))/(a^11 + a^3*b^8 - 4*a^5*b^6 + 6*a^7*b^4 - 4*a^9*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)","B"
200,1,2295,187,9.015985,"\text{Not used}","int(1/(sin(x)^2*(a + b*sin(x))^3),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^3}-\frac{a^2+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^5\,b-12\,a^3\,b^3+7\,a\,b^5\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^6-2\,a^4\,b^2-17\,a^2\,b^4+12\,b^6\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^6-26\,a^2\,b^4+16\,b^6\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(2\,a^6\,b-12\,a^4\,b^3-9\,a^2\,b^5+10\,b^7\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a^5+8\,a^3\,b^2\right)+2\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)+2\,a^5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+8\,a^4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+8\,a^4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^4}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{18\,a^8\,b^2-27\,a^6\,b^4+12\,a^4\,b^6}{a^{10}-2\,a^8\,b^2+a^6\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}\,b-60\,a^{10}\,b^3+162\,a^8\,b^5-192\,a^6\,b^7+108\,a^4\,b^9-24\,a^2\,b^{11}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{3\,b^2\,\left(\frac{2\,a^{12}\,b-4\,a^{10}\,b^3+2\,a^8\,b^5}{a^{10}-2\,a^8\,b^2+a^6\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{16}-32\,a^{14}\,b^2+68\,a^{12}\,b^4-72\,a^{10}\,b^6+38\,a^8\,b^8-8\,a^6\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}\,b-60\,a^{10}\,b^3+162\,a^8\,b^5-192\,a^6\,b^7+108\,a^4\,b^9-24\,a^2\,b^{11}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}-\frac{18\,a^8\,b^2-27\,a^6\,b^4+12\,a^4\,b^6}{a^{10}-2\,a^8\,b^2+a^6\,b^4}+\frac{3\,b^2\,\left(\frac{2\,a^{12}\,b-4\,a^{10}\,b^3+2\,a^8\,b^5}{a^{10}-2\,a^8\,b^2+a^6\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{16}-32\,a^{14}\,b^2+68\,a^{12}\,b^4-72\,a^{10}\,b^6+38\,a^8\,b^8-8\,a^6\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{2\,\left(36\,a^4\,b^3-45\,a^2\,b^5+18\,b^7\right)}{a^{10}-2\,a^8\,b^2+a^6\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-72\,a^6\,b^4+126\,a^4\,b^6-81\,a^2\,b^8+18\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{3\,b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{18\,a^8\,b^2-27\,a^6\,b^4+12\,a^4\,b^6}{a^{10}-2\,a^8\,b^2+a^6\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}\,b-60\,a^{10}\,b^3+162\,a^8\,b^5-192\,a^6\,b^7+108\,a^4\,b^9-24\,a^2\,b^{11}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}+\frac{3\,b^2\,\left(\frac{2\,a^{12}\,b-4\,a^{10}\,b^3+2\,a^8\,b^5}{a^{10}-2\,a^8\,b^2+a^6\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{16}-32\,a^{14}\,b^2+68\,a^{12}\,b^4-72\,a^{10}\,b^6+38\,a^8\,b^8-8\,a^6\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{3\,b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{12}\,b-60\,a^{10}\,b^3+162\,a^8\,b^5-192\,a^6\,b^7+108\,a^4\,b^9-24\,a^2\,b^{11}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}-\frac{18\,a^8\,b^2-27\,a^6\,b^4+12\,a^4\,b^6}{a^{10}-2\,a^8\,b^2+a^6\,b^4}+\frac{3\,b^2\,\left(\frac{2\,a^{12}\,b-4\,a^{10}\,b^3+2\,a^8\,b^5}{a^{10}-2\,a^8\,b^2+a^6\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{16}-32\,a^{14}\,b^2+68\,a^{12}\,b^4-72\,a^{10}\,b^6+38\,a^8\,b^8-8\,a^6\,b^{10}\right)}{a^{13}-4\,a^{11}\,b^2+6\,a^9\,b^4-4\,a^7\,b^6+a^5\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}}","Not used",1,"tan(x/2)/(2*a^3) - (a^2 + (2*tan(x/2)*(7*a*b^5 + 2*a^5*b - 12*a^3*b^3))/(a^4 + b^4 - 2*a^2*b^2) + (tan(x/2)^4*(a^6 + 12*b^6 - 17*a^2*b^4 - 2*a^4*b^2))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(x/2)^2*(a^6 + 16*b^6 - 26*a^2*b^4))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(x/2)^3*(2*a^6*b + 10*b^7 - 9*a^2*b^5 - 12*a^4*b^3))/(a*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^3*(4*a^5 + 8*a^3*b^2) + 2*a^5*tan(x/2) + 2*a^5*tan(x/2)^5 + 8*a^4*b*tan(x/2)^2 + 8*a^4*b*tan(x/2)^4) - (3*b*log(tan(x/2)))/a^4 - (b^2*atan(((b^2*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*((12*a^4*b^6 - 27*a^6*b^4 + 18*a^8*b^2)/(a^10 + a^6*b^4 - 2*a^8*b^2) - (tan(x/2)*(6*a^12*b - 24*a^2*b^11 + 108*a^4*b^9 - 192*a^6*b^7 + 162*a^8*b^5 - 60*a^10*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (3*b^2*((2*a^12*b + 2*a^8*b^5 - 4*a^10*b^3)/(a^10 + a^6*b^4 - 2*a^8*b^2) - (tan(x/2)*(6*a^16 - 8*a^6*b^10 + 38*a^8*b^8 - 72*a^10*b^6 + 68*a^12*b^4 - 32*a^14*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*3i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*((tan(x/2)*(6*a^12*b - 24*a^2*b^11 + 108*a^4*b^9 - 192*a^6*b^7 + 162*a^8*b^5 - 60*a^10*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (12*a^4*b^6 - 27*a^6*b^4 + 18*a^8*b^2)/(a^10 + a^6*b^4 - 2*a^8*b^2) + (3*b^2*((2*a^12*b + 2*a^8*b^5 - 4*a^10*b^3)/(a^10 + a^6*b^4 - 2*a^8*b^2) - (tan(x/2)*(6*a^16 - 8*a^6*b^10 + 38*a^8*b^8 - 72*a^10*b^6 + 68*a^12*b^4 - 32*a^14*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*3i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((2*(18*b^7 - 45*a^2*b^5 + 36*a^4*b^3))/(a^10 + a^6*b^4 - 2*a^8*b^2) + (2*tan(x/2)*(18*b^10 - 81*a^2*b^8 + 126*a^4*b^6 - 72*a^6*b^4))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (3*b^2*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*((12*a^4*b^6 - 27*a^6*b^4 + 18*a^8*b^2)/(a^10 + a^6*b^4 - 2*a^8*b^2) - (tan(x/2)*(6*a^12*b - 24*a^2*b^11 + 108*a^4*b^9 - 192*a^6*b^7 + 162*a^8*b^5 - 60*a^10*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) + (3*b^2*((2*a^12*b + 2*a^8*b^5 - 4*a^10*b^3)/(a^10 + a^6*b^4 - 2*a^8*b^2) - (tan(x/2)*(6*a^16 - 8*a^6*b^10 + 38*a^8*b^8 - 72*a^10*b^6 + 68*a^12*b^4 - 32*a^14*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (3*b^2*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*((tan(x/2)*(6*a^12*b - 24*a^2*b^11 + 108*a^4*b^9 - 192*a^6*b^7 + 162*a^8*b^5 - 60*a^10*b^3))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2) - (12*a^4*b^6 - 27*a^6*b^4 + 18*a^8*b^2)/(a^10 + a^6*b^4 - 2*a^8*b^2) + (3*b^2*((2*a^12*b + 2*a^8*b^5 - 4*a^10*b^3)/(a^10 + a^6*b^4 - 2*a^8*b^2) - (tan(x/2)*(6*a^16 - 8*a^6*b^10 + 38*a^8*b^8 - 72*a^10*b^6 + 68*a^12*b^4 - 32*a^14*b^2))/(a^13 + a^5*b^8 - 4*a^7*b^6 + 6*a^9*b^4 - 4*a^11*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*3i)/(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)","B"
201,1,2405,241,9.276946,"\text{Not used}","int(1/(sin(x)^3*(a + b*sin(x))^3),x)","\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{a^3}{2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-a^7+24\,a^5\,b^2-85\,a^3\,b^4+50\,a\,b^6\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(3\,a^6\,b-6\,a^4\,b^3-19\,a^2\,b^5+16\,b^7\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(5\,a^6\,b+2\,a^4\,b^3-77\,a^2\,b^5+52\,b^7\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^8-50\,a^6\,b^2+177\,a^4\,b^4+56\,a^2\,b^6-112\,b^8\right)}{2\,a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(8\,a^6+16\,a^4\,b^2\right)+4\,a^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+4\,a^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+16\,a^5\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+16\,a^5\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^3}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^2+12\,b^2\right)}{2\,a^5}-\frac{3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^4}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(\frac{a^{11}\,b+30\,a^9\,b^3-52\,a^7\,b^5+24\,a^5\,b^7}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{15}+6\,a^{13}\,b^2-98\,a^{11}\,b^4+290\,a^9\,b^6-363\,a^7\,b^8+212\,a^5\,b^{10}-48\,a^3\,b^{12}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}+\frac{b^3\,\left(\frac{2\,a^{14}\,b-4\,a^{12}\,b^3+2\,a^{10}\,b^5}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{18}-32\,a^{16}\,b^2+68\,a^{14}\,b^4-72\,a^{12}\,b^6+38\,a^{10}\,b^8-8\,a^8\,b^{10}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}-\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{15}+6\,a^{13}\,b^2-98\,a^{11}\,b^4+290\,a^9\,b^6-363\,a^7\,b^8+212\,a^5\,b^{10}-48\,a^3\,b^{12}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}-\frac{a^{11}\,b+30\,a^9\,b^3-52\,a^7\,b^5+24\,a^5\,b^7}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}+\frac{b^3\,\left(\frac{2\,a^{14}\,b-4\,a^{12}\,b^3+2\,a^{10}\,b^5}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{18}-32\,a^{16}\,b^2+68\,a^{14}\,b^4-72\,a^{12}\,b^6+38\,a^{10}\,b^8-8\,a^8\,b^{10}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}{\frac{20\,a^6\,b^3+211\,a^4\,b^5-336\,a^2\,b^7+144\,b^9}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(20\,a^8\,b^4-229\,a^6\,b^6+422\,a^4\,b^8-294\,a^2\,b^{10}+72\,b^{12}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}+\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(\frac{a^{11}\,b+30\,a^9\,b^3-52\,a^7\,b^5+24\,a^5\,b^7}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{15}+6\,a^{13}\,b^2-98\,a^{11}\,b^4+290\,a^9\,b^6-363\,a^7\,b^8+212\,a^5\,b^{10}-48\,a^3\,b^{12}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}+\frac{b^3\,\left(\frac{2\,a^{14}\,b-4\,a^{12}\,b^3+2\,a^{10}\,b^5}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{18}-32\,a^{16}\,b^2+68\,a^{14}\,b^4-72\,a^{12}\,b^6+38\,a^{10}\,b^8-8\,a^8\,b^{10}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^{15}+6\,a^{13}\,b^2-98\,a^{11}\,b^4+290\,a^9\,b^6-363\,a^7\,b^8+212\,a^5\,b^{10}-48\,a^3\,b^{12}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}-\frac{a^{11}\,b+30\,a^9\,b^3-52\,a^7\,b^5+24\,a^5\,b^7}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}+\frac{b^3\,\left(\frac{2\,a^{14}\,b-4\,a^{12}\,b^3+2\,a^{10}\,b^5}{a^{12}-2\,a^{10}\,b^2+a^8\,b^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^{18}-32\,a^{16}\,b^2+68\,a^{14}\,b^4-72\,a^{12}\,b^6+38\,a^{10}\,b^8-8\,a^8\,b^{10}\right)}{a^{15}-4\,a^{13}\,b^2+6\,a^{11}\,b^4-4\,a^9\,b^6+a^7\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}}","Not used",1,"(4*a^2*b*tan(x/2) - a^3/2 + (tan(x/2)^2*(50*a*b^6 - a^7 - 85*a^3*b^4 + 24*a^5*b^2))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(x/2)^5*(3*a^6*b + 16*b^7 - 19*a^2*b^5 - 6*a^4*b^3))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(x/2)^3*(5*a^6*b + 52*b^7 - 77*a^2*b^5 + 2*a^4*b^3))/(a^4 + b^4 - 2*a^2*b^2) - (tan(x/2)^4*(a^8 - 112*b^8 + 56*a^2*b^6 + 177*a^4*b^4 - 50*a^6*b^2))/(2*a*(a^4 + b^4 - 2*a^2*b^2)))/(tan(x/2)^4*(8*a^6 + 16*a^4*b^2) + 4*a^6*tan(x/2)^2 + 4*a^6*tan(x/2)^6 + 16*a^5*b*tan(x/2)^3 + 16*a^5*b*tan(x/2)^5) + tan(x/2)^2/(8*a^3) + (log(tan(x/2))*(a^2 + 12*b^2))/(2*a^5) - (3*b*tan(x/2))/(2*a^4) + (b^3*atan(((b^3*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*((a^11*b + 24*a^5*b^7 - 52*a^7*b^5 + 30*a^9*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) - (tan(x/2)*(a^15 - 48*a^3*b^12 + 212*a^5*b^10 - 363*a^7*b^8 + 290*a^9*b^6 - 98*a^11*b^4 + 6*a^13*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2) + (b^3*((2*a^14*b + 2*a^10*b^5 - 4*a^12*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) - (tan(x/2)*(6*a^18 - 8*a^8*b^10 + 38*a^10*b^8 - 72*a^12*b^6 + 68*a^14*b^4 - 32*a^16*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) - (b^3*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*((tan(x/2)*(a^15 - 48*a^3*b^12 + 212*a^5*b^10 - 363*a^7*b^8 + 290*a^9*b^6 - 98*a^11*b^4 + 6*a^13*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2) - (a^11*b + 24*a^5*b^7 - 52*a^7*b^5 + 30*a^9*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) + (b^3*((2*a^14*b + 2*a^10*b^5 - 4*a^12*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) - (tan(x/2)*(6*a^18 - 8*a^8*b^10 + 38*a^10*b^8 - 72*a^12*b^6 + 68*a^14*b^4 - 32*a^16*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))/((144*b^9 - 336*a^2*b^7 + 211*a^4*b^5 + 20*a^6*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) + (2*tan(x/2)*(72*b^12 - 294*a^2*b^10 + 422*a^4*b^8 - 229*a^6*b^6 + 20*a^8*b^4))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2) + (b^3*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*((a^11*b + 24*a^5*b^7 - 52*a^7*b^5 + 30*a^9*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) - (tan(x/2)*(a^15 - 48*a^3*b^12 + 212*a^5*b^10 - 363*a^7*b^8 + 290*a^9*b^6 - 98*a^11*b^4 + 6*a^13*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2) + (b^3*((2*a^14*b + 2*a^10*b^5 - 4*a^12*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) - (tan(x/2)*(6*a^18 - 8*a^8*b^10 + 38*a^10*b^8 - 72*a^12*b^6 + 68*a^14*b^4 - 32*a^16*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b^3*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*((tan(x/2)*(a^15 - 48*a^3*b^12 + 212*a^5*b^10 - 363*a^7*b^8 + 290*a^9*b^6 - 98*a^11*b^4 + 6*a^13*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2) - (a^11*b + 24*a^5*b^7 - 52*a^7*b^5 + 30*a^9*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) + (b^3*((2*a^14*b + 2*a^10*b^5 - 4*a^12*b^3)/(a^12 + a^8*b^4 - 2*a^10*b^2) - (tan(x/2)*(6*a^18 - 8*a^8*b^10 + 38*a^10*b^8 - 72*a^12*b^6 + 68*a^14*b^4 - 32*a^16*b^2))/(a^15 + a^7*b^8 - 4*a^9*b^6 + 6*a^11*b^4 - 4*a^13*b^2))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*1i)/(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)","B"
202,1,708,182,10.384254,"\text{Not used}","int(1/(a + b*sin(c + d*x))^4,x)","\frac{\frac{18\,a^4\,b-5\,a^2\,b^3+2\,b^5}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^6\,b+20\,a^4\,b^3-3\,a^2\,b^5+2\,b^7\right)}{a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^6\,b+27\,a^4\,b^3-12\,a^2\,b^5+4\,b^7\right)}{a^2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(27\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,a^4\,b-6\,a^2\,b^3+2\,b^5\right)}{a\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2+2\,b^2\right)\,\left(18\,a^4\,b-5\,a^2\,b^3+2\,b^5\right)}{3\,a^3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b+8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{a\,\mathrm{atan}\left(\frac{\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+3\,b^2\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}+\frac{a\,\left(2\,a^2+3\,b^2\right)\,\left(2\,a^6\,b-6\,a^4\,b^3+6\,a^2\,b^5-2\,b^7\right)}{2\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{2\,a^3+3\,a\,b^2}\right)\,\left(2\,a^2+3\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((18*a^4*b + 2*b^5 - 5*a^2*b^3)/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^2*(6*a^6*b + 2*b^7 - 3*a^2*b^5 + 20*a^4*b^3))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (tan(c/2 + (d*x)/2)^4*(6*a^6*b + 4*b^7 - 12*a^2*b^5 + 27*a^4*b^3))/(a^2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b*tan(c/2 + (d*x)/2)*(27*a^4*b + 2*b^5 - 4*a^2*b^3))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (b*tan(c/2 + (d*x)/2)^5*(9*a^4*b + 2*b^5 - 6*a^2*b^3))/(a*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*b*tan(c/2 + (d*x)/2)^3*(3*a^2 + 2*b^2)*(18*a^4*b + 2*b^5 - 5*a^2*b^3))/(3*a^3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(a^3*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^2*(12*a*b^2 + 3*a^3) + tan(c/2 + (d*x)/2)^4*(12*a*b^2 + 3*a^3) + tan(c/2 + (d*x)/2)^3*(12*a^2*b + 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5)) + (a*atan((((a^2*tan(c/2 + (d*x)/2)*(2*a^2 + 3*b^2))/((a + b)^(7/2)*(a - b)^(7/2)) + (a*(2*a^2 + 3*b^2)*(2*a^6*b - 2*b^7 + 6*a^2*b^5 - 6*a^4*b^3))/(2*(a + b)^(7/2)*(a - b)^(7/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/(3*a*b^2 + 2*a^3))*(2*a^2 + 3*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
203,0,-1,172,0.000000,"\text{Not used}","int(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2),x)","\int \sin\left(e+f\,x\right)\,\sqrt{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2), x)","F"
204,1,55,62,6.871156,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2),x)","\frac{2\,\mathrm{E}\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{a+b\,\sin\left(e+f\,x\right)}}{f\,\sqrt{\frac{a+b\,\sin\left(e+f\,x\right)}{a+b}}}","Not used",1,"(2*ellipticE(e/2 - pi/4 + (f*x)/2, (2*b)/(a + b))*(a + b*sin(e + f*x))^(1/2))/(f*((a + b*sin(e + f*x))/(a + b))^(1/2))","B"
205,0,-1,128,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/sin(e + f*x),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/sin(e + f*x), x)","F"
206,0,-1,213,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/sin(e + f*x)^2,x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/sin(e + f*x)^2, x)","F"
207,1,118,132,7.206773,"\text{Not used}","int(sin(e + f*x)/(a + b*sin(e + f*x))^(1/2),x)","\frac{\left(2\,a\,\mathrm{F}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|\frac{2\,b}{a+b}\right)-2\,\left(a+b\right)\,\mathrm{E}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|\frac{2\,b}{a+b}\right)\right)\,\sqrt{{\cos\left(e+f\,x\right)}^2}\,\sqrt{\frac{a+b\,\sin\left(e+f\,x\right)}{a+b}}}{b\,f\,\cos\left(e+f\,x\right)\,\sqrt{a+b\,\sin\left(e+f\,x\right)}}","Not used",1,"((2*a*ellipticF(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), (2*b)/(a + b)) - 2*(a + b)*ellipticE(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), (2*b)/(a + b)))*(cos(e + f*x)^2)^(1/2)*((a + b*sin(e + f*x))/(a + b))^(1/2))/(b*f*cos(e + f*x)*(a + b*sin(e + f*x))^(1/2))","B"
208,1,55,62,6.912790,"\text{Not used}","int(1/(a + b*sin(e + f*x))^(1/2),x)","-\frac{2\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\sin\left(e+f\,x\right)}{a+b}}}{f\,\sqrt{a+b\,\sin\left(e+f\,x\right)}}","Not used",1,"-(2*ellipticF(pi/4 - e/2 - (f*x)/2, (2*b)/(a + b))*((a + b*sin(e + f*x))/(a + b))^(1/2))/(f*(a + b*sin(e + f*x))^(1/2))","B"
209,0,-1,63,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\sqrt{a+b\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2)), x)","F"
210,0,-1,222,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,\sqrt{a+b\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(a + b*sin(e + f*x))^(1/2)), x)","F"
211,0,-1,371,0.000000,"\text{Not used}","int(sin(c + d*x)^(1/2)*(a + b*sin(c + d*x))^(1/2),x)","\int \sqrt{\sin\left(c+d\,x\right)}\,\sqrt{a+b\,\sin\left(c+d\,x\right)} \,d x","Not used",1,"int(sin(c + d*x)^(1/2)*(a + b*sin(c + d*x))^(1/2), x)","F"
212,0,-1,109,0.000000,"\text{Not used}","int(1/(sin(c + d*x)^(1/2)*(a + b*sin(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\sin\left(c+d\,x\right)}\,\sqrt{a+b\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(sin(c + d*x)^(1/2)*(a + b*sin(c + d*x))^(1/2)), x)","F"
213,0,-1,270,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m*(a + b*sin(e + f*x))^3,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^m\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((d*sin(e + f*x))^m*(a + b*sin(e + f*x))^3, x)","F"
214,0,-1,194,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m*(a + b*sin(e + f*x))^2,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^m\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((d*sin(e + f*x))^m*(a + b*sin(e + f*x))^2, x)","F"
215,0,-1,139,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m*(a + b*sin(e + f*x)),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^m\,\left(a+b\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((d*sin(e + f*x))^m*(a + b*sin(e + f*x)), x)","F"
216,0,-1,195,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m/(a + b*sin(e + f*x)),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^m}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^m/(a + b*sin(e + f*x)), x)","F"
217,0,-1,306,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^m}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((d*sin(e + f*x))^m/(a + b*sin(e + f*x))^2, x)","F"
218,0,-1,406,0.000000,"\text{Not used}","int((d*sin(e + f*x))^m/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^m}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((d*sin(e + f*x))^m/(a + b*sin(e + f*x))^3, x)","F"
219,0,-1,142,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^2/sin(c + d*x)^(a^2/(a^2 + b^2) + 1),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^2}{{\sin\left(c+d\,x\right)}^{\frac{a^2}{a^2+b^2}+1}} \,d x","Not used",1,"int((a + b*sin(c + d*x))^2/sin(c + d*x)^(a^2/(a^2 + b^2) + 1), x)","F"
220,1,127,73,7.472920,"\text{Not used}","int((2*sin(c + d*x) + 1)^2/sin(c + d*x)^(6/5),x)","-\frac{4\,\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^{4/5}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{3}{5};\ \frac{3}{2};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\left({\sin\left(c+d\,x\right)}^2\right)}^{2/5}}-\frac{\cos\left(c+d\,x\right)\,{\left({\sin\left(c+d\,x\right)}^2\right)}^{1/10}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{10};\ \frac{3}{2};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\sin\left(c+d\,x\right)}^{1/5}}-\frac{4\,\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^{9/5}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{10},\frac{1}{2};\ \frac{3}{2};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\left({\sin\left(c+d\,x\right)}^2\right)}^{9/10}}","Not used",1,"- (4*cos(c + d*x)*sin(c + d*x)^(4/5)*hypergeom([1/2, 3/5], 3/2, cos(c + d*x)^2))/(d*(sin(c + d*x)^2)^(2/5)) - (cos(c + d*x)*(sin(c + d*x)^2)^(1/10)*hypergeom([1/2, 11/10], 3/2, cos(c + d*x)^2))/(d*sin(c + d*x)^(1/5)) - (4*cos(c + d*x)*sin(c + d*x)^(9/5)*hypergeom([1/10, 1/2], 3/2, cos(c + d*x)^2))/(d*(sin(c + d*x)^2)^(9/10))","B"
221,0,-1,24,0.000000,"\text{Not used}","int(sin(c + d*x)^m*(a + b*sin(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^m\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",0,"int(sin(c + d*x)^m*(a + b*sin(c + d*x))^n, x)","F"
222,0,-1,351,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + b*sin(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^3*(a + b*sin(c + d*x))^n, x)","F"
223,0,-1,274,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + b*sin(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^2*(a + b*sin(c + d*x))^n, x)","F"
224,0,-1,220,0.000000,"\text{Not used}","int(sin(c + d*x)*(a + b*sin(c + d*x))^n,x)","\int \sin\left(c+d\,x\right)\,{\left(a+b\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int(sin(c + d*x)*(a + b*sin(c + d*x))^n, x)","F"
225,0,-1,104,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^n,x)","\int {\left(a+b\,\sin\left(c+d\,x\right)\right)}^n \,d x","Not used",1,"int((a + b*sin(c + d*x))^n, x)","F"
226,0,-1,22,0.000000,"\text{Not used}","int((a + b*sin(c + d*x))^n/sin(c + d*x),x)","\int \frac{{\left(a+b\,\sin\left(c+d\,x\right)\right)}^n}{\sin\left(c+d\,x\right)} \,d x","Not used",0,"int((a + b*sin(c + d*x))^n/sin(c + d*x), x)","F"
227,1,292,116,8.859220,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^4,x)","\frac{7\,a\,c^4\,x}{8}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a\,c^4\,\left(105\,e+105\,f\,x\right)}{24}-\frac{a\,c^4\,\left(525\,e+525\,f\,x+640\right)}{120}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a\,c^4\,\left(105\,e+105\,f\,x\right)}{24}-\frac{a\,c^4\,\left(525\,e+525\,f\,x+720\right)}{120}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a\,c^4\,\left(105\,e+105\,f\,x\right)}{12}-\frac{a\,c^4\,\left(1050\,e+1050\,f\,x+800\right)}{120}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{a\,c^4\,\left(105\,e+105\,f\,x\right)}{12}-\frac{a\,c^4\,\left(1050\,e+1050\,f\,x+1920\right)}{120}\right)-\frac{a\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}-\frac{13\,a\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{2}+\frac{13\,a\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{2}+\frac{a\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{4}+\frac{a\,c^4\,\left(105\,e+105\,f\,x\right)}{120}-\frac{a\,c^4\,\left(105\,e+105\,f\,x+272\right)}{120}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(7*a*c^4*x)/8 - (tan(e/2 + (f*x)/2)^2*((a*c^4*(105*e + 105*f*x))/24 - (a*c^4*(525*e + 525*f*x + 640))/120) + tan(e/2 + (f*x)/2)^8*((a*c^4*(105*e + 105*f*x))/24 - (a*c^4*(525*e + 525*f*x + 720))/120) + tan(e/2 + (f*x)/2)^4*((a*c^4*(105*e + 105*f*x))/12 - (a*c^4*(1050*e + 1050*f*x + 800))/120) + tan(e/2 + (f*x)/2)^6*((a*c^4*(105*e + 105*f*x))/12 - (a*c^4*(1050*e + 1050*f*x + 1920))/120) - (a*c^4*tan(e/2 + (f*x)/2))/4 - (13*a*c^4*tan(e/2 + (f*x)/2)^3)/2 + (13*a*c^4*tan(e/2 + (f*x)/2)^7)/2 + (a*c^4*tan(e/2 + (f*x)/2)^9)/4 + (a*c^4*(105*e + 105*f*x))/120 - (a*c^4*(105*e + 105*f*x + 272))/120)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
228,1,250,83,9.004431,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^3,x)","\frac{5\,a\,c^3\,x}{8}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a\,c^3\,\left(15\,e+15\,f\,x\right)}{6}-\frac{a\,c^3\,\left(60\,e+60\,f\,x+32\right)}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{a\,c^3\,\left(15\,e+15\,f\,x\right)}{6}-\frac{a\,c^3\,\left(60\,e+60\,f\,x+96\right)}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a\,c^3\,\left(15\,e+15\,f\,x\right)}{4}-\frac{a\,c^3\,\left(90\,e+90\,f\,x+96\right)}{24}\right)-\frac{3\,a\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}-\frac{11\,a\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{4}+\frac{11\,a\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{4}+\frac{3\,a\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{4}+\frac{a\,c^3\,\left(15\,e+15\,f\,x\right)}{24}-\frac{a\,c^3\,\left(15\,e+15\,f\,x+32\right)}{24}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(5*a*c^3*x)/8 - (tan(e/2 + (f*x)/2)^2*((a*c^3*(15*e + 15*f*x))/6 - (a*c^3*(60*e + 60*f*x + 32))/24) + tan(e/2 + (f*x)/2)^6*((a*c^3*(15*e + 15*f*x))/6 - (a*c^3*(60*e + 60*f*x + 96))/24) + tan(e/2 + (f*x)/2)^4*((a*c^3*(15*e + 15*f*x))/4 - (a*c^3*(90*e + 90*f*x + 96))/24) - (3*a*c^3*tan(e/2 + (f*x)/2))/4 - (11*a*c^3*tan(e/2 + (f*x)/2)^3)/4 + (11*a*c^3*tan(e/2 + (f*x)/2)^5)/4 + (3*a*c^3*tan(e/2 + (f*x)/2)^7)/4 + (a*c^3*(15*e + 15*f*x))/24 - (a*c^3*(15*e + 15*f*x + 32))/24)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^4)","B"
229,1,125,52,8.963167,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^2,x)","\frac{a\,c^2\,x}{2}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{3\,a\,c^2\,\left(e+f\,x\right)}{2}-\frac{a\,c^2\,\left(9\,e+9\,f\,x+12\right)}{6}\right)-a\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{a\,c^2\,\left(e+f\,x\right)}{2}+a\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-\frac{a\,c^2\,\left(3\,e+3\,f\,x+4\right)}{6}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(a*c^2*x)/2 - (tan(e/2 + (f*x)/2)^4*((3*a*c^2*(e + f*x))/2 - (a*c^2*(9*e + 9*f*x + 12))/6) - a*c^2*tan(e/2 + (f*x)/2) + (a*c^2*(e + f*x))/2 + a*c^2*tan(e/2 + (f*x)/2)^5 - (a*c^2*(3*e + 3*f*x + 4))/6)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^3)","B"
230,1,54,29,7.153984,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x)),x)","\frac{a\,c\,x}{2}-\frac{a\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-a\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(a*c*x)/2 - (a*c*tan(e/2 + (f*x)/2)^3 - a*c*tan(e/2 + (f*x)/2))/(f*(tan(e/2 + (f*x)/2)^2 + 1)^2)","B"
231,1,46,33,6.809433,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x)),x)","-\frac{a\,x}{c}-\frac{a\,\left(e+f\,x\right)-a\,\left(e+f\,x-4\right)}{c\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}","Not used",1,"- (a*x)/c - (a*(e + f*x) - a*(e + f*x - 4))/(c*f*(tan(e/2 + (f*x)/2) - 1))","B"
232,1,56,30,6.725518,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^2,x)","-\frac{2\,a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-3\right)}{3\,c^2\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^3}","Not used",1,"-(2*a*cos(e/2 + (f*x)/2)*(2*cos(e/2 + (f*x)/2)^2 - 3))/(3*c^2*f*(cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2))^3)","B"
233,1,136,60,7.103685,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^3,x)","\frac{2\,a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-5\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+25\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-15\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+15\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\right)}{15\,c^3\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^5}","Not used",1,"(2*a*cos(e/2 + (f*x)/2)*(4*cos(e/2 + (f*x)/2)^4 + 15*sin(e/2 + (f*x)/2)^4 - 15*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^3 - 5*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2) + 25*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2))/(15*c^3*f*(cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2))^5)","B"
234,1,97,92,7.353349,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^4,x)","\frac{\sqrt{2}\,a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{25\,\cos\left(3\,e+3\,f\,x\right)}{8}-\frac{595\,\sin\left(e+f\,x\right)}{8}-\frac{43\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{353\,\cos\left(e+f\,x\right)}{8}+\frac{77\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{21\,\sin\left(3\,e+3\,f\,x\right)}{8}+\frac{171}{2}\right)}{840\,c^4\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^7}","Not used",1,"(2^(1/2)*a*cos(e/2 + (f*x)/2)*((25*cos(3*e + 3*f*x))/8 - (595*sin(e + f*x))/8 - (43*cos(2*e + 2*f*x))/2 - (353*cos(e + f*x))/8 + (77*sin(2*e + 2*f*x))/4 + (21*sin(3*e + 3*f*x))/8 + 171/2))/(840*c^4*f*cos(e/2 + pi/4 + (f*x)/2)^7)","B"
235,1,119,126,8.769256,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^5,x)","\frac{\sqrt{2}\,a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{121\,\cos\left(3\,e+3\,f\,x\right)}{4}-\frac{1575\,\sin\left(e+f\,x\right)}{4}-\frac{625\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{635\,\cos\left(e+f\,x\right)}{4}+\frac{7\,\cos\left(4\,e+4\,f\,x\right)}{2}+\frac{399\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{141\,\sin\left(3\,e+3\,f\,x\right)}{4}-\frac{15\,\sin\left(4\,e+4\,f\,x\right)}{4}+\frac{1357}{4}\right)}{5040\,c^5\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^9}","Not used",1,"(2^(1/2)*a*cos(e/2 + (f*x)/2)*((121*cos(3*e + 3*f*x))/4 - (1575*sin(e + f*x))/4 - (625*cos(2*e + 2*f*x))/4 - (635*cos(e + f*x))/4 + (7*cos(4*e + 4*f*x))/2 + (399*sin(2*e + 2*f*x))/4 + (141*sin(3*e + 3*f*x))/4 - (15*sin(4*e + 4*f*x))/4 + 1357/4))/(5040*c^5*f*cos(e/2 + pi/4 + (f*x)/2)^9)","B"
236,1,452,152,9.229282,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^5,x)","\frac{9\,a^2\,c^5\,x}{16}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{80}-\frac{a^2\,c^5\,\left(2205\,e+2205\,f\,x+1792\right)}{560}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(\frac{a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{80}-\frac{a^2\,c^5\,\left(2205\,e+2205\,f\,x+3360\right)}{560}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{3\,a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{80}-\frac{a^2\,c^5\,\left(6615\,e+6615\,f\,x+6496\right)}{560}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(\frac{3\,a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{80}-\frac{a^2\,c^5\,\left(6615\,e+6615\,f\,x+8960\right)}{560}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{16}-\frac{a^2\,c^5\,\left(11025\,e+11025\,f\,x+7840\right)}{560}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{16}-\frac{a^2\,c^5\,\left(11025\,e+11025\,f\,x+17920\right)}{560}\right)-\frac{17\,a^2\,c^5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{2}+\frac{13\,a^2\,c^5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{8}-\frac{13\,a^2\,c^5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{8}+\frac{17\,a^2\,c^5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}}{2}+\frac{7\,a^2\,c^5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}}{8}+\frac{a^2\,c^5\,\left(315\,e+315\,f\,x\right)}{560}-\frac{a^2\,c^5\,\left(315\,e+315\,f\,x+736\right)}{560}-\frac{7\,a^2\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(9*a^2*c^5*x)/16 - (tan(e/2 + (f*x)/2)^2*((a^2*c^5*(315*e + 315*f*x))/80 - (a^2*c^5*(2205*e + 2205*f*x + 1792))/560) + tan(e/2 + (f*x)/2)^12*((a^2*c^5*(315*e + 315*f*x))/80 - (a^2*c^5*(2205*e + 2205*f*x + 3360))/560) + tan(e/2 + (f*x)/2)^4*((3*a^2*c^5*(315*e + 315*f*x))/80 - (a^2*c^5*(6615*e + 6615*f*x + 6496))/560) + tan(e/2 + (f*x)/2)^10*((3*a^2*c^5*(315*e + 315*f*x))/80 - (a^2*c^5*(6615*e + 6615*f*x + 8960))/560) + tan(e/2 + (f*x)/2)^8*((a^2*c^5*(315*e + 315*f*x))/16 - (a^2*c^5*(11025*e + 11025*f*x + 7840))/560) + tan(e/2 + (f*x)/2)^6*((a^2*c^5*(315*e + 315*f*x))/16 - (a^2*c^5*(11025*e + 11025*f*x + 17920))/560) - (17*a^2*c^5*tan(e/2 + (f*x)/2)^3)/2 + (13*a^2*c^5*tan(e/2 + (f*x)/2)^5)/8 - (13*a^2*c^5*tan(e/2 + (f*x)/2)^9)/8 + (17*a^2*c^5*tan(e/2 + (f*x)/2)^11)/2 + (7*a^2*c^5*tan(e/2 + (f*x)/2)^13)/8 + (a^2*c^5*(315*e + 315*f*x))/560 - (a^2*c^5*(315*e + 315*f*x + 736))/560 - (7*a^2*c^5*tan(e/2 + (f*x)/2))/8)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^7)","B"
237,1,284,118,8.901156,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^4,x)","\frac{a^2\,c^4\,\left(105\,e+270\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+192\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+890\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+1920\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-660\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+1920\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+660\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+960\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8-890\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+960\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-270\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+105\,f\,x+630\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(e+f\,x\right)+1575\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(e+f\,x\right)+2100\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(e+f\,x\right)+1575\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(e+f\,x\right)+630\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(e+f\,x\right)+105\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(e+f\,x\right)+192\right)}{240\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(a^2*c^4*(105*e + 270*tan(e/2 + (f*x)/2) + 192*tan(e/2 + (f*x)/2)^2 + 890*tan(e/2 + (f*x)/2)^3 + 1920*tan(e/2 + (f*x)/2)^4 - 660*tan(e/2 + (f*x)/2)^5 + 1920*tan(e/2 + (f*x)/2)^6 + 660*tan(e/2 + (f*x)/2)^7 + 960*tan(e/2 + (f*x)/2)^8 - 890*tan(e/2 + (f*x)/2)^9 + 960*tan(e/2 + (f*x)/2)^10 - 270*tan(e/2 + (f*x)/2)^11 + 105*f*x + 630*tan(e/2 + (f*x)/2)^2*(e + f*x) + 1575*tan(e/2 + (f*x)/2)^4*(e + f*x) + 2100*tan(e/2 + (f*x)/2)^6*(e + f*x) + 1575*tan(e/2 + (f*x)/2)^8*(e + f*x) + 630*tan(e/2 + (f*x)/2)^10*(e + f*x) + 105*tan(e/2 + (f*x)/2)^12*(e + f*x) + 192))/(240*f*(tan(e/2 + (f*x)/2)^2 + 1)^6)","B"
238,1,220,85,10.003769,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^3,x)","\frac{3\,a^2\,c^3\,x}{8}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a^2\,c^3\,\left(75\,e+75\,f\,x+80\right)}{40}-\frac{15\,a^2\,c^3\,\left(e+f\,x\right)}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^2\,c^3\,\left(150\,e+150\,f\,x+160\right)}{40}-\frac{15\,a^2\,c^3\,\left(e+f\,x\right)}{4}\right)+\frac{a^2\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{2}-\frac{a^2\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{2}-\frac{5\,a^2\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{4}+\frac{a^2\,c^3\,\left(15\,e+15\,f\,x+16\right)}{40}+\frac{5\,a^2\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}-\frac{3\,a^2\,c^3\,\left(e+f\,x\right)}{8}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a^2*c^3*x)/8 + (tan(e/2 + (f*x)/2)^8*((a^2*c^3*(75*e + 75*f*x + 80))/40 - (15*a^2*c^3*(e + f*x))/8) + tan(e/2 + (f*x)/2)^4*((a^2*c^3*(150*e + 150*f*x + 160))/40 - (15*a^2*c^3*(e + f*x))/4) + (a^2*c^3*tan(e/2 + (f*x)/2)^3)/2 - (a^2*c^3*tan(e/2 + (f*x)/2)^7)/2 - (5*a^2*c^3*tan(e/2 + (f*x)/2)^9)/4 + (a^2*c^3*(15*e + 15*f*x + 16))/40 + (5*a^2*c^3*tan(e/2 + (f*x)/2))/4 - (3*a^2*c^3*(e + f*x))/8)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
239,1,36,64,6.741544,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^2,x)","\frac{a^2\,c^2\,\left(8\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)+12\,f\,x\right)}{32\,f}","Not used",1,"(a^2*c^2*(8*sin(2*e + 2*f*x) + sin(4*e + 4*f*x) + 12*f*x))/(32*f)","B"
240,1,125,52,9.016686,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)),x)","\frac{a^2\,c\,x}{2}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{3\,a^2\,c\,\left(e+f\,x\right)}{2}-\frac{a^2\,c\,\left(9\,e+9\,f\,x-12\right)}{6}\right)-a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{a^2\,c\,\left(e+f\,x\right)}{2}+a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-\frac{a^2\,c\,\left(3\,e+3\,f\,x-4\right)}{6}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(a^2*c*x)/2 - (tan(e/2 + (f*x)/2)^4*((3*a^2*c*(e + f*x))/2 - (a^2*c*(9*e + 9*f*x - 12))/6) - a^2*c*tan(e/2 + (f*x)/2) + (a^2*c*(e + f*x))/2 + a^2*c*tan(e/2 + (f*x)/2)^5 - (a^2*c*(3*e + 3*f*x - 4))/6)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^3)","B"
241,1,118,57,6.905310,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x)),x)","\frac{3\,\sqrt{2}\,a^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-\frac{\sqrt{2}\,a^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,e+6\,f\,x-16\right)}{2}}{c\,f\,\left(\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sqrt{2}\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{3\,a^2\,x}{c}+\frac{2\,a^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{c\,f}","Not used",1,"(3*2^(1/2)*a^2*sin(e/2 + (f*x)/2)*(e + f*x) - (2^(1/2)*a^2*sin(e/2 + (f*x)/2)*(6*e + 6*f*x - 16))/2)/(c*f*(2^(1/2)*cos(e/2 + (f*x)/2) - 2^(1/2)*sin(e/2 + (f*x)/2))) - (3*a^2*x)/c + (2*a^2*cos(e/2 + (f*x)/2)^2)/(c*f)","B"
242,1,90,72,6.872567,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^2,x)","\frac{a^2\,x}{c^2}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^2\,\left(e+f\,x\right)-\frac{a^2\,\left(9\,e+9\,f\,x-24\right)}{3}\right)-a^2\,\left(e+f\,x\right)+\frac{a^2\,\left(3\,e+3\,f\,x-8\right)}{3}}{c^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^3}","Not used",1,"(a^2*x)/c^2 - (tan(e/2 + (f*x)/2)*(3*a^2*(e + f*x) - (a^2*(9*e + 9*f*x - 24))/3) - a^2*(e + f*x) + (a^2*(3*e + 3*f*x - 8))/3)/(c^2*f*(tan(e/2 + (f*x)/2) - 1)^3)","B"
243,1,92,34,6.993403,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^3,x)","\frac{2\,a^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\right)}{5\,c^3\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^5}","Not used",1,"(2*a^2*cos(e/2 + (f*x)/2)*(cos(e/2 + (f*x)/2)^4 + 5*sin(e/2 + (f*x)/2)^4 + 10*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2))/(5*c^3*f*(cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2))^5)","B"
244,1,99,67,7.295778,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^4,x)","\frac{\sqrt{2}\,a^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{5\,\cos\left(3\,e+3\,f\,x\right)}{8}-\frac{105\,\sin\left(e+f\,x\right)}{8}-\frac{27\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{121\,\cos\left(e+f\,x\right)}{8}+\frac{7\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{7\,\sin\left(3\,e+3\,f\,x\right)}{8}+\frac{109}{4}\right)}{280\,c^4\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^7}","Not used",1,"(2^(1/2)*a^2*cos(e/2 + (f*x)/2)*((5*cos(3*e + 3*f*x))/8 - (105*sin(e + f*x))/8 - (27*cos(2*e + 2*f*x))/4 - (121*cos(e + f*x))/8 + (7*sin(2*e + 2*f*x))/2 + (7*sin(3*e + 3*f*x))/8 + 109/4))/(280*c^4*f*cos(e/2 + pi/4 + (f*x)/2)^7)","B"
245,1,121,98,8.809899,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^5,x)","\frac{\sqrt{2}\,a^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{89\,\cos\left(3\,e+3\,f\,x\right)}{4}-\frac{2205\,\sin\left(e+f\,x\right)}{8}-\frac{265\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{625\,\cos\left(e+f\,x\right)}{4}+\frac{49\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{567\,\sin\left(2\,e+2\,f\,x\right)}{8}+\frac{243\,\sin\left(3\,e+3\,f\,x\right)}{8}-\frac{45\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{4967}{16}\right)}{5040\,c^5\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^9}","Not used",1,"(2^(1/2)*a^2*cos(e/2 + (f*x)/2)*((89*cos(3*e + 3*f*x))/4 - (2205*sin(e + f*x))/8 - (265*cos(2*e + 2*f*x))/2 - (625*cos(e + f*x))/4 + (49*cos(4*e + 4*f*x))/16 + (567*sin(2*e + 2*f*x))/8 + (243*sin(3*e + 3*f*x))/8 - (45*sin(4*e + 4*f*x))/16 + 4967/16))/(5040*c^5*f*cos(e/2 + pi/4 + (f*x)/2)^9)","B"
246,1,143,132,9.357017,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^6,x)","-\frac{\sqrt{2}\,a^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(697\,\cos\left(e+f\,x\right)+\frac{7623\,\sin\left(e+f\,x\right)}{4}+\frac{3977\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{3203\,\cos\left(3\,e+3\,f\,x\right)}{16}-\frac{461\,\cos\left(4\,e+4\,f\,x\right)}{8}+\frac{75\,\cos\left(5\,e+5\,f\,x\right)}{16}-462\,\sin\left(2\,e+2\,f\,x\right)-\frac{4983\,\sin\left(3\,e+3\,f\,x\right)}{16}+\frac{187\,\sin\left(4\,e+4\,f\,x\right)}{4}+\frac{77\,\sin\left(5\,e+5\,f\,x\right)}{16}-\frac{12721}{8}\right)}{36960\,c^6\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^{11}}","Not used",1,"-(2^(1/2)*a^2*cos(e/2 + (f*x)/2)*(697*cos(e + f*x) + (7623*sin(e + f*x))/4 + (3977*cos(2*e + 2*f*x))/4 - (3203*cos(3*e + 3*f*x))/16 - (461*cos(4*e + 4*f*x))/8 + (75*cos(5*e + 5*f*x))/16 - 462*sin(2*e + 2*f*x) - (4983*sin(3*e + 3*f*x))/16 + (187*sin(4*e + 4*f*x))/4 + (77*sin(5*e + 5*f*x))/16 - 12721/8))/(36960*c^6*f*cos(e/2 + pi/4 + (f*x)/2)^11)","B"
247,1,403,180,9.306634,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^6,x)","\frac{a^3\,c^6\,\left(3465\,e+9198\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+18432\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+79716\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+138240\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-4284\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+387072\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+176148\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+290304\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+645120\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-176148\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+236544\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+4284\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}+129024\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}-79716\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{15}+48384\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}-9198\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{17}+3465\,f\,x+31185\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(e+f\,x\right)+124740\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(e+f\,x\right)+291060\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(e+f\,x\right)+436590\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(e+f\,x\right)+436590\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(e+f\,x\right)+291060\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(e+f\,x\right)+124740\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}\,\left(e+f\,x\right)+31185\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}\,\left(e+f\,x\right)+3465\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{18}\,\left(e+f\,x\right)+7424\right)}{8064\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(a^3*c^6*(3465*e + 9198*tan(e/2 + (f*x)/2) + 18432*tan(e/2 + (f*x)/2)^2 + 79716*tan(e/2 + (f*x)/2)^3 + 138240*tan(e/2 + (f*x)/2)^4 - 4284*tan(e/2 + (f*x)/2)^5 + 387072*tan(e/2 + (f*x)/2)^6 + 176148*tan(e/2 + (f*x)/2)^7 + 290304*tan(e/2 + (f*x)/2)^8 + 645120*tan(e/2 + (f*x)/2)^10 - 176148*tan(e/2 + (f*x)/2)^11 + 236544*tan(e/2 + (f*x)/2)^12 + 4284*tan(e/2 + (f*x)/2)^13 + 129024*tan(e/2 + (f*x)/2)^14 - 79716*tan(e/2 + (f*x)/2)^15 + 48384*tan(e/2 + (f*x)/2)^16 - 9198*tan(e/2 + (f*x)/2)^17 + 3465*f*x + 31185*tan(e/2 + (f*x)/2)^2*(e + f*x) + 124740*tan(e/2 + (f*x)/2)^4*(e + f*x) + 291060*tan(e/2 + (f*x)/2)^6*(e + f*x) + 436590*tan(e/2 + (f*x)/2)^8*(e + f*x) + 436590*tan(e/2 + (f*x)/2)^10*(e + f*x) + 291060*tan(e/2 + (f*x)/2)^12*(e + f*x) + 124740*tan(e/2 + (f*x)/2)^14*(e + f*x) + 31185*tan(e/2 + (f*x)/2)^16*(e + f*x) + 3465*tan(e/2 + (f*x)/2)^18*(e + f*x) + 7424))/(8064*f*(tan(e/2 + (f*x)/2)^2 + 1)^9)","B"
248,1,372,145,9.123112,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^5,x)","\frac{a^3\,c^5\,\left(\frac{315\,e}{2}+581\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+256\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2065\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+5376\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+5376\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+5705\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+8960\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8-5705\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+8960\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+1792\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}-2065\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}+1792\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}-581\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{15}+\frac{315\,f\,x}{2}+1260\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(e+f\,x\right)+4410\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(e+f\,x\right)+8820\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(e+f\,x\right)+11025\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(e+f\,x\right)+8820\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(e+f\,x\right)+4410\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(e+f\,x\right)+1260\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}\,\left(e+f\,x\right)+\frac{315\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}\,\left(e+f\,x\right)}{2}+256\right)}{448\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(a^3*c^5*((315*e)/2 + 581*tan(e/2 + (f*x)/2) + 256*tan(e/2 + (f*x)/2)^2 + 2065*tan(e/2 + (f*x)/2)^3 + 5376*tan(e/2 + (f*x)/2)^4 + 21*tan(e/2 + (f*x)/2)^5 + 5376*tan(e/2 + (f*x)/2)^6 + 5705*tan(e/2 + (f*x)/2)^7 + 8960*tan(e/2 + (f*x)/2)^8 - 5705*tan(e/2 + (f*x)/2)^9 + 8960*tan(e/2 + (f*x)/2)^10 - 21*tan(e/2 + (f*x)/2)^11 + 1792*tan(e/2 + (f*x)/2)^12 - 2065*tan(e/2 + (f*x)/2)^13 + 1792*tan(e/2 + (f*x)/2)^14 - 581*tan(e/2 + (f*x)/2)^15 + (315*f*x)/2 + 1260*tan(e/2 + (f*x)/2)^2*(e + f*x) + 4410*tan(e/2 + (f*x)/2)^4*(e + f*x) + 8820*tan(e/2 + (f*x)/2)^6*(e + f*x) + 11025*tan(e/2 + (f*x)/2)^8*(e + f*x) + 8820*tan(e/2 + (f*x)/2)^10*(e + f*x) + 4410*tan(e/2 + (f*x)/2)^12*(e + f*x) + 1260*tan(e/2 + (f*x)/2)^14*(e + f*x) + (315*tan(e/2 + (f*x)/2)^16*(e + f*x))/2 + 256))/(448*f*(tan(e/2 + (f*x)/2)^2 + 1)^8)","B"
249,1,301,112,10.453669,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(\frac{a^3\,c^4\,\left(735\,e+735\,f\,x+672\right)}{336}-\frac{35\,a^3\,c^4\,\left(e+f\,x\right)}{16}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^3\,c^4\,\left(2205\,e+2205\,f\,x+2016\right)}{336}-\frac{105\,a^3\,c^4\,\left(e+f\,x\right)}{16}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a^3\,c^4\,\left(3675\,e+3675\,f\,x+3360\right)}{336}-\frac{175\,a^3\,c^4\,\left(e+f\,x\right)}{16}\right)+\frac{7\,a^3\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{6}+\frac{85\,a^3\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{24}-\frac{85\,a^3\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{24}-\frac{7\,a^3\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}}{6}-\frac{11\,a^3\,c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}}{8}+\frac{a^3\,c^4\,\left(105\,e+105\,f\,x+96\right)}{336}+\frac{11\,a^3\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8}-\frac{5\,a^3\,c^4\,\left(e+f\,x\right)}{16}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^7}+\frac{5\,a^3\,c^4\,x}{16}","Not used",1,"(tan(e/2 + (f*x)/2)^12*((a^3*c^4*(735*e + 735*f*x + 672))/336 - (35*a^3*c^4*(e + f*x))/16) + tan(e/2 + (f*x)/2)^4*((a^3*c^4*(2205*e + 2205*f*x + 2016))/336 - (105*a^3*c^4*(e + f*x))/16) + tan(e/2 + (f*x)/2)^8*((a^3*c^4*(3675*e + 3675*f*x + 3360))/336 - (175*a^3*c^4*(e + f*x))/16) + (7*a^3*c^4*tan(e/2 + (f*x)/2)^3)/6 + (85*a^3*c^4*tan(e/2 + (f*x)/2)^5)/24 - (85*a^3*c^4*tan(e/2 + (f*x)/2)^9)/24 - (7*a^3*c^4*tan(e/2 + (f*x)/2)^11)/6 - (11*a^3*c^4*tan(e/2 + (f*x)/2)^13)/8 + (a^3*c^4*(105*e + 105*f*x + 96))/336 + (11*a^3*c^4*tan(e/2 + (f*x)/2))/8 - (5*a^3*c^4*(e + f*x))/16)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^7) + (5*a^3*c^4*x)/16","B"
250,1,143,91,10.139133,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^3,x)","\frac{5\,a^3\,c^3\,x}{16}-\frac{\frac{11\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}}{8}-\frac{5\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{24}+\frac{15\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{4}-\frac{15\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{4}+\frac{5\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24}-\frac{11\,a^3\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(5*a^3*c^3*x)/16 - ((5*a^3*c^3*tan(e/2 + (f*x)/2)^3)/24 - (15*a^3*c^3*tan(e/2 + (f*x)/2)^5)/4 + (15*a^3*c^3*tan(e/2 + (f*x)/2)^7)/4 - (5*a^3*c^3*tan(e/2 + (f*x)/2)^9)/24 + (11*a^3*c^3*tan(e/2 + (f*x)/2)^11)/8 - (11*a^3*c^3*tan(e/2 + (f*x)/2))/8)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^6)","B"
251,1,220,85,10.318399,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^2,x)","\frac{3\,a^3\,c^2\,x}{8}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a^3\,c^2\,\left(75\,e+75\,f\,x-80\right)}{40}-\frac{15\,a^3\,c^2\,\left(e+f\,x\right)}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^3\,c^2\,\left(150\,e+150\,f\,x-160\right)}{40}-\frac{15\,a^3\,c^2\,\left(e+f\,x\right)}{4}\right)+\frac{a^3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{2}-\frac{a^3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{2}-\frac{5\,a^3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{4}+\frac{a^3\,c^2\,\left(15\,e+15\,f\,x-16\right)}{40}+\frac{5\,a^3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}-\frac{3\,a^3\,c^2\,\left(e+f\,x\right)}{8}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a^3*c^2*x)/8 + (tan(e/2 + (f*x)/2)^8*((a^3*c^2*(75*e + 75*f*x - 80))/40 - (15*a^3*c^2*(e + f*x))/8) + tan(e/2 + (f*x)/2)^4*((a^3*c^2*(150*e + 150*f*x - 160))/40 - (15*a^3*c^2*(e + f*x))/4) + (a^3*c^2*tan(e/2 + (f*x)/2)^3)/2 - (a^3*c^2*tan(e/2 + (f*x)/2)^7)/2 - (5*a^3*c^2*tan(e/2 + (f*x)/2)^9)/4 + (a^3*c^2*(15*e + 15*f*x - 16))/40 + (5*a^3*c^2*tan(e/2 + (f*x)/2))/4 - (3*a^3*c^2*(e + f*x))/8)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
252,1,250,82,8.811924,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x)),x)","\frac{5\,a^3\,c\,x}{8}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^3\,c\,\left(15\,e+15\,f\,x\right)}{6}-\frac{a^3\,c\,\left(60\,e+60\,f\,x-32\right)}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{a^3\,c\,\left(15\,e+15\,f\,x\right)}{6}-\frac{a^3\,c\,\left(60\,e+60\,f\,x-96\right)}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^3\,c\,\left(15\,e+15\,f\,x\right)}{4}-\frac{a^3\,c\,\left(90\,e+90\,f\,x-96\right)}{24}\right)-\frac{3\,a^3\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}-\frac{11\,a^3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{4}+\frac{11\,a^3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{4}+\frac{3\,a^3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{4}+\frac{a^3\,c\,\left(15\,e+15\,f\,x\right)}{24}-\frac{a^3\,c\,\left(15\,e+15\,f\,x-32\right)}{24}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(5*a^3*c*x)/8 - (tan(e/2 + (f*x)/2)^2*((a^3*c*(15*e + 15*f*x))/6 - (a^3*c*(60*e + 60*f*x - 32))/24) + tan(e/2 + (f*x)/2)^6*((a^3*c*(15*e + 15*f*x))/6 - (a^3*c*(60*e + 60*f*x - 96))/24) + tan(e/2 + (f*x)/2)^4*((a^3*c*(15*e + 15*f*x))/4 - (a^3*c*(90*e + 90*f*x - 96))/24) - (3*a^3*c*tan(e/2 + (f*x)/2))/4 - (11*a^3*c*tan(e/2 + (f*x)/2)^3)/4 + (11*a^3*c*tan(e/2 + (f*x)/2)^5)/4 + (3*a^3*c*tan(e/2 + (f*x)/2)^7)/4 + (a^3*c*(15*e + 15*f*x))/24 - (a^3*c*(15*e + 15*f*x - 32))/24)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^4)","B"
253,1,219,94,9.123015,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x)),x)","-\frac{15\,a^3\,x}{2\,c}-\frac{\frac{15\,a^3\,\left(e+f\,x\right)}{2}-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{15\,a^3\,\left(e+f\,x\right)}{2}-\frac{a^3\,\left(15\,e+15\,f\,x-14\right)}{2}\right)-\frac{a^3\,\left(15\,e+15\,f\,x-48\right)}{2}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{15\,a^3\,\left(e+f\,x\right)}{2}-\frac{a^3\,\left(15\,e+15\,f\,x-34\right)}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(15\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(30\,e+30\,f\,x-18\right)}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(15\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(30\,e+30\,f\,x-78\right)}{2}\right)}{c\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"- (15*a^3*x)/(2*c) - ((15*a^3*(e + f*x))/2 - tan(e/2 + (f*x)/2)*((15*a^3*(e + f*x))/2 - (a^3*(15*e + 15*f*x - 14))/2) - (a^3*(15*e + 15*f*x - 48))/2 + tan(e/2 + (f*x)/2)^4*((15*a^3*(e + f*x))/2 - (a^3*(15*e + 15*f*x - 34))/2) - tan(e/2 + (f*x)/2)^3*(15*a^3*(e + f*x) - (a^3*(30*e + 30*f*x - 18))/2) + tan(e/2 + (f*x)/2)^2*(15*a^3*(e + f*x) - (a^3*(30*e + 30*f*x - 78))/2))/(c*f*(tan(e/2 + (f*x)/2) - 1)*(tan(e/2 + (f*x)/2)^2 + 1)^2)","B"
254,1,218,92,9.751706,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^2,x)","\frac{5\,a^3\,x}{c^2}+\frac{5\,a^3\,\left(e+f\,x\right)-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(15\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(45\,e+45\,f\,x-114\right)}{3}\right)-\frac{a^3\,\left(15\,e+15\,f\,x-46\right)}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(15\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(45\,e+45\,f\,x-24\right)}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(20\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(60\,e+60\,f\,x-82\right)}{3}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(20\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(60\,e+60\,f\,x-102\right)}{3}\right)}{c^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^3\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*a^3*x)/c^2 + (5*a^3*(e + f*x) - tan(e/2 + (f*x)/2)*(15*a^3*(e + f*x) - (a^3*(45*e + 45*f*x - 114))/3) - (a^3*(15*e + 15*f*x - 46))/3 + tan(e/2 + (f*x)/2)^4*(15*a^3*(e + f*x) - (a^3*(45*e + 45*f*x - 24))/3) + tan(e/2 + (f*x)/2)^2*(20*a^3*(e + f*x) - (a^3*(60*e + 60*f*x - 82))/3) - tan(e/2 + (f*x)/2)^3*(20*a^3*(e + f*x) - (a^3*(60*e + 60*f*x - 102))/3))/(c^2*f*(tan(e/2 + (f*x)/2) - 1)^3*(tan(e/2 + (f*x)/2)^2 + 1))","B"
255,1,203,106,8.480053,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^3,x)","-\frac{a^3\,x}{c^3}-\frac{a^3\,\left(e+f\,x\right)-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(75\,e+75\,f\,x-200\right)}{15}\right)-\frac{a^3\,\left(15\,e+15\,f\,x-52\right)}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(5\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(75\,e+75\,f\,x-60\right)}{15}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(10\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(150\,e+150\,f\,x-120\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(10\,a^3\,\left(e+f\,x\right)-\frac{a^3\,\left(150\,e+150\,f\,x-400\right)}{15}\right)}{c^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^5}","Not used",1,"- (a^3*x)/c^3 - (a^3*(e + f*x) - tan(e/2 + (f*x)/2)*(5*a^3*(e + f*x) - (a^3*(75*e + 75*f*x - 200))/15) - (a^3*(15*e + 15*f*x - 52))/15 + tan(e/2 + (f*x)/2)^4*(5*a^3*(e + f*x) - (a^3*(75*e + 75*f*x - 60))/15) - tan(e/2 + (f*x)/2)^3*(10*a^3*(e + f*x) - (a^3*(150*e + 150*f*x - 120))/15) + tan(e/2 + (f*x)/2)^2*(10*a^3*(e + f*x) - (a^3*(150*e + 150*f*x - 400))/15))/(c^3*f*(tan(e/2 + (f*x)/2) - 1)^5)","B"
256,1,116,34,7.009833,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^4,x)","\frac{2\,a^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+21\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+35\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+7\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\right)}{7\,c^4\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^7}","Not used",1,"(2*a^3*cos(e/2 + (f*x)/2)*(cos(e/2 + (f*x)/2)^6 + 7*sin(e/2 + (f*x)/2)^6 + 35*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^4 + 21*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2)^2))/(7*c^4*f*(cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2))^7)","B"
257,1,121,69,8.578299,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^5,x)","\frac{\sqrt{2}\,a^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{37\,\cos\left(3\,e+3\,f\,x\right)}{8}-\frac{63\,\sin\left(e+f\,x\right)}{2}-\frac{113\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{257\,\cos\left(e+f\,x\right)}{8}+\frac{7\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{63\,\sin\left(2\,e+2\,f\,x\right)}{8}+\frac{9\,\sin\left(3\,e+3\,f\,x\right)}{2}-\frac{9\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{1013}{16}\right)}{1008\,c^5\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^9}","Not used",1,"(2^(1/2)*a^3*cos(e/2 + (f*x)/2)*((37*cos(3*e + 3*f*x))/8 - (63*sin(e + f*x))/2 - (113*cos(2*e + 2*f*x))/4 - (257*cos(e + f*x))/8 + (7*cos(4*e + 4*f*x))/16 + (63*sin(2*e + 2*f*x))/8 + (9*sin(3*e + 3*f*x))/2 - (9*sin(4*e + 4*f*x))/16 + 1013/16))/(1008*c^5*f*cos(e/2 + pi/4 + (f*x)/2)^9)","B"
258,1,143,101,9.339417,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^6,x)","-\frac{\sqrt{2}\,a^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{6635\,\cos\left(e+f\,x\right)}{16}+\frac{13629\,\sin\left(e+f\,x\right)}{16}+565\,\cos\left(2\,e+2\,f\,x\right)-\frac{3527\,\cos\left(3\,e+3\,f\,x\right)}{32}-29\,\cos\left(4\,e+4\,f\,x\right)+\frac{81\,\cos\left(5\,e+5\,f\,x\right)}{32}-\frac{1617\,\sin\left(2\,e+2\,f\,x\right)}{8}-\frac{5049\,\sin\left(3\,e+3\,f\,x\right)}{32}+\frac{407\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{77\,\sin\left(5\,e+5\,f\,x\right)}{32}-922\right)}{22176\,c^6\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^{11}}","Not used",1,"-(2^(1/2)*a^3*cos(e/2 + (f*x)/2)*((6635*cos(e + f*x))/16 + (13629*sin(e + f*x))/16 + 565*cos(2*e + 2*f*x) - (3527*cos(3*e + 3*f*x))/32 - 29*cos(4*e + 4*f*x) + (81*cos(5*e + 5*f*x))/32 - (1617*sin(2*e + 2*f*x))/8 - (5049*sin(3*e + 3*f*x))/32 + (407*sin(4*e + 4*f*x))/16 + (77*sin(5*e + 5*f*x))/32 - 922))/(22176*c^6*f*cos(e/2 + pi/4 + (f*x)/2)^11)","B"
259,1,165,132,10.171432,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^7,x)","-\frac{\sqrt{2}\,a^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8993\,\cos\left(e+f\,x\right)}{4}+\frac{57915\,\sin\left(e+f\,x\right)}{8}+\frac{73423\,\cos\left(2\,e+2\,f\,x\right)}{16}-\frac{15365\,\cos\left(3\,e+3\,f\,x\right)}{16}-\frac{6943\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{937\,\cos\left(5\,e+5\,f\,x\right)}{16}+\frac{77\,\cos\left(6\,e+6\,f\,x\right)}{16}-\frac{6435\,\sin\left(2\,e+2\,f\,x\right)}{4}-\frac{27027\,\sin\left(3\,e+3\,f\,x\right)}{16}+\frac{5005\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{1079\,\sin\left(5\,e+5\,f\,x\right)}{16}-\frac{39\,\sin\left(6\,e+6\,f\,x\right)}{8}-\frac{93061}{16}\right)}{192192\,c^7\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^{13}}","Not used",1,"-(2^(1/2)*a^3*cos(e/2 + (f*x)/2)*((8993*cos(e + f*x))/4 + (57915*sin(e + f*x))/8 + (73423*cos(2*e + 2*f*x))/16 - (15365*cos(3*e + 3*f*x))/16 - (6943*cos(4*e + 4*f*x))/16 + (937*cos(5*e + 5*f*x))/16 + (77*cos(6*e + 6*f*x))/16 - (6435*sin(2*e + 2*f*x))/4 - (27027*sin(3*e + 3*f*x))/16 + (5005*sin(4*e + 4*f*x))/16 + (1079*sin(5*e + 5*f*x))/16 - (39*sin(6*e + 6*f*x))/8 - 93061/16))/(192192*c^7*f*cos(e/2 + pi/4 + (f*x)/2)^13)","B"
260,1,187,166,11.198381,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^8,x)","\frac{\sqrt{2}\,a^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{3497111\,\cos\left(3\,e+3\,f\,x\right)}{128}-\frac{25501905\,\sin\left(e+f\,x\right)}{128}-\frac{257861\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{5734111\,\cos\left(e+f\,x\right)}{128}+\frac{72047\,\cos\left(4\,e+4\,f\,x\right)}{4}-\frac{378579\,\cos\left(5\,e+5\,f\,x\right)}{128}-\frac{1059\,\cos\left(6\,e+6\,f\,x\right)}{2}+\frac{4251\,\cos\left(7\,e+7\,f\,x\right)}{128}+\frac{2633345\,\sin\left(2\,e+2\,f\,x\right)}{64}+\frac{7210775\,\sin\left(3\,e+3\,f\,x\right)}{128}-\frac{89375\,\sin\left(4\,e+4\,f\,x\right)}{8}-\frac{504205\,\sin\left(5\,e+5\,f\,x\right)}{128}+\frac{29765\,\sin\left(6\,e+6\,f\,x\right)}{64}+\frac{4235\,\sin\left(7\,e+7\,f\,x\right)}{128}+\frac{544369}{4}\right)}{5765760\,c^8\,f\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^{15}}","Not used",1,"(2^(1/2)*a^3*cos(e/2 + (f*x)/2)*((3497111*cos(3*e + 3*f*x))/128 - (25501905*sin(e + f*x))/128 - (257861*cos(2*e + 2*f*x))/2 - (5734111*cos(e + f*x))/128 + (72047*cos(4*e + 4*f*x))/4 - (378579*cos(5*e + 5*f*x))/128 - (1059*cos(6*e + 6*f*x))/2 + (4251*cos(7*e + 7*f*x))/128 + (2633345*sin(2*e + 2*f*x))/64 + (7210775*sin(3*e + 3*f*x))/128 - (89375*sin(4*e + 4*f*x))/8 - (504205*sin(5*e + 5*f*x))/128 + (29765*sin(6*e + 6*f*x))/64 + (4235*sin(7*e + 7*f*x))/128 + 544369/4))/(5765760*c^8*f*cos(e/2 + pi/4 + (f*x)/2)^15)","B"
261,1,290,118,10.529834,"\text{Not used}","int((c - c*sin(e + f*x))^4/(a + a*sin(e + f*x)),x)","\frac{\frac{35\,c^4\,\left(e+f\,x\right)}{2}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{35\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(105\,e+105\,f\,x+110\right)}{6}\right)-\frac{c^4\,\left(105\,e+105\,f\,x+332\right)}{6}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{35\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(105\,e+105\,f\,x+222\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{105\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(315\,e+315\,f\,x+162\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{105\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(315\,e+315\,f\,x+288\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{105\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(315\,e+315\,f\,x+708\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{105\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(315\,e+315\,f\,x+834\right)}{6}\right)}{a\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}-\frac{35\,c^4\,x}{2\,a}","Not used",1,"((35*c^4*(e + f*x))/2 + tan(e/2 + (f*x)/2)*((35*c^4*(e + f*x))/2 - (c^4*(105*e + 105*f*x + 110))/6) - (c^4*(105*e + 105*f*x + 332))/6 + tan(e/2 + (f*x)/2)^6*((35*c^4*(e + f*x))/2 - (c^4*(105*e + 105*f*x + 222))/6) + tan(e/2 + (f*x)/2)^5*((105*c^4*(e + f*x))/2 - (c^4*(315*e + 315*f*x + 162))/6) + tan(e/2 + (f*x)/2)^3*((105*c^4*(e + f*x))/2 - (c^4*(315*e + 315*f*x + 288))/6) + tan(e/2 + (f*x)/2)^4*((105*c^4*(e + f*x))/2 - (c^4*(315*e + 315*f*x + 708))/6) + tan(e/2 + (f*x)/2)^2*((105*c^4*(e + f*x))/2 - (c^4*(315*e + 315*f*x + 834))/6))/(a*f*(tan(e/2 + (f*x)/2) + 1)*(tan(e/2 + (f*x)/2)^2 + 1)^3) - (35*c^4*x)/(2*a)","B"
262,1,216,92,8.708595,"\text{Not used}","int((c - c*sin(e + f*x))^3/(a + a*sin(e + f*x)),x)","\frac{\frac{15\,c^3\,\left(e+f\,x\right)}{2}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{15\,c^3\,\left(e+f\,x\right)}{2}-\frac{c^3\,\left(15\,e+15\,f\,x+14\right)}{2}\right)-\frac{c^3\,\left(15\,e+15\,f\,x+48\right)}{2}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{15\,c^3\,\left(e+f\,x\right)}{2}-\frac{c^3\,\left(15\,e+15\,f\,x+34\right)}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(15\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(30\,e+30\,f\,x+18\right)}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(15\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(30\,e+30\,f\,x+78\right)}{2}\right)}{a\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}-\frac{15\,c^3\,x}{2\,a}","Not used",1,"((15*c^3*(e + f*x))/2 + tan(e/2 + (f*x)/2)*((15*c^3*(e + f*x))/2 - (c^3*(15*e + 15*f*x + 14))/2) - (c^3*(15*e + 15*f*x + 48))/2 + tan(e/2 + (f*x)/2)^4*((15*c^3*(e + f*x))/2 - (c^3*(15*e + 15*f*x + 34))/2) + tan(e/2 + (f*x)/2)^3*(15*c^3*(e + f*x) - (c^3*(30*e + 30*f*x + 18))/2) + tan(e/2 + (f*x)/2)^2*(15*c^3*(e + f*x) - (c^3*(30*e + 30*f*x + 78))/2))/(a*f*(tan(e/2 + (f*x)/2) + 1)*(tan(e/2 + (f*x)/2)^2 + 1)^2) - (15*c^3*x)/(2*a)","B"
263,1,118,56,6.994052,"\text{Not used}","int((c - c*sin(e + f*x))^2/(a + a*sin(e + f*x)),x)","-\frac{3\,c^2\,x}{a}-\frac{3\,\sqrt{2}\,c^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-\frac{\sqrt{2}\,c^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,e+6\,f\,x+16\right)}{2}}{a\,f\,\left(\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sqrt{2}\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{2\,c^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{a\,f}","Not used",1,"- (3*c^2*x)/a - (3*2^(1/2)*c^2*sin(e/2 + (f*x)/2)*(e + f*x) - (2^(1/2)*c^2*sin(e/2 + (f*x)/2)*(6*e + 6*f*x + 16))/2)/(a*f*(2^(1/2)*cos(e/2 + (f*x)/2) + 2^(1/2)*sin(e/2 + (f*x)/2))) - (2*c^2*cos(e/2 + (f*x)/2)^2)/(a*f)","B"
264,1,45,32,6.645000,"\text{Not used}","int((c - c*sin(e + f*x))/(a + a*sin(e + f*x)),x)","\frac{c\,\left(e+f\,x\right)-c\,\left(e+f\,x+4\right)}{a\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}-\frac{c\,x}{a}","Not used",1,"(c*(e + f*x) - c*(e + f*x + 4))/(a*f*(tan(e/2 + (f*x)/2) + 1)) - (c*x)/a","B"
265,1,35,16,6.849191,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))),x)","-\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{a\,c\,f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}","Not used",1,"-(2*tan(e/2 + (f*x)/2))/(a*c*f*(tan(e/2 + (f*x)/2)^2 - 1))","B"
266,1,74,53,7.011919,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^2),x)","-\frac{2\,\left(3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}{3\,a\,c^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^3\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}","Not used",1,"-(2*(tan(e/2 + (f*x)/2) - 3*tan(e/2 + (f*x)/2)^2 + 3*tan(e/2 + (f*x)/2)^3 + 1))/(3*a*c^2*f*(tan(e/2 + (f*x)/2) - 1)^3*(tan(e/2 + (f*x)/2) + 1))","B"
267,1,89,85,7.158055,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^3),x)","-\frac{2\,\left(5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\right)}{5\,a\,c^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^5\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}","Not used",1,"-(2*(10*tan(e/2 + (f*x)/2)^3 - 3*tan(e/2 + (f*x)/2) - 10*tan(e/2 + (f*x)/2)^4 + 5*tan(e/2 + (f*x)/2)^5 + 2))/(5*a*c^3*f*(tan(e/2 + (f*x)/2) - 1)^5*(tan(e/2 + (f*x)/2) + 1))","B"
268,1,96,118,7.273162,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^4),x)","\frac{\frac{2\,\sin\left(e+f\,x\right)}{5}+\frac{2\,\cos\left(2\,e+2\,f\,x\right)}{5}-\frac{\cos\left(4\,e+4\,f\,x\right)}{35}-\frac{6\,\sin\left(3\,e+3\,f\,x\right)}{35}}{a\,c^4\,f\,\left(\frac{7\,\cos\left(e+f\,x\right)}{4}-\frac{3\,\cos\left(3\,e+3\,f\,x\right)}{4}-\frac{7\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{\sin\left(4\,e+4\,f\,x\right)}{8}\right)}","Not used",1,"((2*sin(e + f*x))/5 + (2*cos(2*e + 2*f*x))/5 - cos(4*e + 4*f*x)/35 - (6*sin(3*e + 3*f*x))/35)/(a*c^4*f*((7*cos(e + f*x))/4 - (3*cos(3*e + 3*f*x))/4 - (7*sin(2*e + 2*f*x))/4 + sin(4*e + 4*f*x)/8))","B"
269,1,372,148,10.855435,"\text{Not used}","int((c - c*sin(e + f*x))^5/(a + a*sin(e + f*x))^2,x)","\frac{105\,c^5\,x}{2\,a^2}-\frac{\frac{105\,c^5\,\left(e+f\,x\right)}{2}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{315\,c^5\,\left(e+f\,x\right)}{2}-\frac{c^5\,\left(945\,e+945\,f\,x+2346\right)}{6}\right)-\frac{c^5\,\left(315\,e+315\,f\,x+988\right)}{6}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{315\,c^5\,\left(e+f\,x\right)}{2}-\frac{c^5\,\left(945\,e+945\,f\,x+618\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(315\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(1890\,e+1890\,f\,x+1938\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(315\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(1890\,e+1890\,f\,x+3990\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(525\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(3150\,e+3150\,f\,x+3386\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(525\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(3150\,e+3150\,f\,x+6494\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(630\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(3780\,e+3780\,f\,x+5802\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(630\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(3780\,e+3780\,f\,x+6054\right)}{6}\right)}{a^2\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"(105*c^5*x)/(2*a^2) - ((105*c^5*(e + f*x))/2 + tan(e/2 + (f*x)/2)*((315*c^5*(e + f*x))/2 - (c^5*(945*e + 945*f*x + 2346))/6) - (c^5*(315*e + 315*f*x + 988))/6 + tan(e/2 + (f*x)/2)^8*((315*c^5*(e + f*x))/2 - (c^5*(945*e + 945*f*x + 618))/6) + tan(e/2 + (f*x)/2)^7*(315*c^5*(e + f*x) - (c^5*(1890*e + 1890*f*x + 1938))/6) + tan(e/2 + (f*x)/2)^2*(315*c^5*(e + f*x) - (c^5*(1890*e + 1890*f*x + 3990))/6) + tan(e/2 + (f*x)/2)^6*(525*c^5*(e + f*x) - (c^5*(3150*e + 3150*f*x + 3386))/6) + tan(e/2 + (f*x)/2)^3*(525*c^5*(e + f*x) - (c^5*(3150*e + 3150*f*x + 6494))/6) + tan(e/2 + (f*x)/2)^4*(630*c^5*(e + f*x) - (c^5*(3780*e + 3780*f*x + 5802))/6) + tan(e/2 + (f*x)/2)^5*(630*c^5*(e + f*x) - (c^5*(3780*e + 3780*f*x + 6054))/6))/(a^2*f*(tan(e/2 + (f*x)/2) + tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^3 + 1)^3)","B"
270,1,291,135,10.090593,"\text{Not used}","int((c - c*sin(e + f*x))^4/(a + a*sin(e + f*x))^2,x)","\frac{35\,c^4\,x}{2\,a^2}-\frac{\frac{35\,c^4\,\left(e+f\,x\right)}{2}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{105\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(315\,e+315\,f\,x+786\right)}{6}\right)-\frac{c^4\,\left(105\,e+105\,f\,x+328\right)}{6}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{105\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(315\,e+315\,f\,x+198\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{175\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(525\,e+525\,f\,x+666\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{175\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(525\,e+525\,f\,x+974\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{245\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(735\,e+735\,f\,x+868\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{245\,c^4\,\left(e+f\,x\right)}{2}-\frac{c^4\,\left(735\,e+735\,f\,x+1428\right)}{6}\right)}{a^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(35*c^4*x)/(2*a^2) - ((35*c^4*(e + f*x))/2 + tan(e/2 + (f*x)/2)*((105*c^4*(e + f*x))/2 - (c^4*(315*e + 315*f*x + 786))/6) - (c^4*(105*e + 105*f*x + 328))/6 + tan(e/2 + (f*x)/2)^6*((105*c^4*(e + f*x))/2 - (c^4*(315*e + 315*f*x + 198))/6) + tan(e/2 + (f*x)/2)^5*((175*c^4*(e + f*x))/2 - (c^4*(525*e + 525*f*x + 666))/6) + tan(e/2 + (f*x)/2)^2*((175*c^4*(e + f*x))/2 - (c^4*(525*e + 525*f*x + 974))/6) + tan(e/2 + (f*x)/2)^4*((245*c^4*(e + f*x))/2 - (c^4*(735*e + 735*f*x + 868))/6) + tan(e/2 + (f*x)/2)^3*((245*c^4*(e + f*x))/2 - (c^4*(735*e + 735*f*x + 1428))/6))/(a^2*f*(tan(e/2 + (f*x)/2) + 1)^3*(tan(e/2 + (f*x)/2)^2 + 1)^2)","B"
271,1,217,90,9.622872,"\text{Not used}","int((c - c*sin(e + f*x))^3/(a + a*sin(e + f*x))^2,x)","\frac{5\,c^3\,x}{a^2}-\frac{5\,c^3\,\left(e+f\,x\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(15\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(45\,e+45\,f\,x+114\right)}{3}\right)-\frac{c^3\,\left(15\,e+15\,f\,x+46\right)}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(15\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(45\,e+45\,f\,x+24\right)}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(20\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(60\,e+60\,f\,x+82\right)}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(20\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(60\,e+60\,f\,x+102\right)}{3}\right)}{a^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*c^3*x)/a^2 - (5*c^3*(e + f*x) + tan(e/2 + (f*x)/2)*(15*c^3*(e + f*x) - (c^3*(45*e + 45*f*x + 114))/3) - (c^3*(15*e + 15*f*x + 46))/3 + tan(e/2 + (f*x)/2)^4*(15*c^3*(e + f*x) - (c^3*(45*e + 45*f*x + 24))/3) + tan(e/2 + (f*x)/2)^2*(20*c^3*(e + f*x) - (c^3*(60*e + 60*f*x + 82))/3) + tan(e/2 + (f*x)/2)^3*(20*c^3*(e + f*x) - (c^3*(60*e + 60*f*x + 102))/3))/(a^2*f*(tan(e/2 + (f*x)/2) + 1)^3*(tan(e/2 + (f*x)/2)^2 + 1))","B"
272,1,89,70,7.066644,"\text{Not used}","int((c - c*sin(e + f*x))^2/(a + a*sin(e + f*x))^2,x)","\frac{c^2\,x}{a^2}-\frac{c^2\,\left(e+f\,x\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c^2\,\left(e+f\,x\right)-\frac{c^2\,\left(9\,e+9\,f\,x+24\right)}{3}\right)-\frac{c^2\,\left(3\,e+3\,f\,x+8\right)}{3}}{a^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"(c^2*x)/a^2 - (c^2*(e + f*x) + tan(e/2 + (f*x)/2)*(3*c^2*(e + f*x) - (c^2*(9*e + 9*f*x + 24))/3) - (c^2*(3*e + 3*f*x + 8))/3)/(a^2*f*(tan(e/2 + (f*x)/2) + 1)^3)","B"
273,1,54,29,7.028581,"\text{Not used}","int((c - c*sin(e + f*x))/(a + a*sin(e + f*x))^2,x)","\frac{2\,c\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-3\right)}{3\,a^2\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^3}","Not used",1,"(2*c*cos(e/2 + (f*x)/2)*(2*cos(e/2 + (f*x)/2)^2 - 3))/(3*a^2*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^3)","B"
274,1,74,52,6.994491,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))),x)","-\frac{2\,\left(3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}{3\,a^2\,c\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(tan(e/2 + (f*x)/2) + 3*tan(e/2 + (f*x)/2)^2 + 3*tan(e/2 + (f*x)/2)^3 - 1))/(3*a^2*c*f*(tan(e/2 + (f*x)/2) - 1)*(tan(e/2 + (f*x)/2) + 1)^3)","B"
275,1,63,38,6.838885,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^2),x)","-\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\right)}{3\,a^2\,c^2\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}^3}","Not used",1,"-(2*tan(e/2 + (f*x)/2)*(3*tan(e/2 + (f*x)/2)^4 - 2*tan(e/2 + (f*x)/2)^2 + 3))/(3*a^2*c^2*f*(tan(e/2 + (f*x)/2)^2 - 1)^3)","B"
276,1,128,76,7.826855,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^3),x)","-\frac{2\,\left(15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7-15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+25\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+13\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+9\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+3\right)}{15\,a^2\,c^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^5\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(9*tan(e/2 + (f*x)/2) - 21*tan(e/2 + (f*x)/2)^2 + 13*tan(e/2 + (f*x)/2)^3 + 25*tan(e/2 + (f*x)/2)^4 - 5*tan(e/2 + (f*x)/2)^5 - 15*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^7 + 3))/(15*a^2*c^3*f*(tan(e/2 + (f*x)/2) - 1)^5*(tan(e/2 + (f*x)/2) + 1)^3)","B"
277,1,119,111,6.979466,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^4),x)","-\frac{\frac{\sin\left(e+f\,x\right)}{3}+\frac{4\,\cos\left(2\,e+2\,f\,x\right)}{21}+\frac{2\,\cos\left(4\,e+4\,f\,x\right)}{21}+\frac{\sin\left(3\,e+3\,f\,x\right)}{14}-\frac{\sin\left(5\,e+5\,f\,x\right)}{42}}{a^2\,c^4\,f\,\left(\frac{\cos\left(5\,e+5\,f\,x\right)}{16}-\frac{3\,\cos\left(3\,e+3\,f\,x\right)}{16}-\frac{7\,\cos\left(e+f\,x\right)}{8}+\frac{\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{\sin\left(4\,e+4\,f\,x\right)}{4}\right)}","Not used",1,"-(sin(e + f*x)/3 + (4*cos(2*e + 2*f*x))/21 + (2*cos(4*e + 4*f*x))/21 + sin(3*e + 3*f*x)/14 - sin(5*e + 5*f*x)/42)/(a^2*c^4*f*(cos(5*e + 5*f*x)/16 - (3*cos(3*e + 3*f*x))/16 - (7*cos(e + f*x))/8 + sin(2*e + 2*f*x)/2 + sin(4*e + 4*f*x)/4))","B"
278,1,180,144,9.290024,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^5),x)","-\frac{2\,\left(63\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}-189\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+273\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+63\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8-378\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+294\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+306\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-450\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+235\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+39\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-51\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+19\right)}{63\,a^2\,c^5\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^9\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(39*tan(e/2 + (f*x)/2)^2 - 51*tan(e/2 + (f*x)/2) + 235*tan(e/2 + (f*x)/2)^3 - 450*tan(e/2 + (f*x)/2)^4 + 306*tan(e/2 + (f*x)/2)^5 + 294*tan(e/2 + (f*x)/2)^6 - 378*tan(e/2 + (f*x)/2)^7 + 63*tan(e/2 + (f*x)/2)^8 + 273*tan(e/2 + (f*x)/2)^9 - 189*tan(e/2 + (f*x)/2)^10 + 63*tan(e/2 + (f*x)/2)^11 + 19))/(63*a^2*c^5*f*(tan(e/2 + (f*x)/2) - 1)^9*(tan(e/2 + (f*x)/2) + 1)^3)","B"
279,1,364,161,11.144891,"\text{Not used}","int((c - c*sin(e + f*x))^5/(a + a*sin(e + f*x))^3,x)","\frac{\frac{63\,c^5\,\left(e+f\,x\right)}{2}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{315\,c^5\,\left(e+f\,x\right)}{2}-\frac{c^5\,\left(1575\,e+1575\,f\,x+4310\right)}{10}\right)-\frac{c^5\,\left(315\,e+315\,f\,x+992\right)}{10}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{315\,c^5\,\left(e+f\,x\right)}{2}-\frac{c^5\,\left(1575\,e+1575\,f\,x+650\right)}{10}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(378\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(3780\,e+3780\,f\,x+3090\right)}{10}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(378\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(3780\,e+3780\,f\,x+8814\right)}{10}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(630\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(6300\,e+6300\,f\,x+7610\right)}{10}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(630\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(6300\,e+6300\,f\,x+12230\right)}{10}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(819\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(8190\,e+8190\,f\,x+11090\right)}{10}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(819\,c^5\,\left(e+f\,x\right)-\frac{c^5\,\left(8190\,e+8190\,f\,x+14702\right)}{10}\right)}{a^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}-\frac{63\,c^5\,x}{2\,a^3}","Not used",1,"((63*c^5*(e + f*x))/2 + tan(e/2 + (f*x)/2)*((315*c^5*(e + f*x))/2 - (c^5*(1575*e + 1575*f*x + 4310))/10) - (c^5*(315*e + 315*f*x + 992))/10 + tan(e/2 + (f*x)/2)^8*((315*c^5*(e + f*x))/2 - (c^5*(1575*e + 1575*f*x + 650))/10) + tan(e/2 + (f*x)/2)^7*(378*c^5*(e + f*x) - (c^5*(3780*e + 3780*f*x + 3090))/10) + tan(e/2 + (f*x)/2)^2*(378*c^5*(e + f*x) - (c^5*(3780*e + 3780*f*x + 8814))/10) + tan(e/2 + (f*x)/2)^6*(630*c^5*(e + f*x) - (c^5*(6300*e + 6300*f*x + 7610))/10) + tan(e/2 + (f*x)/2)^3*(630*c^5*(e + f*x) - (c^5*(6300*e + 6300*f*x + 12230))/10) + tan(e/2 + (f*x)/2)^5*(819*c^5*(e + f*x) - (c^5*(8190*e + 8190*f*x + 11090))/10) + tan(e/2 + (f*x)/2)^4*(819*c^5*(e + f*x) - (c^5*(8190*e + 8190*f*x + 14702))/10))/(a^3*f*(tan(e/2 + (f*x)/2) + 1)^5*(tan(e/2 + (f*x)/2)^2 + 1)^2) - (63*c^5*x)/(2*a^3)","B"
280,1,290,124,10.904223,"\text{Not used}","int((c - c*sin(e + f*x))^4/(a + a*sin(e + f*x))^3,x)","\frac{7\,c^4\,\left(e+f\,x\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(35\,c^4\,\left(e+f\,x\right)-\frac{c^4\,\left(525\,e+525\,f\,x+1430\right)}{15}\right)-\frac{c^4\,\left(105\,e+105\,f\,x+334\right)}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(35\,c^4\,\left(e+f\,x\right)-\frac{c^4\,\left(525\,e+525\,f\,x+240\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(77\,c^4\,\left(e+f\,x\right)-\frac{c^4\,\left(1155\,e+1155\,f\,x+990\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(77\,c^4\,\left(e+f\,x\right)-\frac{c^4\,\left(1155\,e+1155\,f\,x+2684\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(105\,c^4\,\left(e+f\,x\right)-\frac{c^4\,\left(1575\,e+1575\,f\,x+2470\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(105\,c^4\,\left(e+f\,x\right)-\frac{c^4\,\left(1575\,e+1575\,f\,x+2540\right)}{15}\right)}{a^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{7\,c^4\,x}{a^3}","Not used",1,"(7*c^4*(e + f*x) + tan(e/2 + (f*x)/2)*(35*c^4*(e + f*x) - (c^4*(525*e + 525*f*x + 1430))/15) - (c^4*(105*e + 105*f*x + 334))/15 + tan(e/2 + (f*x)/2)^6*(35*c^4*(e + f*x) - (c^4*(525*e + 525*f*x + 240))/15) + tan(e/2 + (f*x)/2)^5*(77*c^4*(e + f*x) - (c^4*(1155*e + 1155*f*x + 990))/15) + tan(e/2 + (f*x)/2)^2*(77*c^4*(e + f*x) - (c^4*(1155*e + 1155*f*x + 2684))/15) + tan(e/2 + (f*x)/2)^4*(105*c^4*(e + f*x) - (c^4*(1575*e + 1575*f*x + 2470))/15) + tan(e/2 + (f*x)/2)^3*(105*c^4*(e + f*x) - (c^4*(1575*e + 1575*f*x + 2540))/15))/(a^3*f*(tan(e/2 + (f*x)/2) + 1)^5*(tan(e/2 + (f*x)/2)^2 + 1)) - (7*c^4*x)/a^3","B"
281,1,200,103,8.939460,"\text{Not used}","int((c - c*sin(e + f*x))^3/(a + a*sin(e + f*x))^3,x)","\frac{c^3\,\left(e+f\,x\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(75\,e+75\,f\,x+200\right)}{15}\right)-\frac{c^3\,\left(15\,e+15\,f\,x+52\right)}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(5\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(75\,e+75\,f\,x+60\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(10\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(150\,e+150\,f\,x+120\right)}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(10\,c^3\,\left(e+f\,x\right)-\frac{c^3\,\left(150\,e+150\,f\,x+400\right)}{15}\right)}{a^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5}-\frac{c^3\,x}{a^3}","Not used",1,"(c^3*(e + f*x) + tan(e/2 + (f*x)/2)*(5*c^3*(e + f*x) - (c^3*(75*e + 75*f*x + 200))/15) - (c^3*(15*e + 15*f*x + 52))/15 + tan(e/2 + (f*x)/2)^4*(5*c^3*(e + f*x) - (c^3*(75*e + 75*f*x + 60))/15) + tan(e/2 + (f*x)/2)^3*(10*c^3*(e + f*x) - (c^3*(150*e + 150*f*x + 120))/15) + tan(e/2 + (f*x)/2)^2*(10*c^3*(e + f*x) - (c^3*(150*e + 150*f*x + 400))/15))/(a^3*f*(tan(e/2 + (f*x)/2) + 1)^5) - (c^3*x)/a^3","B"
282,1,90,33,7.214902,"\text{Not used}","int((c - c*sin(e + f*x))^2/(a + a*sin(e + f*x))^3,x)","-\frac{2\,c^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\right)}{5\,a^3\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^5}","Not used",1,"-(2*c^2*cos(e/2 + (f*x)/2)*(cos(e/2 + (f*x)/2)^4 + 5*sin(e/2 + (f*x)/2)^4 + 10*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2))/(5*a^3*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^5)","B"
283,1,134,58,7.238304,"\text{Not used}","int((c - c*sin(e + f*x))/(a + a*sin(e + f*x))^3,x)","-\frac{2\,c\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+25\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+15\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+15\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\right)}{15\,a^3\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^5}","Not used",1,"-(2*c*cos(e/2 + (f*x)/2)*(4*cos(e/2 + (f*x)/2)^4 + 15*sin(e/2 + (f*x)/2)^4 + 15*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^3 + 5*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2) + 25*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2))/(15*a^3*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^5)","B"
284,1,89,83,7.375678,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))),x)","-\frac{2\,\left(5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\right)}{5\,a^3\,c\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(10*tan(e/2 + (f*x)/2)^3 - 3*tan(e/2 + (f*x)/2) + 10*tan(e/2 + (f*x)/2)^4 + 5*tan(e/2 + (f*x)/2)^5 - 2))/(5*a^3*c*f*(tan(e/2 + (f*x)/2) - 1)*(tan(e/2 + (f*x)/2) + 1)^5)","B"
285,1,128,75,8.425297,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^2),x)","-\frac{2\,\left(15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-25\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+13\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+9\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-3\right)}{15\,a^3\,c^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^3\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(9*tan(e/2 + (f*x)/2) + 21*tan(e/2 + (f*x)/2)^2 + 13*tan(e/2 + (f*x)/2)^3 - 25*tan(e/2 + (f*x)/2)^4 - 5*tan(e/2 + (f*x)/2)^5 + 15*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^7 - 3))/(15*a^3*c^2*f*(tan(e/2 + (f*x)/2) - 1)^3*(tan(e/2 + (f*x)/2) + 1)^5)","B"
286,1,89,59,8.342646,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^3),x)","-\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+58\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+15\right)}{15\,a^3\,c^3\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}^5}","Not used",1,"-(2*tan(e/2 + (f*x)/2)*(58*tan(e/2 + (f*x)/2)^4 - 20*tan(e/2 + (f*x)/2)^2 - 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 15))/(15*a^3*c^3*f*(tan(e/2 + (f*x)/2)^2 - 1)^5)","B"
287,1,180,97,9.416001,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^4),x)","-\frac{2\,\left(35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}-35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+105\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+126\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7-182\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+26\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+130\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-55\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+25\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+5\right)}{35\,a^3\,c^4\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^7\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(25*tan(e/2 + (f*x)/2) - 55*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^3 + 130*tan(e/2 + (f*x)/2)^4 + 26*tan(e/2 + (f*x)/2)^5 - 182*tan(e/2 + (f*x)/2)^6 + 126*tan(e/2 + (f*x)/2)^7 + 105*tan(e/2 + (f*x)/2)^8 - 35*tan(e/2 + (f*x)/2)^9 - 35*tan(e/2 + (f*x)/2)^10 + 35*tan(e/2 + (f*x)/2)^11 + 5))/(35*a^3*c^4*f*(tan(e/2 + (f*x)/2) - 1)^7*(tan(e/2 + (f*x)/2) + 1)^5)","B"
288,1,190,131,8.197658,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^5),x)","-\frac{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{65\,\cos\left(\frac{5\,e}{2}+\frac{5\,f\,x}{2}\right)}{32}-\frac{225\,\cos\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}{32}-5\,\cos\left(\frac{7\,e}{2}+\frac{7\,f\,x}{2}\right)+\cos\left(\frac{9\,e}{2}+\frac{9\,f\,x}{2}\right)-\frac{37\,\cos\left(\frac{11\,e}{2}+\frac{11\,f\,x}{2}\right)}{32}+\frac{5\,\cos\left(\frac{13\,e}{2}+\frac{13\,f\,x}{2}\right)}{32}-\frac{89\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}+11\,\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)-\frac{63\,\sin\left(\frac{5\,e}{2}+\frac{5\,f\,x}{2}\right)}{8}+\frac{25\,\sin\left(\frac{7\,e}{2}+\frac{7\,f\,x}{2}\right)}{8}-\frac{5\,\sin\left(\frac{9\,e}{2}+\frac{9\,f\,x}{2}\right)}{8}+\frac{3\,\sin\left(\frac{11\,e}{2}+\frac{11\,f\,x}{2}\right)}{8}+\frac{\sin\left(\frac{13\,e}{2}+\frac{13\,f\,x}{2}\right)}{4}\right)}{2880\,a^3\,c^5\,f\,{\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}^5\,{\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}^9}","Not used",1,"-(cos(e/2 + (f*x)/2)*((65*cos((5*e)/2 + (5*f*x)/2))/32 - (225*cos((3*e)/2 + (3*f*x)/2))/32 - 5*cos((7*e)/2 + (7*f*x)/2) + cos((9*e)/2 + (9*f*x)/2) - (37*cos((11*e)/2 + (11*f*x)/2))/32 + (5*cos((13*e)/2 + (13*f*x)/2))/32 - (89*sin(e/2 + (f*x)/2))/4 + 11*sin((3*e)/2 + (3*f*x)/2) - (63*sin((5*e)/2 + (5*f*x)/2))/8 + (25*sin((7*e)/2 + (7*f*x)/2))/8 - (5*sin((9*e)/2 + (9*f*x)/2))/8 + (3*sin((11*e)/2 + (11*f*x)/2))/8 + sin((13*e)/2 + (13*f*x)/2)/4))/(2880*a^3*c^5*f*cos(e/2 - pi/4 + (f*x)/2)^5*cos(e/2 + pi/4 + (f*x)/2)^9)","B"
289,1,185,167,8.616095,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^6),x)","-\frac{\frac{2\,\sin\left(e+f\,x\right)}{9}+\frac{2\,\cos\left(2\,e+2\,f\,x\right)}{15}+\frac{10\,\cos\left(4\,e+4\,f\,x\right)}{99}+\frac{2\,\cos\left(6\,e+6\,f\,x\right)}{99}-\frac{\cos\left(8\,e+8\,f\,x\right)}{495}+\frac{34\,\sin\left(3\,e+3\,f\,x\right)}{495}-\frac{2\,\sin\left(5\,e+5\,f\,x\right)}{99}-\frac{2\,\sin\left(7\,e+7\,f\,x\right)}{165}}{a^3\,c^6\,f\,\left(\frac{5\,\cos\left(5\,e+5\,f\,x\right)}{64}-\frac{17\,\cos\left(3\,e+3\,f\,x\right)}{64}-\frac{55\,\cos\left(e+f\,x\right)}{64}+\frac{3\,\cos\left(7\,e+7\,f\,x\right)}{64}+\frac{33\,\sin\left(2\,e+2\,f\,x\right)}{64}+\frac{25\,\sin\left(4\,e+4\,f\,x\right)}{64}+\frac{5\,\sin\left(6\,e+6\,f\,x\right)}{64}-\frac{\sin\left(8\,e+8\,f\,x\right)}{128}\right)}","Not used",1,"-((2*sin(e + f*x))/9 + (2*cos(2*e + 2*f*x))/15 + (10*cos(4*e + 4*f*x))/99 + (2*cos(6*e + 6*f*x))/99 - cos(8*e + 8*f*x)/495 + (34*sin(3*e + 3*f*x))/495 - (2*sin(5*e + 5*f*x))/99 - (2*sin(7*e + 7*f*x))/165)/(a^3*c^6*f*((5*cos(5*e + 5*f*x))/64 - (17*cos(3*e + 3*f*x))/64 - (55*cos(e + f*x))/64 + (3*cos(7*e + 7*f*x))/64 + (33*sin(2*e + 2*f*x))/64 + (25*sin(4*e + 4*f*x))/64 + (5*sin(6*e + 6*f*x))/64 - sin(8*e + 8*f*x)/128))","B"
290,0,-1,137,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2), x)","F"
291,0,-1,103,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2), x)","F"
292,0,-1,69,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2), x)","F"
293,0,-1,34,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2), x)","F"
294,0,-1,77,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(1/2), x)","F"
295,0,-1,76,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(3/2), x)","F"
296,0,-1,113,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(5/2), x)","F"
297,0,-1,145,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c - c*sin(e + f*x))^(7/2), x)","F"
298,0,-1,145,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(7/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(7/2), x)","F"
299,0,-1,109,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2), x)","F"
300,0,-1,73,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2), x)","F"
301,0,-1,36,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2), x)","F"
302,0,-1,115,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(1/2), x)","F"
303,0,-1,115,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(3/2), x)","F"
304,0,-1,122,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(5/2), x)","F"
305,0,-1,156,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(7/2), x)","F"
306,0,-1,190,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c - c*sin(e + f*x))^(9/2), x)","F"
307,0,-1,145,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(7/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(7/2), x)","F"
308,0,-1,109,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2), x)","F"
309,0,-1,73,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2), x)","F"
310,0,-1,36,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2), x)","F"
311,0,-1,151,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(1/2), x)","F"
312,0,-1,150,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(3/2), x)","F"
313,0,-1,157,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(5/2), x)","F"
314,0,-1,157,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(7/2), x)","F"
315,0,-1,191,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(9/2), x)","F"
316,0,-1,225,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c - c*sin(e + f*x))^(11/2), x)","F"
317,0,-1,132,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x)),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x)), x)","F"
318,0,-1,98,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x)),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x)), x)","F"
319,1,90,60,7.289720,"\text{Not used}","int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x)),x)","-\frac{2\,c\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(22\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2+4\,\sin\left(2\,e+2\,f\,x\right)-12\right)}{a\,f\,\left(4\,{\sin\left(e+f\,x\right)}^2+\sin\left(e+f\,x\right)+\sin\left(3\,e+3\,f\,x\right)-4\right)}","Not used",1,"-(2*c*(-c*(sin(e + f*x) - 1))^(1/2)*(4*sin(2*e + 2*f*x) + 22*sin(e/2 + (f*x)/2)^2 + 2*sin((3*e)/2 + (3*f*x)/2)^2 - 12))/(a*f*(sin(e + f*x) + sin(3*e + 3*f*x) + 4*sin(e + f*x)^2 - 4))","B"
320,1,40,29,0.197007,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x)),x)","-\frac{4\,\cos\left(e+f\,x\right)\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{a\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(4*cos(e + f*x)*(-c*(sin(e + f*x) - 1))^(1/2))/(a*f*(cos(2*e + 2*f*x) + 1))","B"
321,0,-1,83,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2)), x)","F"
322,0,-1,117,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{1}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2)), x)","F"
323,0,-1,156,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{1}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2)), x)","F"
324,0,-1,176,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(9/2)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(9/2)/(a + a*sin(e + f*x))^2, x)","F"
325,0,-1,136,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^2, x)","F"
326,1,360,100,11.683240,"\text{Not used}","int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^2,x)","\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,c^2}{a^2\,f}-\frac{c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{a^2\,f}\right)}{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}}+\frac{16\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{a^2\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}-\frac{c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,32{}\mathrm{i}}{3\,a^2\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}-\frac{32\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{3\,a^2\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}","Not used",1,"((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((2*c^2)/(a^2*f) - (c^2*exp(e*1i + f*x*1i)*2i)/(a^2*f)))/(exp(e*1i + f*x*1i) - 1i) + (16*c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(a^2*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)) - (c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*32i)/(3*a^2*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) - (32*c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(3*a^2*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3)","B"
327,1,120,68,10.323431,"\text{Not used}","int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^2,x)","-\frac{4\,c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,3{}\mathrm{i}+3{}\mathrm{i}\right)}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3\,\left(1+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}\right)}","Not used",1,"-(4*c*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(2*exp(e*1i + f*x*1i) - exp(e*2i + f*x*2i)*3i + 3i))/(3*a^2*f*(exp(e*1i + f*x*1i) + 1i)^3*(exp(e*1i + f*x*1i)*1i + 1))","B"
328,1,227,36,9.347321,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^2,x)","-\frac{4\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(\sin\left(2\,e+2\,f\,x\right)-4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-{\sin\left(e+f\,x\right)}^2\,2{}\mathrm{i}+2+2{}\mathrm{i}\right)}{3\,a^2\,f\,\left(-4\,{\sin\left(e+f\,x\right)}^2+\sin\left(e+f\,x\right)+\sin\left(3\,e+3\,f\,x\right)+4\right)}+\frac{4\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(-{\sin\left(e+f\,x\right)}^2\,4{}\mathrm{i}+\sin\left(e+f\,x\right)\,1{}\mathrm{i}-2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2+2\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(3\,e+3\,f\,x\right)\,1{}\mathrm{i}+4{}\mathrm{i}\right)}{3\,a^2\,f\,\left(-8\,{\sin\left(e+f\,x\right)}^2+4\,\sin\left(e+f\,x\right)+2\,{\sin\left(2\,e+2\,f\,x\right)}^2+4\,\sin\left(3\,e+3\,f\,x\right)+8\right)}","Not used",1,"(4*(-c*(sin(e + f*x) - 1))^(1/2)*(sin(e + f*x)*1i + 2*sin(2*e + 2*f*x) + sin(3*e + 3*f*x)*1i - 2*sin(e/2 + (f*x)/2)^2 + 2*sin((3*e)/2 + (3*f*x)/2)^2 - sin(e + f*x)^2*4i + 4i))/(3*a^2*f*(4*sin(e + f*x) + 4*sin(3*e + 3*f*x) + 2*sin(2*e + 2*f*x)^2 - 8*sin(e + f*x)^2 + 8)) - (4*(-c*(sin(e + f*x) - 1))^(1/2)*(sin(2*e + 2*f*x) - 4*sin(e/2 + (f*x)/2)^2 - sin(e + f*x)^2*2i + (2 + 2i)))/(3*a^2*f*(sin(e + f*x) + sin(3*e + 3*f*x) - 4*sin(e + f*x)^2 + 4))","B"
329,0,-1,124,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2)), x)","F"
330,0,-1,155,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2)), x)","F"
331,0,-1,192,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2)), x)","F"
332,0,-1,174,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(9/2)/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(9/2)/(a + a*sin(e + f*x))^3, x)","F"
333,1,542,134,13.874459,"\text{Not used}","int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^3,x)","-\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,c^3}{a^3\,f}-\frac{c^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{a^3\,f}\right)}{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}}-\frac{24\,c^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}+\frac{c^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,32{}\mathrm{i}}{a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}+\frac{288\,c^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}-\frac{c^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,256{}\mathrm{i}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^4}-\frac{128\,c^3\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5}","Not used",1,"(c^3*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*32i)/(a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) - (24*c^3*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)) - ((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((2*c^3)/(a^3*f) - (c^3*exp(e*1i + f*x*1i)*2i)/(a^3*f)))/(exp(e*1i + f*x*1i) - 1i) + (288*c^3*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) - (c^3*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*256i)/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^4) - (128*c^3*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^5)","B"
334,1,453,104,11.949327,"\text{Not used}","int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^3,x)","-\frac{4\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,32{}\mathrm{i}}{3\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}+\frac{352\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{15\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}-\frac{c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,128{}\mathrm{i}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^4}-\frac{64\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5}","Not used",1,"(c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*32i)/(3*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) - (4*c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)) + (352*c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(15*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) - (c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*128i)/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^4) - (64*c^2*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^5)","B"
335,1,355,73,10.911696,"\text{Not used}","int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^3,x)","\frac{c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,8{}\mathrm{i}}{3\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}+\frac{136\,c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{15\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}-\frac{c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,64{}\mathrm{i}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^4}-\frac{32\,c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5}","Not used",1,"(c*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*8i)/(3*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) + (136*c*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(15*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) - (c*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*64i)/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^4) - (32*c*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^5)","B"
336,1,90,36,9.882124,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^3,x)","\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,16{}\mathrm{i}}{5\,a^3\,f\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5\,\left(1+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}\right)}","Not used",1,"(exp(e*3i + f*x*3i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*16i)/(5*a^3*f*(exp(e*1i + f*x*1i) + 1i)^5*(exp(e*1i + f*x*1i)*1i + 1))","B"
337,0,-1,160,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2)), x)","F"
338,0,-1,191,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2)), x)","F"
339,0,-1,228,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2)), x)","F"
340,1,99,43,8.250283,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{c^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(28\,\cos\left(e+f\,x\right)+27\,\cos\left(3\,e+3\,f\,x\right)-\cos\left(5\,e+5\,f\,x\right)+48\,\sin\left(2\,e+2\,f\,x\right)-8\,\sin\left(4\,e+4\,f\,x\right)\right)}{32\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(28*cos(e + f*x) + 27*cos(3*e + 3*f*x) - cos(5*e + 5*f*x) + 48*sin(2*e + 2*f*x) - 8*sin(4*e + 4*f*x)))/(32*f*(cos(2*e + 2*f*x) + 1))","B"
341,1,88,43,7.706528,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(6\,\cos\left(e+f\,x\right)+6\,\cos\left(3\,e+3\,f\,x\right)+14\,\sin\left(2\,e+2\,f\,x\right)-\sin\left(4\,e+4\,f\,x\right)\right)}{12\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(6*cos(e + f*x) + 6*cos(3*e + 3*f*x) + 14*sin(2*e + 2*f*x) - sin(4*e + 4*f*x)))/(12*f*(cos(2*e + 2*f*x) + 1))","B"
342,1,71,43,0.844551,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2),x)","\frac{c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(\cos\left(e+f\,x\right)+\cos\left(3\,e+3\,f\,x\right)+4\,\sin\left(2\,e+2\,f\,x\right)\right)}{4\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(cos(e + f*x) + cos(3*e + 3*f*x) + 4*sin(2*e + 2*f*x)))/(4*f*(cos(2*e + 2*f*x) + 1))","B"
343,1,47,41,7.009668,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2),x)","\frac{\sin\left(2\,e+2\,f\,x\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{2\,f\,{\cos\left(e+f\,x\right)}^2}","Not used",1,"(sin(2*e + 2*f*x)*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2))/(2*f*cos(e + f*x)^2)","B"
344,0,-1,52,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(c - c*sin(e + f*x))^(1/2), x)","F"
345,0,-1,40,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(c - c*sin(e + f*x))^(3/2), x)","F"
346,1,142,43,8.894564,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c - c*sin(e + f*x))^(5/2),x)","\frac{4\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(10\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2+4\,\sin\left(2\,e+2\,f\,x\right)-4\right)}{c^3\,f\,\left(30\,{\sin\left(e+f\,x\right)}^2+48\,\sin\left(e+f\,x\right)-52\,{\sin\left(2\,e+2\,f\,x\right)}^2+2\,{\sin\left(3\,e+3\,f\,x\right)}^2+40\,\sin\left(3\,e+3\,f\,x\right)-8\,\sin\left(5\,e+5\,f\,x\right)-32\right)}","Not used",1,"(4*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(4*sin(2*e + 2*f*x) + 10*sin(e/2 + (f*x)/2)^2 - 2*sin((3*e)/2 + (3*f*x)/2)^2 - 4))/(c^3*f*(48*sin(e + f*x) + 40*sin(3*e + 3*f*x) - 8*sin(5*e + 5*f*x) - 52*sin(2*e + 2*f*x)^2 + 2*sin(3*e + 3*f*x)^2 + 30*sin(e + f*x)^2 - 32))","B"
347,1,190,43,10.982059,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c - c*sin(e + f*x))^(7/2),x)","-\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,16{}\mathrm{i}}{3\,c^4\,f\,\left(1+14\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}-{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}-14\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,6{}\mathrm{i}-{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,14{}\mathrm{i}-{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,14{}\mathrm{i}+{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,6{}\mathrm{i}\right)}","Not used",1,"-(exp(e*4i + f*x*4i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*16i)/(3*c^4*f*(exp(e*1i + f*x*1i)*6i - 14*exp(e*2i + f*x*2i) - exp(e*3i + f*x*3i)*14i - exp(e*5i + f*x*5i)*14i + 14*exp(e*6i + f*x*6i) + exp(e*7i + f*x*7i)*6i - exp(e*8i + f*x*8i) + 1))","B"
348,1,111,89,8.917465,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{a\,c^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(20\,\cos\left(e+f\,x\right)+25\,\cos\left(3\,e+3\,f\,x\right)+5\,\cos\left(5\,e+5\,f\,x\right)+75\,\sin\left(2\,e+2\,f\,x\right)+4\,\sin\left(4\,e+4\,f\,x\right)-\sin\left(6\,e+6\,f\,x\right)\right)}{80\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a*c^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(20*cos(e + f*x) + 25*cos(3*e + 3*f*x) + 5*cos(5*e + 5*f*x) + 75*sin(2*e + 2*f*x) + 4*sin(4*e + 4*f*x) - sin(6*e + 6*f*x)))/(80*f*(cos(2*e + 2*f*x) + 1))","B"
349,1,100,89,1.749673,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{a\,c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(12\,\cos\left(e+f\,x\right)+15\,\cos\left(3\,e+3\,f\,x\right)+3\,\cos\left(5\,e+5\,f\,x\right)+80\,\sin\left(2\,e+2\,f\,x\right)+8\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a*c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(12*cos(e + f*x) + 15*cos(3*e + 3*f*x) + 3*cos(5*e + 5*f*x) + 80*sin(2*e + 2*f*x) + 8*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
350,1,66,89,0.889341,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2),x)","\frac{a\,c\,\left(10\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{12\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a*c*(10*sin(2*e + 2*f*x) + sin(4*e + 4*f*x))*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2))/(12*f*(cos(2*e + 2*f*x) + 1))","B"
351,1,71,43,7.348168,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(\cos\left(e+f\,x\right)+\cos\left(3\,e+3\,f\,x\right)-4\,\sin\left(2\,e+2\,f\,x\right)\right)}{4\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(cos(e + f*x) + cos(3*e + 3*f*x) - 4*sin(2*e + 2*f*x)))/(4*f*(cos(2*e + 2*f*x) + 1))","B"
352,0,-1,96,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(1/2), x)","F"
353,0,-1,97,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(3/2), x)","F"
354,0,-1,42,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(5/2), x)","F"
355,1,124,88,10.650462,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(7/2),x)","-\frac{a\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}+3\,a\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\frac{9\,c^4\,f\,\cos\left(3\,e+3\,f\,x\right)}{2}+\frac{21\,c^4\,f\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{3\,c^4\,f\,\sin\left(4\,e+4\,f\,x\right)}{4}-\frac{21\,c^4\,f\,\cos\left(e+f\,x\right)}{2}}","Not used",1,"-(a*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2) + 3*a*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/((9*c^4*f*cos(3*e + 3*f*x))/2 + (21*c^4*f*sin(2*e + 2*f*x))/2 - (3*c^4*f*sin(4*e + 4*f*x))/4 - (21*c^4*f*cos(e + f*x))/2)","B"
356,1,195,92,11.814164,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(9/2),x)","\frac{\left(\frac{16\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^5\,f}+\frac{32\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^5\,f}\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{84\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}-54\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)+2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)-96\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)+16\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)}","Not used",1,"(((16*a*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2))/(3*c^5*f) + (32*a*exp(e*5i + f*x*5i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^5*f))*(c - c*sin(e + f*x))^(1/2))/(84*cos(e + f*x)*exp(e*5i + f*x*5i) - 54*exp(e*5i + f*x*5i)*cos(3*e + 3*f*x) + 2*exp(e*5i + f*x*5i)*cos(5*e + 5*f*x) - 96*exp(e*5i + f*x*5i)*sin(2*e + 2*f*x) + 16*exp(e*5i + f*x*5i)*sin(4*e + 4*f*x))","B"
357,1,225,92,12.589076,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c - c*sin(e + f*x))^(11/2),x)","\frac{\left(\frac{a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,48{}\mathrm{i}}{5\,c^6\,f}+\frac{a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,16{}\mathrm{i}}{c^6\,f}\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,264{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)\,220{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)\,20{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)\,330{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)\,88{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)\,2{}\mathrm{i}}","Not used",1,"(((a*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*48i)/(5*c^6*f) + (a*exp(e*6i + f*x*6i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*16i)/(c^6*f))*(c - c*sin(e + f*x))^(1/2))/(cos(e + f*x)*exp(e*6i + f*x*6i)*264i - exp(e*6i + f*x*6i)*cos(3*e + 3*f*x)*220i + exp(e*6i + f*x*6i)*cos(5*e + 5*f*x)*20i - exp(e*6i + f*x*6i)*sin(2*e + 2*f*x)*330i + exp(e*6i + f*x*6i)*sin(4*e + 4*f*x)*88i - exp(e*6i + f*x*6i)*sin(6*e + 6*f*x)*2i)","B"
358,1,124,134,9.942770,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{a^2\,c^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(75\,\cos\left(e+f\,x\right)+105\,\cos\left(3\,e+3\,f\,x\right)+35\,\cos\left(5\,e+5\,f\,x\right)+5\,\cos\left(7\,e+7\,f\,x\right)+700\,\sin\left(2\,e+2\,f\,x\right)+112\,\sin\left(4\,e+4\,f\,x\right)+12\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a^2*c^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(75*cos(e + f*x) + 105*cos(3*e + 3*f*x) + 35*cos(5*e + 5*f*x) + 5*cos(7*e + 7*f*x) + 700*sin(2*e + 2*f*x) + 112*sin(4*e + 4*f*x) + 12*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
359,1,83,134,1.500862,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{a^2\,c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(175\,\sin\left(2\,e+2\,f\,x\right)+28\,\sin\left(4\,e+4\,f\,x\right)+3\,\sin\left(6\,e+6\,f\,x\right)\right)}{240\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a^2*c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(175*sin(2*e + 2*f*x) + 28*sin(4*e + 4*f*x) + 3*sin(6*e + 6*f*x)))/(240*f*(cos(2*e + 2*f*x) + 1))","B"
360,1,100,89,8.271188,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{a^2\,c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(12\,\cos\left(e+f\,x\right)+15\,\cos\left(3\,e+3\,f\,x\right)+3\,\cos\left(5\,e+5\,f\,x\right)-80\,\sin\left(2\,e+2\,f\,x\right)-8\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(12*cos(e + f*x) + 15*cos(3*e + 3*f*x) + 3*cos(5*e + 5*f*x) - 80*sin(2*e + 2*f*x) - 8*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
361,1,86,43,7.747436,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(6\,\cos\left(e+f\,x\right)+6\,\cos\left(3\,e+3\,f\,x\right)-14\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)\right)}{12\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(6*cos(e + f*x) + 6*cos(3*e + 3*f*x) - 14*sin(2*e + 2*f*x) + sin(4*e + 4*f*x)))/(12*f*(cos(2*e + 2*f*x) + 1))","B"
362,0,-1,141,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(1/2), x)","F"
363,0,-1,144,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(3/2), x)","F"
364,0,-1,147,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(5/2), x)","F"
365,0,-1,42,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(7/2), x)","F"
366,1,242,88,11.574827,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(9/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{40\,a^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^5\,f}+\frac{32\,a^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^5\,f}-\frac{8\,a^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^5\,f}\right)}{84\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}-54\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)+2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)-96\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)+16\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((40*a^2*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2))/(3*c^5*f) + (32*a^2*exp(e*5i + f*x*5i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^5*f) - (8*a^2*exp(e*5i + f*x*5i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^5*f)))/(84*cos(e + f*x)*exp(e*5i + f*x*5i) - 54*exp(e*5i + f*x*5i)*cos(3*e + 3*f*x) + 2*exp(e*5i + f*x*5i)*cos(5*e + 5*f*x) - 96*exp(e*5i + f*x*5i)*sin(2*e + 2*f*x) + 16*exp(e*5i + f*x*5i)*sin(4*e + 4*f*x))","B"
367,1,273,133,12.075814,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(11/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,96{}\mathrm{i}}{5\,c^6\,f}+\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,64{}\mathrm{i}}{3\,c^6\,f}-\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,32{}\mathrm{i}}{3\,c^6\,f}\right)}{\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,264{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)\,220{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)\,20{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)\,330{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)\,88{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)\,2{}\mathrm{i}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((a^2*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*96i)/(5*c^6*f) + (a^2*exp(e*6i + f*x*6i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*64i)/(3*c^6*f) - (a^2*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2)*32i)/(3*c^6*f)))/(cos(e + f*x)*exp(e*6i + f*x*6i)*264i - exp(e*6i + f*x*6i)*cos(3*e + 3*f*x)*220i + exp(e*6i + f*x*6i)*cos(5*e + 5*f*x)*20i - exp(e*6i + f*x*6i)*sin(2*e + 2*f*x)*330i + exp(e*6i + f*x*6i)*sin(4*e + 4*f*x)*88i - exp(e*6i + f*x*6i)*sin(6*e + 6*f*x)*2i)","B"
368,1,287,140,12.239756,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c - c*sin(e + f*x))^(13/2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{464\,a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,c^7\,f}+\frac{192\,a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^7\,f}-\frac{16\,a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^7\,f}\right)}{-858\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+858\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)-130\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)+2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(7\,e+7\,f\,x\right)+1144\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)-416\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)+24\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((464*a^2*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^(1/2))/(15*c^7*f) + (192*a^2*exp(e*7i + f*x*7i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(5*c^7*f) - (16*a^2*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^7*f)))/(858*exp(e*7i + f*x*7i)*cos(3*e + 3*f*x) - 858*cos(e + f*x)*exp(e*7i + f*x*7i) - 130*exp(e*7i + f*x*7i)*cos(5*e + 5*f*x) + 2*exp(e*7i + f*x*7i)*cos(7*e + 7*f*x) + 1144*exp(e*7i + f*x*7i)*sin(2*e + 2*f*x) - 416*exp(e*7i + f*x*7i)*sin(4*e + 4*f*x) + 24*exp(e*7i + f*x*7i)*sin(6*e + 6*f*x))","B"
369,1,376,179,11.301197,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(9/2),x)","\frac{{\mathrm{e}}^{-e\,8{}\mathrm{i}-f\,x\,8{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{35\,a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{7\,a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{128\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{512\,f}+\frac{7\,a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*8i - f*x*8i)*(c - c*sin(e + f*x))^(1/2)*((35*a^3*c^4*exp(e*8i + f*x*8i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*a^3*c^4*exp(e*8i + f*x*8i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (7*a^3*c^4*exp(e*8i + f*x*8i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(128*f) + (a^3*c^4*exp(e*8i + f*x*8i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (a^3*c^4*exp(e*8i + f*x*8i)*cos(8*e + 8*f*x)*(a + a*sin(e + f*x))^(1/2))/(512*f) + (7*a^3*c^4*exp(e*8i + f*x*8i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*a^3*c^4*exp(e*8i + f*x*8i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (a^3*c^4*exp(e*8i + f*x*8i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f)))/(2*cos(e + f*x))","B"
370,1,179,179,10.647785,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{\frac{1225\,a^3\,c^3\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}+\frac{245\,a^3\,c^3\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}+\frac{49\,a^3\,c^3\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}+\frac{5\,a^3\,c^3\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{32}}{70\,f\,\cos\left(e+f\,x\right)}","Not used",1,"((1225*a^3*c^3*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32 + (245*a^3*c^3*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32 + (49*a^3*c^3*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32 + (5*a^3*c^3*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/32)/(70*f*cos(e + f*x))","B"
371,1,124,134,10.286864,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(5/2),x)","-\frac{a^3\,c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(75\,\cos\left(e+f\,x\right)+105\,\cos\left(3\,e+3\,f\,x\right)+35\,\cos\left(5\,e+5\,f\,x\right)+5\,\cos\left(7\,e+7\,f\,x\right)-700\,\sin\left(2\,e+2\,f\,x\right)-112\,\sin\left(4\,e+4\,f\,x\right)-12\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^3*c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(75*cos(e + f*x) + 105*cos(3*e + 3*f*x) + 35*cos(5*e + 5*f*x) + 5*cos(7*e + 7*f*x) - 700*sin(2*e + 2*f*x) - 112*sin(4*e + 4*f*x) - 12*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
372,1,109,89,9.186506,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{a^3\,c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(20\,\cos\left(e+f\,x\right)+25\,\cos\left(3\,e+3\,f\,x\right)+5\,\cos\left(5\,e+5\,f\,x\right)-75\,\sin\left(2\,e+2\,f\,x\right)-4\,\sin\left(4\,e+4\,f\,x\right)+\sin\left(6\,e+6\,f\,x\right)\right)}{80\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^3*c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(20*cos(e + f*x) + 25*cos(3*e + 3*f*x) + 5*cos(5*e + 5*f*x) - 75*sin(2*e + 2*f*x) - 4*sin(4*e + 4*f*x) + sin(6*e + 6*f*x)))/(80*f*(cos(2*e + 2*f*x) + 1))","B"
373,1,99,43,8.294137,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(28\,\cos\left(e+f\,x\right)+27\,\cos\left(3\,e+3\,f\,x\right)-\cos\left(5\,e+5\,f\,x\right)-48\,\sin\left(2\,e+2\,f\,x\right)+8\,\sin\left(4\,e+4\,f\,x\right)\right)}{32\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(28*cos(e + f*x) + 27*cos(3*e + 3*f*x) - cos(5*e + 5*f*x) - 48*sin(2*e + 2*f*x) + 8*sin(4*e + 4*f*x)))/(32*f*(cos(2*e + 2*f*x) + 1))","B"
374,0,-1,184,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(1/2), x)","F"
375,0,-1,192,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(3/2), x)","F"
376,0,-1,195,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(5/2), x)","F"
377,0,-1,193,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(7/2), x)","F"
378,0,-1,42,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(9/2), x)","F"
379,1,317,88,12.451575,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(11/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,112{}\mathrm{i}}{5\,c^6\,f}+\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,56{}\mathrm{i}}{c^6\,f}-\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,16{}\mathrm{i}}{c^6\,f}-\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,8{}\mathrm{i}}{c^6\,f}\right)}{\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,264{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)\,220{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)\,20{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)\,330{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)\,88{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)\,2{}\mathrm{i}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((a^3*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*112i)/(5*c^6*f) + (a^3*exp(e*6i + f*x*6i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*56i)/(c^6*f) - (a^3*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2)*16i)/(c^6*f) - (a^3*exp(e*6i + f*x*6i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2)*8i)/(c^6*f)))/(cos(e + f*x)*exp(e*6i + f*x*6i)*264i - exp(e*6i + f*x*6i)*cos(3*e + 3*f*x)*220i + exp(e*6i + f*x*6i)*cos(5*e + 5*f*x)*20i - exp(e*6i + f*x*6i)*sin(2*e + 2*f*x)*330i + exp(e*6i + f*x*6i)*sin(4*e + 4*f*x)*88i - exp(e*6i + f*x*6i)*sin(6*e + 6*f*x)*2i)","B"
380,1,330,133,12.057123,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(13/2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{224\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^7\,f}+\frac{416\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^7\,f}-\frac{32\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^7\,f}-\frac{32\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^7\,f}\right)}{-858\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+858\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)-130\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)+2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(7\,e+7\,f\,x\right)+1144\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)-416\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)+24\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((224*a^3*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^(1/2))/(5*c^7*f) + (416*a^3*exp(e*7i + f*x*7i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(5*c^7*f) - (32*a^3*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^7*f) - (32*a^3*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^7*f)))/(858*exp(e*7i + f*x*7i)*cos(3*e + 3*f*x) - 858*cos(e + f*x)*exp(e*7i + f*x*7i) - 130*exp(e*7i + f*x*7i)*cos(5*e + 5*f*x) + 2*exp(e*7i + f*x*7i)*cos(7*e + 7*f*x) + 1144*exp(e*7i + f*x*7i)*sin(2*e + 2*f*x) - 416*exp(e*7i + f*x*7i)*sin(4*e + 4*f*x) + 24*exp(e*7i + f*x*7i)*sin(6*e + 6*f*x))","B"
381,1,647,178,13.324464,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(15/2),x)","\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(-\frac{8\,a^3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{c^8\,f}+\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,144{}\mathrm{i}}{5\,c^8\,f}+\frac{344\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,c^8\,f}-\frac{a^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,2848{}\mathrm{i}}{35\,c^8\,f}-\frac{344\,a^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,c^8\,f}+\frac{a^3\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,144{}\mathrm{i}}{5\,c^8\,f}+\frac{8\,a^3\,{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{c^8\,f}\right)}{1+910\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-2002\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}+2002\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}-910\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}+90\,{\mathrm{e}}^{e\,14{}\mathrm{i}+f\,x\,14{}\mathrm{i}}-{\mathrm{e}}^{e\,16{}\mathrm{i}+f\,x\,16{}\mathrm{i}}-90\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,14{}\mathrm{i}-{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,350{}\mathrm{i}+{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,1638{}\mathrm{i}-{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,1430{}\mathrm{i}-{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,1430{}\mathrm{i}+{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,1638{}\mathrm{i}-{\mathrm{e}}^{e\,13{}\mathrm{i}+f\,x\,13{}\mathrm{i}}\,350{}\mathrm{i}+{\mathrm{e}}^{e\,15{}\mathrm{i}+f\,x\,15{}\mathrm{i}}\,14{}\mathrm{i}}","Not used",1,"((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((a^3*exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*144i)/(5*c^8*f) - (8*a^3*exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(c^8*f) + (344*a^3*exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*c^8*f) - (a^3*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*2848i)/(35*c^8*f) - (344*a^3*exp(e*9i + f*x*9i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*c^8*f) + (a^3*exp(e*10i + f*x*10i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*144i)/(5*c^8*f) + (8*a^3*exp(e*11i + f*x*11i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(c^8*f)))/(exp(e*1i + f*x*1i)*14i - 90*exp(e*2i + f*x*2i) - exp(e*3i + f*x*3i)*350i + 910*exp(e*4i + f*x*4i) + exp(e*5i + f*x*5i)*1638i - 2002*exp(e*6i + f*x*6i) - exp(e*7i + f*x*7i)*1430i - exp(e*9i + f*x*9i)*1430i + 2002*exp(e*10i + f*x*10i) + exp(e*11i + f*x*11i)*1638i - 910*exp(e*12i + f*x*12i) - exp(e*13i + f*x*13i)*350i + 90*exp(e*14i + f*x*14i) + exp(e*15i + f*x*15i)*14i - exp(e*16i + f*x*16i) + 1)","B"
382,1,673,188,13.981119,"\text{Not used}","int((a + a*sin(e + f*x))^(7/2)/(c - c*sin(e + f*x))^(17/2),x)","-\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,64{}\mathrm{i}}{5\,c^9\,f}+\frac{256\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,c^9\,f}-\frac{a^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,832{}\mathrm{i}}{7\,c^9\,f}-\frac{1024\,a^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{7\,c^9\,f}+\frac{a^3\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,832{}\mathrm{i}}{7\,c^9\,f}+\frac{256\,a^3\,{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{5\,c^9\,f}-\frac{a^3\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,64{}\mathrm{i}}{5\,c^9\,f}\right)}{1+1700\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-6188\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}+4862\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}+4862\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}-6188\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}+1700\,{\mathrm{e}}^{e\,14{}\mathrm{i}+f\,x\,14{}\mathrm{i}}-119\,{\mathrm{e}}^{e\,16{}\mathrm{i}+f\,x\,16{}\mathrm{i}}+{\mathrm{e}}^{e\,18{}\mathrm{i}+f\,x\,18{}\mathrm{i}}-119\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,16{}\mathrm{i}-{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,544{}\mathrm{i}+{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,3808{}\mathrm{i}-{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,7072{}\mathrm{i}+{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,7072{}\mathrm{i}-{\mathrm{e}}^{e\,13{}\mathrm{i}+f\,x\,13{}\mathrm{i}}\,3808{}\mathrm{i}+{\mathrm{e}}^{e\,15{}\mathrm{i}+f\,x\,15{}\mathrm{i}}\,544{}\mathrm{i}-{\mathrm{e}}^{e\,17{}\mathrm{i}+f\,x\,17{}\mathrm{i}}\,16{}\mathrm{i}}","Not used",1,"-((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((a^3*exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*64i)/(5*c^9*f) + (256*a^3*exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*c^9*f) - (a^3*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*832i)/(7*c^9*f) - (1024*a^3*exp(e*9i + f*x*9i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(7*c^9*f) + (a^3*exp(e*10i + f*x*10i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*832i)/(7*c^9*f) + (256*a^3*exp(e*11i + f*x*11i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(5*c^9*f) - (a^3*exp(e*12i + f*x*12i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*64i)/(5*c^9*f)))/(exp(e*1i + f*x*1i)*16i - 119*exp(e*2i + f*x*2i) - exp(e*3i + f*x*3i)*544i + 1700*exp(e*4i + f*x*4i) + exp(e*5i + f*x*5i)*3808i - 6188*exp(e*6i + f*x*6i) - exp(e*7i + f*x*7i)*7072i + 4862*exp(e*8i + f*x*8i) + 4862*exp(e*10i + f*x*10i) + exp(e*11i + f*x*11i)*7072i - 6188*exp(e*12i + f*x*12i) - exp(e*13i + f*x*13i)*3808i + 1700*exp(e*14i + f*x*14i) + exp(e*15i + f*x*15i)*544i - 119*exp(e*16i + f*x*16i) - exp(e*17i + f*x*17i)*16i + exp(e*18i + f*x*18i) + 1)","B"
383,0,-1,139,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(1/2), x)","F"
384,0,-1,93,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(1/2), x)","F"
385,0,-1,49,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(1/2), x)","F"
386,0,-1,46,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
387,0,-1,95,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
388,0,-1,140,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
389,0,-1,191,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^(3/2), x)","F"
390,0,-1,143,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(3/2), x)","F"
391,0,-1,97,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(3/2), x)","F"
392,1,52,41,7.518543,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(3/2),x)","-\frac{2\,\cos\left(e+f\,x\right)\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{a\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}}","Not used",1,"-(2*cos(e + f*x)*(-c*(sin(e + f*x) - 1))^(1/2))/(a*f*(cos(2*e + 2*f*x) + 1)*(a*(sin(e + f*x) + 1))^(1/2))","B"
393,0,-1,95,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
394,0,-1,143,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
395,0,-1,191,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
396,0,-1,237,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(9/2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(9/2)/(a + a*sin(e + f*x))^(5/2), x)","F"
397,0,-1,193,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(7/2)/(a + a*sin(e + f*x))^(5/2), x)","F"
398,0,-1,143,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c - c*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(5/2), x)","F"
399,1,118,42,8.213515,"\text{Not used}","int((c - c*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(5/2),x)","\frac{2\,c\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(-2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2+2\,\sin\left(2\,e+2\,f\,x\right)\right)}{a^2\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(-8\,{\sin\left(e+f\,x\right)}^2+4\,\sin\left(e+f\,x\right)+2\,{\sin\left(2\,e+2\,f\,x\right)}^2+4\,\sin\left(3\,e+3\,f\,x\right)+8\right)}","Not used",1,"(2*c*(-c*(sin(e + f*x) - 1))^(1/2)*(2*sin(2*e + 2*f*x) - 2*sin(e/2 + (f*x)/2)^2 + 2*sin((3*e)/2 + (3*f*x)/2)^2))/(a^2*f*(a*(sin(e + f*x) + 1))^(1/2)*(4*sin(e + f*x) + 4*sin(3*e + 3*f*x) + 2*sin(2*e + 2*f*x)^2 - 8*sin(e + f*x)^2 + 8))","B"
400,1,103,43,7.696312,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(5/2),x)","-\frac{2\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(-4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\sin\left(2\,e+2\,f\,x\right)+2\right)}{a^2\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(-8\,{\sin\left(e+f\,x\right)}^2+4\,\sin\left(e+f\,x\right)+2\,{\sin\left(2\,e+2\,f\,x\right)}^2+4\,\sin\left(3\,e+3\,f\,x\right)+8\right)}","Not used",1,"-(2*(-c*(sin(e + f*x) - 1))^(1/2)*(sin(2*e + 2*f*x) - 4*sin(e/2 + (f*x)/2)^2 + 2))/(a^2*f*(a*(sin(e + f*x) + 1))^(1/2)*(4*sin(e + f*x) + 4*sin(3*e + 3*f*x) + 2*sin(2*e + 2*f*x)^2 - 8*sin(e + f*x)^2 + 8))","B"
401,0,-1,140,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
402,0,-1,188,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
403,0,-1,236,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
404,0,-1,110,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
405,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3, x)","F"
406,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2, x)","F"
407,0,-1,84,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(c-c\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)), x)","F"
408,0,-1,76,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x)),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x)), x)","F"
409,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^2,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^2, x)","F"
410,0,-1,86,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^3,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^3, x)","F"
411,1,163,160,10.047905,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2),x)","\frac{c^2\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(3\,\cos\left(3\,e+3\,f\,x\right)-175\,\cos\left(e+f\,x\right)+28\,\sin\left(2\,e+2\,f\,x\right)+16\,m^2\,\sin\left(2\,e+2\,f\,x\right)-104\,m\,\cos\left(e+f\,x\right)+8\,m\,\cos\left(3\,e+3\,f\,x\right)-20\,m^2\,\cos\left(e+f\,x\right)+64\,m\,\sin\left(2\,e+2\,f\,x\right)+4\,m^2\,\cos\left(3\,e+3\,f\,x\right)\right)}{2\,f\,\left(\sin\left(e+f\,x\right)-1\right)\,\left(8\,m^3+36\,m^2+46\,m+15\right)}","Not used",1,"(c^2*(a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(3*cos(3*e + 3*f*x) - 175*cos(e + f*x) + 28*sin(2*e + 2*f*x) + 16*m^2*sin(2*e + 2*f*x) - 104*m*cos(e + f*x) + 8*m*cos(3*e + 3*f*x) - 20*m^2*cos(e + f*x) + 64*m*sin(2*e + 2*f*x) + 4*m^2*cos(3*e + 3*f*x)))/(2*f*(sin(e + f*x) - 1)*(46*m + 36*m^2 + 8*m^3 + 15))","B"
412,1,94,100,1.187899,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2),x)","-\frac{c\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(10\,\cos\left(e+f\,x\right)-\sin\left(2\,e+2\,f\,x\right)+4\,m\,\cos\left(e+f\,x\right)-2\,m\,\sin\left(2\,e+2\,f\,x\right)\right)}{f\,\left(\sin\left(e+f\,x\right)-1\right)\,\left(4\,m^2+8\,m+3\right)}","Not used",1,"-(c*(a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(10*cos(e + f*x) - sin(2*e + 2*f*x) + 4*m*cos(e + f*x) - 2*m*sin(2*e + 2*f*x)))/(f*(sin(e + f*x) - 1)*(8*m + 4*m^2 + 3))","B"
413,1,53,46,0.451037,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2),x)","-\frac{2\,\cos\left(e+f\,x\right)\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}}{f\,\left(2\,m+1\right)\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-(2*cos(e + f*x)*(a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2))/(f*(2*m + 1)*(sin(e + f*x) - 1))","B"
414,0,-1,68,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(1/2), x)","F"
415,0,-1,74,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(3/2), x)","F"
416,0,-1,74,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(5/2), x)","F"
417,0,-1,68,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(1/2), x)","F"
418,0,-1,68,0.000000,"\text{Not used}","int((c + c*sin(e + f*x))^m/(a - a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+c\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{a-a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + c*sin(e + f*x))^m/(a - a*sin(e + f*x))^(1/2), x)","F"
419,1,149,164,8.249170,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(m + 3),x)","-\frac{2\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(15\,\cos\left(e+f\,x\right)-\cos\left(3\,e+3\,f\,x\right)-6\,\sin\left(2\,e+2\,f\,x\right)+24\,m\,\cos\left(e+f\,x\right)+8\,m^2\,\cos\left(e+f\,x\right)-4\,m\,\sin\left(2\,e+2\,f\,x\right)\right)}{c^3\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)\,\left(15\,\sin\left(e+f\,x\right)+6\,\cos\left(2\,e+2\,f\,x\right)-\sin\left(3\,e+3\,f\,x\right)-10\right)}","Not used",1,"-(2*(a*(sin(e + f*x) + 1))^m*(15*cos(e + f*x) - cos(3*e + 3*f*x) - 6*sin(2*e + 2*f*x) + 24*m*cos(e + f*x) + 8*m^2*cos(e + f*x) - 4*m*sin(2*e + 2*f*x)))/(c^3*f*(-c*(sin(e + f*x) - 1))^m*(46*m + 36*m^2 + 8*m^3 + 15)*(15*sin(e + f*x) + 6*cos(2*e + 2*f*x) - sin(3*e + 3*f*x) - 10))","B"
420,1,111,101,0.880166,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(m + 2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(\sin\left(2\,e+2\,f\,x\right)+8\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+4\,m\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)-4\right)}{c^2\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(2\,{\sin\left(e+f\,x\right)}^2-4\,\sin\left(e+f\,x\right)+2\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(sin(2*e + 2*f*x) + 8*sin(e/2 + (f*x)/2)^2 + 4*m*(2*sin(e/2 + (f*x)/2)^2 - 1) - 4))/(c^2*f*(-c*(sin(e + f*x) - 1))^m*(8*m + 4*m^2 + 3)*(2*sin(e + f*x)^2 - 4*sin(e + f*x) + 2))","B"
421,1,58,46,0.409064,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^(m + 1),x)","-\frac{\cos\left(e+f\,x\right)\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m}{c\,f\,\left(2\,m+1\right)\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(\sin\left(e+f\,x\right)-1\right)}","Not used",1,"-(cos(e + f*x)*(a*(sin(e + f*x) + 1))^m)/(c*f*(2*m + 1)*(-c*(sin(e + f*x) - 1))^m*(sin(e + f*x) - 1))","B"
422,0,-1,112,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^m,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^m} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c - c*sin(e + f*x))^m, x)","F"
423,0,-1,114,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{1-m} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m), x)","F"
424,0,-1,114,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(2 - m),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{2-m} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(2 - m), x)","F"
425,1,559,227,9.940876,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^4,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^4+16\,c^3\,d+24\,c^2\,d^2+12\,c\,d^3+3\,d^4\right)}{4\,\left(2\,a\,c^4+4\,a\,c^3\,d+6\,a\,c^2\,d^2+3\,a\,c\,d^3+\frac{3\,a\,d^4}{4}\right)}\right)\,\left(8\,c^4+16\,c^3\,d+24\,c^2\,d^2+12\,c\,d^3+3\,d^4\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(8\,a\,c^4+32\,a\,c^3\,d+40\,a\,c^2\,d^2+\frac{80\,a\,c\,d^3}{3}+\frac{16\,a\,d^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(12\,a\,c^4+48\,a\,c^3\,d+56\,a\,c^2\,d^2+\frac{112\,a\,c\,d^3}{3}+\frac{32\,a\,d^4}{3}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a\,c^3\,d+6\,a\,c^2\,d^2+3\,a\,c\,d^3+\frac{3\,a\,d^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,a\,c^4+8\,a\,d\,c^3\right)+2\,a\,c^4+\frac{16\,a\,d^4}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(8\,a\,c^4+32\,a\,c^3\,d+24\,a\,c^2\,d^2+16\,a\,c\,d^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(4\,a\,c^3\,d+6\,a\,c^2\,d^2+3\,a\,c\,d^3+\frac{3\,a\,d^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(8\,a\,c^3\,d+12\,a\,c^2\,d^2+14\,a\,c\,d^3+\frac{7\,a\,d^4}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(8\,a\,c^3\,d+12\,a\,c^2\,d^2+14\,a\,c\,d^3+\frac{7\,a\,d^4}{2}\right)+8\,a\,c^2\,d^2+\frac{16\,a\,c\,d^3}{3}+8\,a\,c^3\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(e/2 + (f*x)/2)*(12*c*d^3 + 16*c^3*d + 8*c^4 + 3*d^4 + 24*c^2*d^2))/(4*(2*a*c^4 + (3*a*d^4)/4 + 6*a*c^2*d^2 + 3*a*c*d^3 + 4*a*c^3*d)))*(12*c*d^3 + 16*c^3*d + 8*c^4 + 3*d^4 + 24*c^2*d^2))/(4*f) - (tan(e/2 + (f*x)/2)^2*(8*a*c^4 + (16*a*d^4)/3 + 40*a*c^2*d^2 + (80*a*c*d^3)/3 + 32*a*c^3*d) + tan(e/2 + (f*x)/2)^4*(12*a*c^4 + (32*a*d^4)/3 + 56*a*c^2*d^2 + (112*a*c*d^3)/3 + 48*a*c^3*d) + tan(e/2 + (f*x)/2)*((3*a*d^4)/4 + 6*a*c^2*d^2 + 3*a*c*d^3 + 4*a*c^3*d) + tan(e/2 + (f*x)/2)^8*(2*a*c^4 + 8*a*c^3*d) + 2*a*c^4 + (16*a*d^4)/15 + tan(e/2 + (f*x)/2)^6*(8*a*c^4 + 24*a*c^2*d^2 + 16*a*c*d^3 + 32*a*c^3*d) - tan(e/2 + (f*x)/2)^9*((3*a*d^4)/4 + 6*a*c^2*d^2 + 3*a*c*d^3 + 4*a*c^3*d) + tan(e/2 + (f*x)/2)^3*((7*a*d^4)/2 + 12*a*c^2*d^2 + 14*a*c*d^3 + 8*a*c^3*d) - tan(e/2 + (f*x)/2)^7*((7*a*d^4)/2 + 12*a*c^2*d^2 + 14*a*c*d^3 + 8*a*c^3*d) + 8*a*c^2*d^2 + (16*a*c*d^3)/3 + 8*a*c^3*d)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1))","B"
426,1,460,162,8.174893,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{4\,\left(2\,a\,c^3+3\,a\,c^2\,d+3\,a\,c\,d^2+\frac{3\,a\,d^3}{4}\right)}\right)\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{4\,f}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,a\,c^2\,d+3\,a\,c\,d^2+\frac{11\,a\,d^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(3\,a\,c^2\,d+3\,a\,c\,d^2+\frac{3\,a\,d^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(3\,a\,c^2\,d+3\,a\,c\,d^2+\frac{11\,a\,d^3}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,a\,c^3+6\,a\,d\,c^2\right)+2\,a\,c^3+\frac{4\,a\,d^3}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a\,c^3+18\,a\,c^2\,d+12\,a\,c\,d^2+4\,a\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,a\,c^3+18\,a\,c^2\,d+16\,a\,c\,d^2+\frac{16\,a\,d^3}{3}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a\,c^2\,d+3\,a\,c\,d^2+\frac{3\,a\,d^3}{4}\right)+4\,a\,c\,d^2+6\,a\,c^2\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(e/2 + (f*x)/2)*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/(4*(2*a*c^3 + (3*a*d^3)/4 + 3*a*c*d^2 + 3*a*c^2*d)))*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/(4*f) - (a*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/(4*f) - (tan(e/2 + (f*x)/2)^3*((11*a*d^3)/4 + 3*a*c*d^2 + 3*a*c^2*d) - tan(e/2 + (f*x)/2)^7*((3*a*d^3)/4 + 3*a*c*d^2 + 3*a*c^2*d) - tan(e/2 + (f*x)/2)^5*((11*a*d^3)/4 + 3*a*c*d^2 + 3*a*c^2*d) + tan(e/2 + (f*x)/2)^6*(2*a*c^3 + 6*a*c^2*d) + 2*a*c^3 + (4*a*d^3)/3 + tan(e/2 + (f*x)/2)^4*(6*a*c^3 + 4*a*d^3 + 12*a*c*d^2 + 18*a*c^2*d) + tan(e/2 + (f*x)/2)^2*(6*a*c^3 + (16*a*d^3)/3 + 16*a*c*d^2 + 18*a*c^2*d) + tan(e/2 + (f*x)/2)*((3*a*d^3)/4 + 3*a*c*d^2 + 3*a*c^2*d) + 4*a*c*d^2 + 6*a*c^2*d)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1))","B"
427,1,108,99,6.987327,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^2,x)","-\frac{\frac{3\,a\,d^2\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{a\,d^2\,\cos\left(3\,e+3\,f\,x\right)}{2}+6\,a\,c^2\,\cos\left(e+f\,x\right)+\frac{9\,a\,d^2\,\cos\left(e+f\,x\right)}{2}+3\,a\,c\,d\,\sin\left(2\,e+2\,f\,x\right)-6\,a\,c^2\,f\,x-3\,a\,d^2\,f\,x+12\,a\,c\,d\,\cos\left(e+f\,x\right)-6\,a\,c\,d\,f\,x}{6\,f}","Not used",1,"-((3*a*d^2*sin(2*e + 2*f*x))/2 - (a*d^2*cos(3*e + 3*f*x))/2 + 6*a*c^2*cos(e + f*x) + (9*a*d^2*cos(e + f*x))/2 + 3*a*c*d*sin(2*e + 2*f*x) - 6*a*c^2*f*x - 3*a*d^2*f*x + 12*a*c*d*cos(e + f*x) - 6*a*c*d*f*x)/(6*f)","B"
428,1,100,48,6.994317,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x)),x)","a\,c\,x+\frac{a\,d\,x}{2}-\frac{-a\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\left(2\,a\,c+2\,a\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,a\,c+2\,a\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"a*c*x + (a*d*x)/2 - (2*a*c + 2*a*d + tan(e/2 + (f*x)/2)^2*(2*a*c + 2*a*d) - a*d*tan(e/2 + (f*x)/2)^3 + a*d*tan(e/2 + (f*x)/2))/(f*(2*tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^4 + 1))","B"
429,1,25,16,6.718042,"\text{Not used}","int(a + a*sin(e + f*x),x)","a\,x-\frac{2\,a}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x - (2*a)/(f*(tan(e/2 + (f*x)/2)^2 + 1))","B"
430,1,449,63,7.391895,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x)),x)","\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f\,\left(c+d\right)}-\frac{2\,a\,\mathrm{atanh}\left(\frac{3\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}-2\,c^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}-2\,c^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}+d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}+2\,c^2\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}+3\,c^2\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}+c\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}+c\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}+c^3\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}+4\,c\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}-2\,c^3\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}}{2\,\left(d^2+c\,d\right)\,\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,c^3+2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,c^2\,d-\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,c\,d^2-2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,d^3\right)}\right)\,\sqrt{d^2-c^2}}{d\,f\,\left(c+d\right)}+\frac{2\,a\,c\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{d\,f\,\left(c+d\right)}","Not used",1,"(2*a*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(f*(c + d)) - (2*a*atanh((3*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2) - 2*c^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) - 2*c^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2) + d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) + 2*c^2*d^2*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) + 3*c^2*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) + c*d*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2) + c*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) + c^3*d*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) + 4*c*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2) - 2*c^3*d*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2))/(2*(c*d + d^2)*(c^3*cos(e/2 + (f*x)/2) - 2*d^3*sin(e/2 + (f*x)/2) - c*d^2*cos(e/2 + (f*x)/2) + 2*c^2*d*sin(e/2 + (f*x)/2))))*(d^2 - c^2)^(1/2))/(d*f*(c + d)) + (2*a*c*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(d*f*(c + d))","B"
431,1,140,83,6.946397,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^2,x)","\frac{2\,a\,\mathrm{atan}\left(\frac{\left(c+d\right)\,\left(\frac{2\,a\,\left(d^2+c\,d\right)}{{\left(c+d\right)}^{5/2}\,\sqrt{c-d}}+\frac{2\,a\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{{\left(c+d\right)}^{3/2}\,\sqrt{c-d}}\right)}{2\,a}\right)}{f\,{\left(c+d\right)}^{3/2}\,\sqrt{c-d}}-\frac{\frac{2\,a}{c+d}+\frac{2\,a\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{c\,\left(c+d\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}","Not used",1,"(2*a*atan(((c + d)*((2*a*(c*d + d^2))/((c + d)^(5/2)*(c - d)^(1/2)) + (2*a*c*tan(e/2 + (f*x)/2))/((c + d)^(3/2)*(c - d)^(1/2))))/(2*a)))/(f*(c + d)^(3/2)*(c - d)^(1/2)) - ((2*a)/(c + d) + (2*a*d*tan(e/2 + (f*x)/2))/(c*(c + d)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2))","B"
432,1,445,134,8.967289,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^3,x)","-\frac{\frac{-2\,a\,c^2+2\,a\,c\,d+a\,d^2}{-c^3-c^2\,d+c\,d^2+d^3}+\frac{a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(-2\,c^2+2\,c\,d+d^2\right)}{c^2\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{a\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-5\,c^2+6\,c\,d+2\,d^2\right)}{c\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{a\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-3\,c^2+2\,c\,d+2\,d^2\right)}{c\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{a\,\mathrm{atan}\left(\frac{\left(\frac{a\,\left(2\,c-d\right)\,\left(-2\,c^3\,d-2\,c^2\,d^2+2\,c\,d^3+2\,d^4\right)}{2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{3/2}\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{a\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c-d\right)}{{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{3/2}}\right)\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}{2\,a\,c-a\,d}\right)\,\left(2\,c-d\right)}{f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{3/2}}","Not used",1,"- ((a*d^2 - 2*a*c^2 + 2*a*c*d)/(c*d^2 - c^2*d - c^3 + d^3) + (a*tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(2*c*d - 2*c^2 + d^2))/(c^2*(c*d^2 - c^2*d - c^3 + d^3)) + (a*d*tan(e/2 + (f*x)/2)*(6*c*d - 5*c^2 + 2*d^2))/(c*(c*d^2 - c^2*d - c^3 + d^3)) + (a*d*tan(e/2 + (f*x)/2)^3*(2*c*d - 3*c^2 + 2*d^2))/(c*(c*d^2 - c^2*d - c^3 + d^3)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) - (a*atan((((a*(2*c - d)*(2*c*d^3 - 2*c^3*d + 2*d^4 - 2*c^2*d^2))/(2*(c + d)^(5/2)*(c - d)^(3/2)*(c*d^2 - c^2*d - c^3 + d^3)) + (a*c*tan(e/2 + (f*x)/2)*(2*c - d))/((c + d)^(5/2)*(c - d)^(3/2)))*(c*d^2 - c^2*d - c^3 + d^3))/(2*a*c - a*d))*(2*c - d))/(f*(c + d)^(5/2)*(c - d)^(3/2))","B"
433,1,877,192,9.706412,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^4,x)","\frac{a\,\mathrm{atan}\left(\frac{\left(\frac{a\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^2-2\,c\,d+d^2\right)}{{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{5/2}}+\frac{a\,\left(2\,c^2-2\,c\,d+d^2\right)\,\left(2\,c^5\,d+2\,c^4\,d^2-4\,c^3\,d^3-4\,c^2\,d^4+2\,c\,d^5+2\,d^6\right)}{2\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{5/2}\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}\right)\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}{2\,a\,c^2-2\,a\,c\,d+a\,d^2}\right)\,\left(2\,c^2-2\,c\,d+d^2\right)}{f\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{6\,a\,c^4-12\,a\,c^3\,d-2\,a\,c^2\,d^2+3\,a\,c\,d^3+2\,a\,d^4}{3\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}+\frac{a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,c^6-4\,c^5\,d+10\,c^4\,d^2-17\,c^3\,d^3-6\,c^2\,d^4+6\,c\,d^5+4\,d^6\right)}{c^2\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}+\frac{2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^6-4\,c^5\,d+6\,c^4\,d^2-14\,c^3\,d^3+3\,c\,d^5+2\,d^6\right)}{c^2\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}+\frac{a\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^4-19\,c^3\,d+4\,c\,d^3+2\,d^4\right)}{c\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}+\frac{a\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(4\,c^4-5\,c^3\,d-4\,c^2\,d^2+2\,c\,d^3+2\,d^4\right)}{c\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}+\frac{2\,a\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,c^2+2\,d^2\right)\,\left(6\,c^4-12\,c^3\,d-2\,c^2\,d^2+3\,c\,d^3+2\,d^4\right)}{3\,c^3\,\left(c^5+c^4\,d-2\,c^3\,d^2-2\,c^2\,d^3+c\,d^4+d^5\right)}}{f\,\left(c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^2\,d+8\,d^3\right)+c^3+6\,c^2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,c^2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}","Not used",1,"(a*atan((((a*c*tan(e/2 + (f*x)/2)*(2*c^2 - 2*c*d + d^2))/((c + d)^(7/2)*(c - d)^(5/2)) + (a*(2*c^2 - 2*c*d + d^2)*(2*c*d^5 + 2*c^5*d + 2*d^6 - 4*c^2*d^4 - 4*c^3*d^3 + 2*c^4*d^2))/(2*(c + d)^(7/2)*(c - d)^(5/2)*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)))*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2))/(2*a*c^2 + a*d^2 - 2*a*c*d))*(2*c^2 - 2*c*d + d^2))/(f*(c + d)^(7/2)*(c - d)^(5/2)) - ((6*a*c^4 + 2*a*d^4 - 2*a*c^2*d^2 + 3*a*c*d^3 - 12*a*c^3*d)/(3*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)) + (a*tan(e/2 + (f*x)/2)^4*(6*c*d^5 - 4*c^5*d + 2*c^6 + 4*d^6 - 6*c^2*d^4 - 17*c^3*d^3 + 10*c^4*d^2))/(c^2*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)) + (2*a*tan(e/2 + (f*x)/2)^2*(3*c*d^5 - 4*c^5*d + 2*c^6 + 2*d^6 - 14*c^3*d^3 + 6*c^4*d^2))/(c^2*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)) + (a*d*tan(e/2 + (f*x)/2)*(4*c*d^3 - 19*c^3*d + 8*c^4 + 2*d^4))/(c*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)) + (a*d*tan(e/2 + (f*x)/2)^5*(2*c*d^3 - 5*c^3*d + 4*c^4 + 2*d^4 - 4*c^2*d^2))/(c*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)) + (2*a*d*tan(e/2 + (f*x)/2)^3*(3*c^2 + 2*d^2)*(3*c*d^3 - 12*c^3*d + 6*c^4 + 2*d^4 - 2*c^2*d^2))/(3*c^3*(c*d^4 + c^4*d + c^5 + d^5 - 2*c^2*d^3 - 2*c^3*d^2)))/(f*(c^3*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^2*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^4*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^3*(12*c^2*d + 8*d^3) + c^3 + 6*c^2*d*tan(e/2 + (f*x)/2) + 6*c^2*d*tan(e/2 + (f*x)/2)^5))","B"
434,1,865,318,9.923750,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^4,x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,c^4+64\,c^3\,d+84\,c^2\,d^2+48\,c\,d^3+11\,d^4\right)}{8\,\left(3\,a^2\,c^4+8\,a^2\,c^3\,d+\frac{21\,a^2\,c^2\,d^2}{2}+6\,a^2\,c\,d^3+\frac{11\,a^2\,d^4}{8}\right)}\right)\,\left(24\,c^4+64\,c^3\,d+84\,c^2\,d^2+48\,c\,d^3+11\,d^4\right)}{8\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(20\,a^2\,c^4+56\,a^2\,c^3\,d+48\,a^2\,c^2\,d^2+16\,a^2\,c\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(4\,a^2\,c^4+8\,d\,a^2\,c^3\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,c^4+8\,a^2\,c^3\,d+\frac{21\,a^2\,c^2\,d^2}{2}+6\,a^2\,c\,d^3+\frac{11\,a^2\,d^4}{8}\right)+4\,a^2\,c^4+\frac{32\,a^2\,d^4}{15}-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(a^2\,c^4+8\,a^2\,c^3\,d+\frac{21\,a^2\,c^2\,d^2}{2}+6\,a^2\,c\,d^3+\frac{11\,a^2\,d^4}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,a^2\,c^4+16\,a^2\,c^3\,d+33\,a^2\,c^2\,d^2+28\,a^2\,c\,d^3+\frac{47\,a^2\,d^4}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,a^2\,c^4+16\,a^2\,c^3\,d+33\,a^2\,c^2\,d^2+28\,a^2\,c\,d^3+\frac{47\,a^2\,d^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,a^2\,c^4+24\,a^2\,c^3\,d+\frac{87\,a^2\,c^2\,d^2}{2}+34\,a^2\,c\,d^3+\frac{187\,a^2\,d^4}{24}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(3\,a^2\,c^4+24\,a^2\,c^3\,d+\frac{87\,a^2\,c^2\,d^2}{2}+34\,a^2\,c\,d^3+\frac{187\,a^2\,d^4}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(40\,a^2\,c^4+144\,a^2\,c^3\,d+192\,a^2\,c^2\,d^2+128\,a^2\,c\,d^3+32\,a^2\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(20\,a^2\,c^4+72\,a^2\,c^3\,d+96\,a^2\,c^2\,d^2+\frac{288\,a^2\,c\,d^3}{5}+\frac{64\,a^2\,d^4}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(40\,a^2\,c^4+\frac{400\,a^2\,c^3\,d}{3}+160\,a^2\,c^2\,d^2+96\,a^2\,c\,d^3+\frac{64\,a^2\,d^4}{3}\right)+\frac{48\,a^2\,c\,d^3}{5}+\frac{40\,a^2\,c^3\,d}{3}+16\,a^2\,c^2\,d^2}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^2*atan((a^2*tan(e/2 + (f*x)/2)*(48*c*d^3 + 64*c^3*d + 24*c^4 + 11*d^4 + 84*c^2*d^2))/(8*(3*a^2*c^4 + (11*a^2*d^4)/8 + 6*a^2*c*d^3 + 8*a^2*c^3*d + (21*a^2*c^2*d^2)/2)))*(48*c*d^3 + 64*c^3*d + 24*c^4 + 11*d^4 + 84*c^2*d^2))/(8*f) - (tan(e/2 + (f*x)/2)^8*(20*a^2*c^4 + 16*a^2*c*d^3 + 56*a^2*c^3*d + 48*a^2*c^2*d^2) + tan(e/2 + (f*x)/2)^10*(4*a^2*c^4 + 8*a^2*c^3*d) + tan(e/2 + (f*x)/2)*(a^2*c^4 + (11*a^2*d^4)/8 + 6*a^2*c*d^3 + 8*a^2*c^3*d + (21*a^2*c^2*d^2)/2) + 4*a^2*c^4 + (32*a^2*d^4)/15 - tan(e/2 + (f*x)/2)^11*(a^2*c^4 + (11*a^2*d^4)/8 + 6*a^2*c*d^3 + 8*a^2*c^3*d + (21*a^2*c^2*d^2)/2) + tan(e/2 + (f*x)/2)^5*(2*a^2*c^4 + (47*a^2*d^4)/4 + 28*a^2*c*d^3 + 16*a^2*c^3*d + 33*a^2*c^2*d^2) - tan(e/2 + (f*x)/2)^7*(2*a^2*c^4 + (47*a^2*d^4)/4 + 28*a^2*c*d^3 + 16*a^2*c^3*d + 33*a^2*c^2*d^2) + tan(e/2 + (f*x)/2)^3*(3*a^2*c^4 + (187*a^2*d^4)/24 + 34*a^2*c*d^3 + 24*a^2*c^3*d + (87*a^2*c^2*d^2)/2) - tan(e/2 + (f*x)/2)^9*(3*a^2*c^4 + (187*a^2*d^4)/24 + 34*a^2*c*d^3 + 24*a^2*c^3*d + (87*a^2*c^2*d^2)/2) + tan(e/2 + (f*x)/2)^4*(40*a^2*c^4 + 32*a^2*d^4 + 128*a^2*c*d^3 + 144*a^2*c^3*d + 192*a^2*c^2*d^2) + tan(e/2 + (f*x)/2)^2*(20*a^2*c^4 + (64*a^2*d^4)/5 + (288*a^2*c*d^3)/5 + 72*a^2*c^3*d + 96*a^2*c^2*d^2) + tan(e/2 + (f*x)/2)^6*(40*a^2*c^4 + (64*a^2*d^4)/3 + 96*a^2*c*d^3 + (400*a^2*c^3*d)/3 + 160*a^2*c^2*d^2) + (48*a^2*c*d^3)/5 + (40*a^2*c^3*d)/3 + 16*a^2*c^2*d^2)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1))","B"
435,1,611,233,8.419583,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^3,x)","\frac{3\,a^2\,\mathrm{atan}\left(\frac{3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c+d\right)\,\left(2\,c^2+3\,c\,d+2\,d^2\right)}{4\,\left(3\,a^2\,c^3+6\,a^2\,c^2\,d+\frac{21\,a^2\,c\,d^2}{4}+\frac{3\,a^2\,d^3}{2}\right)}\right)\,\left(2\,c+d\right)\,\left(2\,c^2+3\,c\,d+2\,d^2\right)}{4\,f}-\frac{3\,a^2\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(4\,c^3+8\,c^2\,d+7\,c\,d^2+2\,d^3\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(4\,a^2\,c^3+6\,d\,a^2\,c^2\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(a^2\,c^3+6\,a^2\,c^2\,d+\frac{21\,a^2\,c\,d^2}{4}+\frac{3\,a^2\,d^3}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,a^2\,c^3+12\,a^2\,c^2\,d+\frac{33\,a^2\,c\,d^2}{2}+7\,a^2\,d^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,a^2\,c^3+12\,a^2\,c^2\,d+\frac{33\,a^2\,c\,d^2}{2}+7\,a^2\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(16\,a^2\,c^3+36\,a^2\,c^2\,d+24\,a^2\,c\,d^2+4\,a^2\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(16\,a^2\,c^3+44\,a^2\,c^2\,d+40\,a^2\,c\,d^2+12\,a^2\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(24\,a^2\,c^3+64\,a^2\,c^2\,d+56\,a^2\,c\,d^2+20\,a^2\,d^3\right)+4\,a^2\,c^3+\frac{12\,a^2\,d^3}{5}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,c^3+6\,a^2\,c^2\,d+\frac{21\,a^2\,c\,d^2}{4}+\frac{3\,a^2\,d^3}{2}\right)+8\,a^2\,c\,d^2+10\,a^2\,c^2\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(3*a^2*atan((3*a^2*tan(e/2 + (f*x)/2)*(2*c + d)*(3*c*d + 2*c^2 + 2*d^2))/(4*(3*a^2*c^3 + (3*a^2*d^3)/2 + (21*a^2*c*d^2)/4 + 6*a^2*c^2*d)))*(2*c + d)*(3*c*d + 2*c^2 + 2*d^2))/(4*f) - (3*a^2*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(7*c*d^2 + 8*c^2*d + 4*c^3 + 2*d^3))/(4*f) - (tan(e/2 + (f*x)/2)^8*(4*a^2*c^3 + 6*a^2*c^2*d) - tan(e/2 + (f*x)/2)^9*(a^2*c^3 + (3*a^2*d^3)/2 + (21*a^2*c*d^2)/4 + 6*a^2*c^2*d) + tan(e/2 + (f*x)/2)^3*(2*a^2*c^3 + 7*a^2*d^3 + (33*a^2*c*d^2)/2 + 12*a^2*c^2*d) - tan(e/2 + (f*x)/2)^7*(2*a^2*c^3 + 7*a^2*d^3 + (33*a^2*c*d^2)/2 + 12*a^2*c^2*d) + tan(e/2 + (f*x)/2)^6*(16*a^2*c^3 + 4*a^2*d^3 + 24*a^2*c*d^2 + 36*a^2*c^2*d) + tan(e/2 + (f*x)/2)^2*(16*a^2*c^3 + 12*a^2*d^3 + 40*a^2*c*d^2 + 44*a^2*c^2*d) + tan(e/2 + (f*x)/2)^4*(24*a^2*c^3 + 20*a^2*d^3 + 56*a^2*c*d^2 + 64*a^2*c^2*d) + 4*a^2*c^3 + (12*a^2*d^3)/5 + tan(e/2 + (f*x)/2)*(a^2*c^3 + (3*a^2*d^3)/2 + (21*a^2*c*d^2)/4 + 6*a^2*c^2*d) + 8*a^2*c*d^2 + 10*a^2*c^2*d)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1))","B"
436,1,440,156,8.340182,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^2,x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c^2+16\,c\,d+7\,d^2\right)}{4\,\left(3\,a^2\,c^2+4\,a^2\,c\,d+\frac{7\,a^2\,d^2}{4}\right)}\right)\,\left(12\,c^2+16\,c\,d+7\,d^2\right)}{4\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,c^2+4\,a^2\,c\,d+\frac{7\,a^2\,d^2}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(a^2\,c^2+4\,a^2\,c\,d+\frac{7\,a^2\,d^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^2\,c^2+4\,a^2\,c\,d+\frac{15\,a^2\,d^2}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(a^2\,c^2+4\,a^2\,c\,d+\frac{15\,a^2\,d^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(12\,a^2\,c^2+20\,a^2\,c\,d+8\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(12\,a^2\,c^2+\frac{68\,a^2\,c\,d}{3}+\frac{32\,a^2\,d^2}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,a^2\,c^2+4\,d\,a^2\,c\right)+4\,a^2\,c^2+\frac{8\,a^2\,d^2}{3}+\frac{20\,a^2\,c\,d}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{a^2\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(12\,c^2+16\,c\,d+7\,d^2\right)}{4\,f}","Not used",1,"(a^2*atan((a^2*tan(e/2 + (f*x)/2)*(16*c*d + 12*c^2 + 7*d^2))/(4*(3*a^2*c^2 + (7*a^2*d^2)/4 + 4*a^2*c*d)))*(16*c*d + 12*c^2 + 7*d^2))/(4*f) - (tan(e/2 + (f*x)/2)*(a^2*c^2 + (7*a^2*d^2)/4 + 4*a^2*c*d) - tan(e/2 + (f*x)/2)^7*(a^2*c^2 + (7*a^2*d^2)/4 + 4*a^2*c*d) + tan(e/2 + (f*x)/2)^3*(a^2*c^2 + (15*a^2*d^2)/4 + 4*a^2*c*d) - tan(e/2 + (f*x)/2)^5*(a^2*c^2 + (15*a^2*d^2)/4 + 4*a^2*c*d) + tan(e/2 + (f*x)/2)^4*(12*a^2*c^2 + 8*a^2*d^2 + 20*a^2*c*d) + tan(e/2 + (f*x)/2)^2*(12*a^2*c^2 + (32*a^2*d^2)/3 + (68*a^2*c*d)/3) + tan(e/2 + (f*x)/2)^6*(4*a^2*c^2 + 4*a^2*c*d) + 4*a^2*c^2 + (8*a^2*d^2)/3 + (20*a^2*c*d)/3)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1)) - (a^2*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(16*c*d + 12*c^2 + 7*d^2))/(4*f)","B"
437,1,91,94,6.923263,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x)),x)","-\frac{\frac{3\,a^2\,c\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{a^2\,d\,\cos\left(3\,e+3\,f\,x\right)}{2}+3\,a^2\,d\,\sin\left(2\,e+2\,f\,x\right)+12\,a^2\,c\,\cos\left(e+f\,x\right)+\frac{21\,a^2\,d\,\cos\left(e+f\,x\right)}{2}-9\,a^2\,c\,f\,x-6\,a^2\,d\,f\,x}{6\,f}","Not used",1,"-((3*a^2*c*sin(2*e + 2*f*x))/2 - (a^2*d*cos(3*e + 3*f*x))/2 + 3*a^2*d*sin(2*e + 2*f*x) + 12*a^2*c*cos(e + f*x) + (21*a^2*d*cos(e + f*x))/2 - 9*a^2*c*f*x - 6*a^2*d*f*x)/(6*f)","B"
438,1,123,45,6.871370,"\text{Not used}","int((a + a*sin(e + f*x))^2,x)","\frac{3\,a^2\,x}{2}-\frac{a^2\,\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)-a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-a^2\,\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}-4\right)+a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2\,\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)-a^2\,\left(3\,e+3\,f\,x-4\right)\right)}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(3*a^2*x)/2 - (a^2*((3*e)/2 + (3*f*x)/2) - a^2*tan(e/2 + (f*x)/2)^3 - a^2*((3*e)/2 + (3*f*x)/2 - 4) + a^2*tan(e/2 + (f*x)/2) + tan(e/2 + (f*x)/2)^2*(2*a^2*((3*e)/2 + (3*f*x)/2) - a^2*(3*e + 3*f*x - 4)))/(f*(tan(e/2 + (f*x)/2)^2 + 1)^2)","B"
439,1,940,92,7.678361,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x)),x)","\frac{4\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f\,\left(c+d\right)}-\frac{a^2\,\cos\left(e+f\,x\right)}{f\,\left(c+d\right)}+\frac{2\,a^2\,c\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{d\,f\,\left(c+d\right)}-\frac{2\,a^2\,c^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{d^2\,f\,\left(c+d\right)}-\frac{a^2\,c\,\cos\left(e+f\,x\right)}{d\,f\,\left(c+d\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{\left(3\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(-c^4+2\,c^3\,d-2\,c\,d^3+d^4\right)}^{3/2}-2\,c^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}-2\,c^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(-c^4+2\,c^3\,d-2\,c\,d^3+d^4\right)}^{3/2}+7\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}+10\,c\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}+4\,c^5\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}+4\,c^2\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}-3\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}-2\,c^4\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}-9\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}-12\,c^3\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}+6\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}+c\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(-c^4+2\,c^3\,d-2\,c\,d^3+d^4\right)}^{3/2}+4\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}+c^5\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-c^4+2\,c^3\,d-2\,c\,d^3+d^4}\right)\,1{}\mathrm{i}}{d\,\left(c+d\right)\,\left(3\,c^5\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-5\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-10\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+16\,c\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+8\,c^2\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-8\,c^4\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-16\,c^3\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,2{}\mathrm{i}}{d^2\,f\,\left(c+d\right)}","Not used",1,"(4*a^2*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(f*(c + d)) - (a^2*cos(e + f*x))/(f*(c + d)) + (2*a^2*c*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(d*f*(c + d)) - (2*a^2*c^2*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(d^2*f*(c + d)) + (a^2*atan(((3*d^2*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(3/2) - 2*c^6*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) - 2*c^2*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(3/2) + 7*d^6*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) + 10*c*d^5*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) + 4*c^5*d*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) + 4*c^2*d^4*cos(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) - 3*c^3*d^3*cos(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) - 2*c^4*d^2*cos(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) - 9*c^2*d^4*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) - 12*c^3*d^3*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) + 6*c^4*d^2*sin(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) + c*d*cos(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(3/2) + 4*c*d^5*cos(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2) + c^5*d*cos(e/2 + (f*x)/2)*(2*c^3*d - 2*c*d^3 - c^4 + d^4)^(1/2))*1i)/(d*(c + d)*(3*c^5*d*cos(e/2 + (f*x)/2) - 5*c*d^5*cos(e/2 + (f*x)/2) - 10*d^6*sin(e/2 + (f*x)/2) + 16*c*d^5*sin(e/2 + (f*x)/2) + 8*c^2*d^4*cos(e/2 + (f*x)/2) + 2*c^3*d^3*cos(e/2 + (f*x)/2) - 8*c^4*d^2*cos(e/2 + (f*x)/2) + 4*c^2*d^4*sin(e/2 + (f*x)/2) - 16*c^3*d^3*sin(e/2 + (f*x)/2) + 6*c^4*d^2*sin(e/2 + (f*x)/2))))*(-(c + d)*(c - d)^3)^(1/2)*2i)/(d^2*f*(c + d)) - (a^2*c*cos(e + f*x))/(d*f*(c + d))","B"
440,1,2836,112,11.241048,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(a^2\,c-a^2\,d\right)}{d\,\left(c+d\right)}+\frac{2\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(c-d\right)}{c\,\left(c+d\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}+\frac{2\,a^2\,\mathrm{atan}\left(\frac{192\,a^6\,c^3\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{128\,a^6\,c^3\,d^5}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{512\,a^6\,c^2\,d^6}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{320\,a^6\,c\,d^7}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{512\,a^6\,c^4\,d^4}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{192\,a^6\,c^5\,d^3}{c^2\,d^2+2\,c\,d^3+d^4}}-\frac{320\,a^6\,c\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{128\,a^6\,c^3\,d^5}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{512\,a^6\,c^2\,d^6}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{320\,a^6\,c\,d^7}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{512\,a^6\,c^4\,d^4}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{192\,a^6\,c^5\,d^3}{c^2\,d^2+2\,c\,d^3+d^4}}+\frac{128\,a^6\,c^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{128\,a^6\,c^3\,d^5}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{512\,a^6\,c^2\,d^6}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{320\,a^6\,c\,d^7}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{512\,a^6\,c^4\,d^4}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{192\,a^6\,c^5\,d^3}{c^2\,d^2+2\,c\,d^3+d^4}}\right)}{d^2\,f}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\left(a^4\,c^4\,d+2\,a^4\,c^3\,d^2+a^4\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^4\,c^5\,d+4\,a^4\,c^4\,d^2-4\,a^4\,c^3\,d^3-8\,a^4\,c^2\,d^4+2\,a^4\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^4-4\,a^2\,c^3\,d^5+2\,a^2\,c^2\,d^6+4\,a^2\,c\,d^7\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{32\,\left(a^2\,c\,d^6-a^2\,c^3\,d^4\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)\,1{}\mathrm{i}}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\left(a^4\,c^4\,d+2\,a^4\,c^3\,d^2+a^4\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^4\,c^5\,d+4\,a^4\,c^4\,d^2-4\,a^4\,c^3\,d^3-8\,a^4\,c^2\,d^4+2\,a^4\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\left(a^2\,c\,d^6-a^2\,c^3\,d^4\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^4-4\,a^2\,c^3\,d^5+2\,a^2\,c^2\,d^6+4\,a^2\,c\,d^7\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)\,1{}\mathrm{i}}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}}{\frac{64\,\left(2\,a^6\,c^3+2\,a^6\,c^2\,d-4\,a^6\,c\,d^2\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,c^4+4\,a^6\,c^3\,d-2\,a^6\,c^2\,d^2-4\,a^6\,c\,d^3\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\left(a^4\,c^4\,d+2\,a^4\,c^3\,d^2+a^4\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^4\,c^5\,d+4\,a^4\,c^4\,d^2-4\,a^4\,c^3\,d^3-8\,a^4\,c^2\,d^4+2\,a^4\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^4-4\,a^2\,c^3\,d^5+2\,a^2\,c^2\,d^6+4\,a^2\,c\,d^7\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{32\,\left(a^2\,c\,d^6-a^2\,c^3\,d^4\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\left(a^4\,c^4\,d+2\,a^4\,c^3\,d^2+a^4\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^4\,c^5\,d+4\,a^4\,c^4\,d^2-4\,a^4\,c^3\,d^3-8\,a^4\,c^2\,d^4+2\,a^4\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,\left(\frac{32\,\left(a^2\,c\,d^6-a^2\,c^3\,d^4\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^4-4\,a^2\,c^3\,d^5+2\,a^2\,c^2\,d^6+4\,a^2\,c\,d^7\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}\right)}{c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5}}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(c+2\,d\right)\,2{}\mathrm{i}}{f\,\left(c^3\,d^2+3\,c^2\,d^3+3\,c\,d^4+d^5\right)}","Not used",1,"((2*(a^2*c - a^2*d))/(d*(c + d)) + (2*a^2*tan(e/2 + (f*x)/2)*(c - d))/(c*(c + d)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2)) + (2*a^2*atan((192*a^6*c^3*d*tan(e/2 + (f*x)/2))/((128*a^6*c^3*d^5)/(2*c*d^3 + d^4 + c^2*d^2) - (512*a^6*c^2*d^6)/(2*c*d^3 + d^4 + c^2*d^2) - (320*a^6*c*d^7)/(2*c*d^3 + d^4 + c^2*d^2) + (512*a^6*c^4*d^4)/(2*c*d^3 + d^4 + c^2*d^2) + (192*a^6*c^5*d^3)/(2*c*d^3 + d^4 + c^2*d^2)) - (320*a^6*c*d^3*tan(e/2 + (f*x)/2))/((128*a^6*c^3*d^5)/(2*c*d^3 + d^4 + c^2*d^2) - (512*a^6*c^2*d^6)/(2*c*d^3 + d^4 + c^2*d^2) - (320*a^6*c*d^7)/(2*c*d^3 + d^4 + c^2*d^2) + (512*a^6*c^4*d^4)/(2*c*d^3 + d^4 + c^2*d^2) + (192*a^6*c^5*d^3)/(2*c*d^3 + d^4 + c^2*d^2)) + (128*a^6*c^2*d^2*tan(e/2 + (f*x)/2))/((128*a^6*c^3*d^5)/(2*c*d^3 + d^4 + c^2*d^2) - (512*a^6*c^2*d^6)/(2*c*d^3 + d^4 + c^2*d^2) - (320*a^6*c*d^7)/(2*c*d^3 + d^4 + c^2*d^2) + (512*a^6*c^4*d^4)/(2*c*d^3 + d^4 + c^2*d^2) + (192*a^6*c^5*d^3)/(2*c*d^3 + d^4 + c^2*d^2))))/(d^2*f) + (a^2*atan(((a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*(a^4*c^4*d + a^4*c^2*d^3 + 2*a^4*c^3*d^2))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*a^4*c*d^5 + 2*a^4*c^5*d - 8*a^4*c^2*d^4 - 4*a^4*c^3*d^3 + 4*a^4*c^4*d^2))/(2*c*d^4 + d^5 + c^2*d^3) + (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*tan(e/2 + (f*x)/2)*(4*a^2*c*d^7 + 2*a^2*c^2*d^6 - 4*a^2*c^3*d^5 - 2*a^2*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) - (32*(a^2*c*d^6 - a^2*c^3*d^4))/(2*c*d^3 + d^4 + c^2*d^2) + (a^2*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2))*1i)/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2) + (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*(a^4*c^4*d + a^4*c^2*d^3 + 2*a^4*c^3*d^2))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*a^4*c*d^5 + 2*a^4*c^5*d - 8*a^4*c^2*d^4 - 4*a^4*c^3*d^3 + 4*a^4*c^4*d^2))/(2*c*d^4 + d^5 + c^2*d^3) + (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*(a^2*c*d^6 - a^2*c^3*d^4))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(4*a^2*c*d^7 + 2*a^2*c^2*d^6 - 4*a^2*c^3*d^5 - 2*a^2*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) + (a^2*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2))*1i)/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2))/((64*(2*a^6*c^3 - 4*a^6*c*d^2 + 2*a^6*c^2*d))/(2*c*d^3 + d^4 + c^2*d^2) + (64*tan(e/2 + (f*x)/2)*(2*a^6*c^4 - 4*a^6*c*d^3 + 4*a^6*c^3*d - 2*a^6*c^2*d^2))/(2*c*d^4 + d^5 + c^2*d^3) - (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*(a^4*c^4*d + a^4*c^2*d^3 + 2*a^4*c^3*d^2))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*a^4*c*d^5 + 2*a^4*c^5*d - 8*a^4*c^2*d^4 - 4*a^4*c^3*d^3 + 4*a^4*c^4*d^2))/(2*c*d^4 + d^5 + c^2*d^3) + (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*tan(e/2 + (f*x)/2)*(4*a^2*c*d^7 + 2*a^2*c^2*d^6 - 4*a^2*c^3*d^5 - 2*a^2*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) - (32*(a^2*c*d^6 - a^2*c^3*d^4))/(2*c*d^3 + d^4 + c^2*d^2) + (a^2*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2) + (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*(a^4*c^4*d + a^4*c^2*d^3 + 2*a^4*c^3*d^2))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*a^4*c*d^5 + 2*a^4*c^5*d - 8*a^4*c^2*d^4 - 4*a^4*c^3*d^3 + 4*a^4*c^4*d^2))/(2*c*d^4 + d^5 + c^2*d^3) + (a^2*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*((32*(a^2*c*d^6 - a^2*c^3*d^4))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(4*a^2*c*d^7 + 2*a^2*c^2*d^6 - 4*a^2*c^3*d^5 - 2*a^2*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) + (a^2*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))/(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2)))*(-(c + d)^3*(c - d))^(1/2)*(c + 2*d)*2i)/(f*(3*c*d^4 + d^5 + 3*c^2*d^3 + c^3*d^2))","B"
441,1,362,138,9.427303,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^3,x)","\frac{3\,a^2\,\mathrm{atan}\left(\frac{\left(\frac{3\,a^2\,\left(2\,c^2\,d+4\,c\,d^2+2\,d^3\right)}{2\,{\left(c+d\right)}^{5/2}\,\sqrt{c-d}\,\left(c^2+2\,c\,d+d^2\right)}+\frac{3\,a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{{\left(c+d\right)}^{5/2}\,\sqrt{c-d}}\right)\,\left(c^2+2\,c\,d+d^2\right)}{3\,a^2}\right)}{f\,{\left(c+d\right)}^{5/2}\,\sqrt{c-d}}-\frac{\frac{4\,a^2\,c+a^2\,d}{c^2+2\,c\,d+d^2}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,c^2+12\,a^2\,c\,d+2\,a^2\,d^2\right)}{c\,\left(c^2+2\,c\,d+d^2\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-c^2+4\,c\,d+2\,d^2\right)}{c\,\left(c^2+2\,c\,d+d^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(4\,a^2\,c+a^2\,d\right)}{c^2\,\left(c^2+2\,c\,d+d^2\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}","Not used",1,"(3*a^2*atan((((3*a^2*(4*c*d^2 + 2*c^2*d + 2*d^3))/(2*(c + d)^(5/2)*(c - d)^(1/2)*(2*c*d + c^2 + d^2)) + (3*a^2*c*tan(e/2 + (f*x)/2))/((c + d)^(5/2)*(c - d)^(1/2)))*(2*c*d + c^2 + d^2))/(3*a^2)))/(f*(c + d)^(5/2)*(c - d)^(1/2)) - ((4*a^2*c + a^2*d)/(2*c*d + c^2 + d^2) + (tan(e/2 + (f*x)/2)*(a^2*c^2 + 2*a^2*d^2 + 12*a^2*c*d))/(c*(2*c*d + c^2 + d^2)) + (a^2*tan(e/2 + (f*x)/2)^3*(4*c*d - c^2 + 2*d^2))/(c*(2*c*d + c^2 + d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(4*a^2*c + a^2*d))/(c^2*(2*c*d + c^2 + d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2)))","B"
442,1,735,207,10.316074,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^4,x)","-\frac{\frac{-12\,a^2\,c^3+7\,a^2\,c^2\,d+6\,a^2\,c\,d^2+2\,a^2\,d^3}{3\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(c^4-6\,c^3\,d+4\,c\,d^3+2\,d^4\right)}{c\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}+\frac{2\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-4\,c^5+2\,c^4\,d-12\,c^3\,d^2+11\,c^2\,d^3+6\,c\,d^4+2\,d^5\right)}{c^2\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(-4\,c^5+3\,c^4\,d-18\,c^3\,d^2+8\,c^2\,d^3+12\,c\,d^4+4\,d^5\right)}{c^2\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-c^4-18\,c^3\,d+14\,c^2\,d^2+8\,c\,d^3+2\,d^4\right)}{c\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}+\frac{2\,a^2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,c^2+2\,d^2\right)\,\left(-12\,c^3+7\,c^2\,d+6\,c\,d^2+2\,d^3\right)}{3\,c^3\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}}{f\,\left(c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^2\,d+8\,d^3\right)+c^3+6\,c^2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,c^2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}-\frac{a^2\,\mathrm{atan}\left(\frac{\left(\frac{a^2\,\left(3\,c-2\,d\right)\,\left(-2\,c^4\,d-4\,c^3\,d^2+4\,c\,d^4+2\,d^5\right)}{2\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{3/2}\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}+\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c-2\,d\right)}{{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{3/2}}\right)\,\left(-c^4-2\,c^3\,d+2\,c\,d^3+d^4\right)}{3\,a^2\,c-2\,a^2\,d}\right)\,\left(3\,c-2\,d\right)}{f\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{3/2}}","Not used",1,"- ((2*a^2*d^3 - 12*a^2*c^3 + 6*a^2*c*d^2 + 7*a^2*c^2*d)/(3*(2*c*d^3 - 2*c^3*d - c^4 + d^4)) + (a^2*tan(e/2 + (f*x)/2)^5*(4*c*d^3 - 6*c^3*d + c^4 + 2*d^4))/(c*(2*c*d^3 - 2*c^3*d - c^4 + d^4)) + (2*a^2*tan(e/2 + (f*x)/2)^2*(6*c*d^4 + 2*c^4*d - 4*c^5 + 2*d^5 + 11*c^2*d^3 - 12*c^3*d^2))/(c^2*(2*c*d^3 - 2*c^3*d - c^4 + d^4)) + (a^2*tan(e/2 + (f*x)/2)^4*(12*c*d^4 + 3*c^4*d - 4*c^5 + 4*d^5 + 8*c^2*d^3 - 18*c^3*d^2))/(c^2*(2*c*d^3 - 2*c^3*d - c^4 + d^4)) + (a^2*tan(e/2 + (f*x)/2)*(8*c*d^3 - 18*c^3*d - c^4 + 2*d^4 + 14*c^2*d^2))/(c*(2*c*d^3 - 2*c^3*d - c^4 + d^4)) + (2*a^2*d*tan(e/2 + (f*x)/2)^3*(3*c^2 + 2*d^2)*(6*c*d^2 + 7*c^2*d - 12*c^3 + 2*d^3))/(3*c^3*(2*c*d^3 - 2*c^3*d - c^4 + d^4)))/(f*(c^3*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^2*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^4*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^3*(12*c^2*d + 8*d^3) + c^3 + 6*c^2*d*tan(e/2 + (f*x)/2) + 6*c^2*d*tan(e/2 + (f*x)/2)^5)) - (a^2*atan((((a^2*(3*c - 2*d)*(4*c*d^4 - 2*c^4*d + 2*d^5 - 4*c^3*d^2))/(2*(c + d)^(7/2)*(c - d)^(3/2)*(2*c*d^3 - 2*c^3*d - c^4 + d^4)) + (a^2*c*tan(e/2 + (f*x)/2)*(3*c - 2*d))/((c + d)^(7/2)*(c - d)^(3/2)))*(2*c*d^3 - 2*c^3*d - c^4 + d^4))/(3*a^2*c - 2*a^2*d))*(3*c - 2*d))/(f*(c + d)^(7/2)*(c - d)^(3/2))","B"
443,1,1411,286,10.347487,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^5,x)","\frac{a^2\,\mathrm{atan}\left(\frac{4\,\left(\frac{a^2\,\left(12\,c^2-16\,c\,d+7\,d^2\right)\,\left(8\,c^6\,d+16\,c^5\,d^2-8\,c^4\,d^3-32\,c^3\,d^4-8\,c^2\,d^5+16\,c\,d^6+8\,d^7\right)}{32\,{\left(c+d\right)}^{9/2}\,{\left(c-d\right)}^{5/2}\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c^2-16\,c\,d+7\,d^2\right)}{4\,{\left(c+d\right)}^{9/2}\,{\left(c-d\right)}^{5/2}}\right)\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}{12\,a^2\,c^2-16\,a^2\,c\,d+7\,a^2\,d^2}\right)\,\left(12\,c^2-16\,c\,d+7\,d^2\right)}{4\,f\,{\left(c+d\right)}^{9/2}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{48\,a^2\,c^5-68\,a^2\,c^4\,d-16\,a^2\,c^3\,d^2+5\,a^2\,c^2\,d^3+16\,a^2\,c\,d^4+6\,a^2\,d^5}{12\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c^6+288\,c^5\,d-499\,c^4\,d^2-32\,c^3\,d^3+64\,c^2\,d^4+80\,c\,d^5+24\,d^6\right)}{12\,c\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-12\,c^8+480\,c^7\,d-597\,c^6\,d^2+480\,c^5\,d^3-836\,c^4\,d^4-208\,c^3\,d^5+152\,c^2\,d^6+256\,c\,d^7+96\,d^8\right)}{12\,c^3\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^8+672\,c^7\,d-1035\,c^6\,d^2+672\,c^5\,d^3-1220\,c^4\,d^4+80\,c^3\,d^5+152\,c^2\,d^6+256\,c\,d^7+96\,d^8\right)}{12\,c^3\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(16\,c^7-28\,c^6\,d+144\,c^5\,d^2-137\,c^4\,d^3-112\,c^3\,d^4+8\,c^2\,d^5+64\,c\,d^6+24\,d^7\right)}{4\,c^2\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(144\,c^7-188\,c^6\,d+656\,c^5\,d^2-1201\,c^4\,d^3+16\,c^3\,d^4+120\,c^2\,d^5+192\,c\,d^6+72\,d^7\right)}{12\,c^2\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}-\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(4\,c^6-32\,c^5\,d+15\,c^4\,d^2+32\,c^3\,d^3+8\,c^2\,d^4-16\,c\,d^5-8\,d^6\right)}{4\,c\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}+\frac{a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^4+24\,c^2\,d^2+8\,d^4\right)\,\left(48\,c^5-68\,c^4\,d-16\,c^3\,d^2+5\,c^2\,d^3+16\,c\,d^4+6\,d^5\right)}{12\,c^4\,\left(c^6+2\,c^5\,d-c^4\,d^2-4\,c^3\,d^3-c^2\,d^4+2\,c\,d^5+d^6\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,c^4+48\,c^2\,d^2+16\,d^4\right)+c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+c^4+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,c^4+24\,c^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,c^4+24\,c^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(24\,c^3\,d+32\,c\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(24\,c^3\,d+32\,c\,d^3\right)+8\,c^3\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+8\,c^3\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}","Not used",1,"(a^2*atan((4*((a^2*(12*c^2 - 16*c*d + 7*d^2)*(16*c*d^6 + 8*c^6*d + 8*d^7 - 8*c^2*d^5 - 32*c^3*d^4 - 8*c^4*d^3 + 16*c^5*d^2))/(32*(c + d)^(9/2)*(c - d)^(5/2)*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*c*tan(e/2 + (f*x)/2)*(12*c^2 - 16*c*d + 7*d^2))/(4*(c + d)^(9/2)*(c - d)^(5/2)))*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2))/(12*a^2*c^2 + 7*a^2*d^2 - 16*a^2*c*d))*(12*c^2 - 16*c*d + 7*d^2))/(4*f*(c + d)^(9/2)*(c - d)^(5/2)) - ((48*a^2*c^5 + 6*a^2*d^5 + 16*a^2*c*d^4 - 68*a^2*c^4*d + 5*a^2*c^2*d^3 - 16*a^2*c^3*d^2)/(12*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*tan(e/2 + (f*x)/2)*(80*c*d^5 + 288*c^5*d + 12*c^6 + 24*d^6 + 64*c^2*d^4 - 32*c^3*d^3 - 499*c^4*d^2))/(12*c*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*tan(e/2 + (f*x)/2)^5*(256*c*d^7 + 480*c^7*d - 12*c^8 + 96*d^8 + 152*c^2*d^6 - 208*c^3*d^5 - 836*c^4*d^4 + 480*c^5*d^3 - 597*c^6*d^2))/(12*c^3*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*tan(e/2 + (f*x)/2)^3*(256*c*d^7 + 672*c^7*d + 12*c^8 + 96*d^8 + 152*c^2*d^6 + 80*c^3*d^5 - 1220*c^4*d^4 + 672*c^5*d^3 - 1035*c^6*d^2))/(12*c^3*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*tan(e/2 + (f*x)/2)^6*(64*c*d^6 - 28*c^6*d + 16*c^7 + 24*d^7 + 8*c^2*d^5 - 112*c^3*d^4 - 137*c^4*d^3 + 144*c^5*d^2))/(4*c^2*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*tan(e/2 + (f*x)/2)^2*(192*c*d^6 - 188*c^6*d + 144*c^7 + 72*d^7 + 120*c^2*d^5 + 16*c^3*d^4 - 1201*c^4*d^3 + 656*c^5*d^2))/(12*c^2*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) - (a^2*tan(e/2 + (f*x)/2)^7*(4*c^6 - 32*c^5*d - 16*c*d^5 - 8*d^6 + 8*c^2*d^4 + 32*c^3*d^3 + 15*c^4*d^2))/(4*c*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)) + (a^2*tan(e/2 + (f*x)/2)^4*(3*c^4 + 8*d^4 + 24*c^2*d^2)*(16*c*d^4 - 68*c^4*d + 48*c^5 + 6*d^5 + 5*c^2*d^3 - 16*c^3*d^2))/(12*c^4*(2*c*d^5 + 2*c^5*d + c^6 + d^6 - c^2*d^4 - 4*c^3*d^3 - c^4*d^2)))/(f*(tan(e/2 + (f*x)/2)^4*(6*c^4 + 16*d^4 + 48*c^2*d^2) + c^4*tan(e/2 + (f*x)/2)^8 + c^4 + tan(e/2 + (f*x)/2)^2*(4*c^4 + 24*c^2*d^2) + tan(e/2 + (f*x)/2)^6*(4*c^4 + 24*c^2*d^2) + tan(e/2 + (f*x)/2)^3*(32*c*d^3 + 24*c^3*d) + tan(e/2 + (f*x)/2)^5*(32*c*d^3 + 24*c^3*d) + 8*c^3*d*tan(e/2 + (f*x)/2) + 8*c^3*d*tan(e/2 + (f*x)/2)^7))","B"
444,1,773,215,8.479051,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^3,x)","\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(40\,c^3+90\,c^2\,d+78\,c\,d^2+23\,d^3\right)}{8\,\left(5\,a^3\,c^3+\frac{45\,a^3\,c^2\,d}{4}+\frac{39\,a^3\,c\,d^2}{4}+\frac{23\,a^3\,d^3}{8}\right)}\right)\,\left(40\,c^3+90\,c^2\,d+78\,c\,d^2+23\,d^3\right)}{8\,f}-\frac{a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(40\,c^3+90\,c^2\,d+78\,c\,d^2+23\,d^3\right)}{8\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(6\,a^3\,c^3+6\,d\,a^3\,c^2\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(3\,a^3\,c^3+\frac{45\,a^3\,c^2\,d}{4}+\frac{39\,a^3\,c\,d^2}{4}+\frac{23\,a^3\,d^3}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(34\,a^3\,c^3+66\,a^3\,c^2\,d+36\,a^3\,c\,d^2+4\,a^3\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(6\,a^3\,c^3+\frac{57\,a^3\,c^2\,d}{2}+\frac{75\,a^3\,c\,d^2}{2}+\frac{75\,a^3\,d^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(6\,a^3\,c^3+\frac{57\,a^3\,c^2\,d}{2}+\frac{75\,a^3\,c\,d^2}{2}+\frac{75\,a^3\,d^3}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(76\,a^3\,c^3+204\,a^3\,c^2\,d+192\,a^3\,c\,d^2+64\,a^3\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{220\,a^3\,c^3}{3}+180\,a^3\,c^2\,d+152\,a^3\,c\,d^2+\frac{136\,a^3\,d^3}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(38\,a^3\,c^3+102\,a^3\,c^2\,d+\frac{456\,a^3\,c\,d^2}{5}+\frac{136\,a^3\,d^3}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(9\,a^3\,c^3+\frac{159\,a^3\,c^2\,d}{4}+\frac{189\,a^3\,c\,d^2}{4}+\frac{391\,a^3\,d^3}{24}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(9\,a^3\,c^3+\frac{159\,a^3\,c^2\,d}{4}+\frac{189\,a^3\,c\,d^2}{4}+\frac{391\,a^3\,d^3}{24}\right)+\frac{22\,a^3\,c^3}{3}+\frac{68\,a^3\,d^3}{15}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^3\,c^3+\frac{45\,a^3\,c^2\,d}{4}+\frac{39\,a^3\,c\,d^2}{4}+\frac{23\,a^3\,d^3}{8}\right)+\frac{76\,a^3\,c\,d^2}{5}+18\,a^3\,c^2\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*atan((a^3*tan(e/2 + (f*x)/2)*(78*c*d^2 + 90*c^2*d + 40*c^3 + 23*d^3))/(8*(5*a^3*c^3 + (23*a^3*d^3)/8 + (39*a^3*c*d^2)/4 + (45*a^3*c^2*d)/4)))*(78*c*d^2 + 90*c^2*d + 40*c^3 + 23*d^3))/(8*f) - (a^3*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(78*c*d^2 + 90*c^2*d + 40*c^3 + 23*d^3))/(8*f) - (tan(e/2 + (f*x)/2)^10*(6*a^3*c^3 + 6*a^3*c^2*d) - tan(e/2 + (f*x)/2)^11*(3*a^3*c^3 + (23*a^3*d^3)/8 + (39*a^3*c*d^2)/4 + (45*a^3*c^2*d)/4) + tan(e/2 + (f*x)/2)^8*(34*a^3*c^3 + 4*a^3*d^3 + 36*a^3*c*d^2 + 66*a^3*c^2*d) + tan(e/2 + (f*x)/2)^5*(6*a^3*c^3 + (75*a^3*d^3)/4 + (75*a^3*c*d^2)/2 + (57*a^3*c^2*d)/2) - tan(e/2 + (f*x)/2)^7*(6*a^3*c^3 + (75*a^3*d^3)/4 + (75*a^3*c*d^2)/2 + (57*a^3*c^2*d)/2) + tan(e/2 + (f*x)/2)^4*(76*a^3*c^3 + 64*a^3*d^3 + 192*a^3*c*d^2 + 204*a^3*c^2*d) + tan(e/2 + (f*x)/2)^6*((220*a^3*c^3)/3 + (136*a^3*d^3)/3 + 152*a^3*c*d^2 + 180*a^3*c^2*d) + tan(e/2 + (f*x)/2)^2*(38*a^3*c^3 + (136*a^3*d^3)/5 + (456*a^3*c*d^2)/5 + 102*a^3*c^2*d) + tan(e/2 + (f*x)/2)^3*(9*a^3*c^3 + (391*a^3*d^3)/24 + (189*a^3*c*d^2)/4 + (159*a^3*c^2*d)/4) - tan(e/2 + (f*x)/2)^9*(9*a^3*c^3 + (391*a^3*d^3)/24 + (189*a^3*c*d^2)/4 + (159*a^3*c^2*d)/4) + (22*a^3*c^3)/3 + (68*a^3*d^3)/15 + tan(e/2 + (f*x)/2)*(3*a^3*c^3 + (23*a^3*d^3)/8 + (39*a^3*c*d^2)/4 + (45*a^3*c^2*d)/4) + (76*a^3*c*d^2)/5 + 18*a^3*c^2*d)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1))","B"
445,1,493,164,8.358897,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^2,x)","\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(20\,c^2+30\,c\,d+13\,d^2\right)}{4\,\left(5\,a^3\,c^2+\frac{15\,a^3\,c\,d}{2}+\frac{13\,a^3\,d^2}{4}\right)}\right)\,\left(20\,c^2+30\,c\,d+13\,d^2\right)}{4\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^3\,c^2+\frac{15\,a^3\,c\,d}{2}+\frac{13\,a^3\,d^2}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(3\,a^3\,c^2+\frac{15\,a^3\,c\,d}{2}+\frac{13\,a^3\,d^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(6\,a^3\,c^2+19\,a^3\,c\,d+\frac{25\,a^3\,d^2}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(6\,a^3\,c^2+19\,a^3\,c\,d+\frac{25\,a^3\,d^2}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(28\,a^3\,c^2+40\,a^3\,c\,d+12\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{92\,a^3\,c^2}{3}+56\,a^3\,c\,d+\frac{76\,a^3\,d^2}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{136\,a^3\,c^2}{3}+80\,a^3\,c\,d+\frac{116\,a^3\,d^2}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(6\,a^3\,c^2+4\,d\,a^3\,c\right)+\frac{22\,a^3\,c^2}{3}+\frac{76\,a^3\,d^2}{15}+12\,a^3\,c\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(20\,c^2+30\,c\,d+13\,d^2\right)}{4\,f}","Not used",1,"(a^3*atan((a^3*tan(e/2 + (f*x)/2)*(30*c*d + 20*c^2 + 13*d^2))/(4*(5*a^3*c^2 + (13*a^3*d^2)/4 + (15*a^3*c*d)/2)))*(30*c*d + 20*c^2 + 13*d^2))/(4*f) - (tan(e/2 + (f*x)/2)*(3*a^3*c^2 + (13*a^3*d^2)/4 + (15*a^3*c*d)/2) - tan(e/2 + (f*x)/2)^9*(3*a^3*c^2 + (13*a^3*d^2)/4 + (15*a^3*c*d)/2) + tan(e/2 + (f*x)/2)^3*(6*a^3*c^2 + (25*a^3*d^2)/2 + 19*a^3*c*d) - tan(e/2 + (f*x)/2)^7*(6*a^3*c^2 + (25*a^3*d^2)/2 + 19*a^3*c*d) + tan(e/2 + (f*x)/2)^6*(28*a^3*c^2 + 12*a^3*d^2 + 40*a^3*c*d) + tan(e/2 + (f*x)/2)^2*((92*a^3*c^2)/3 + (76*a^3*d^2)/3 + 56*a^3*c*d) + tan(e/2 + (f*x)/2)^4*((136*a^3*c^2)/3 + (116*a^3*d^2)/3 + 80*a^3*c*d) + tan(e/2 + (f*x)/2)^8*(6*a^3*c^2 + 4*a^3*c*d) + (22*a^3*c^2)/3 + (76*a^3*d^2)/15 + 12*a^3*c*d)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1)) - (a^3*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(30*c*d + 20*c^2 + 13*d^2))/(4*f)","B"
446,1,330,110,8.066947,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x)),x)","\frac{5\,a^3\,\mathrm{atan}\left(\frac{5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,c+3\,d\right)}{4\,\left(5\,a^3\,c+\frac{15\,a^3\,d}{4}\right)}\right)\,\left(4\,c+3\,d\right)}{4\,f}-\frac{5\,a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(4\,c+3\,d\right)}{4\,f}-\frac{\frac{22\,a^3\,c}{3}+6\,a^3\,d+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^3\,c+\frac{15\,a^3\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(6\,a^3\,c+2\,a^3\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(3\,a^3\,c+\frac{15\,a^3\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,a^3\,c+\frac{23\,a^3\,d}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(3\,a^3\,c+\frac{23\,a^3\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(22\,a^3\,c+18\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{70\,a^3\,c}{3}+22\,a^3\,d\right)}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(5*a^3*atan((5*a^3*tan(e/2 + (f*x)/2)*(4*c + 3*d))/(4*(5*a^3*c + (15*a^3*d)/4)))*(4*c + 3*d))/(4*f) - (5*a^3*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(4*c + 3*d))/(4*f) - ((22*a^3*c)/3 + 6*a^3*d + tan(e/2 + (f*x)/2)*(3*a^3*c + (15*a^3*d)/4) + tan(e/2 + (f*x)/2)^6*(6*a^3*c + 2*a^3*d) - tan(e/2 + (f*x)/2)^7*(3*a^3*c + (15*a^3*d)/4) + tan(e/2 + (f*x)/2)^3*(3*a^3*c + (23*a^3*d)/4) - tan(e/2 + (f*x)/2)^5*(3*a^3*c + (23*a^3*d)/4) + tan(e/2 + (f*x)/2)^4*(22*a^3*c + 18*a^3*d) + tan(e/2 + (f*x)/2)^2*((70*a^3*c)/3 + 22*a^3*d))/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1))","B"
447,1,156,63,9.120136,"\text{Not used}","int((a + a*sin(e + f*x))^3,x)","\frac{5\,a^3\,x}{2}-\frac{\frac{5\,a^3\,\left(e+f\,x\right)}{2}-3\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-\frac{a^3\,\left(15\,e+15\,f\,x-44\right)}{6}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{15\,a^3\,\left(e+f\,x\right)}{2}-\frac{a^3\,\left(45\,e+45\,f\,x-36\right)}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{15\,a^3\,\left(e+f\,x\right)}{2}-\frac{a^3\,\left(45\,e+45\,f\,x-96\right)}{6}\right)+3\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(5*a^3*x)/2 - ((5*a^3*(e + f*x))/2 - 3*a^3*tan(e/2 + (f*x)/2)^5 - (a^3*(15*e + 15*f*x - 44))/6 + tan(e/2 + (f*x)/2)^4*((15*a^3*(e + f*x))/2 - (a^3*(45*e + 45*f*x - 36))/6) + tan(e/2 + (f*x)/2)^2*((15*a^3*(e + f*x))/2 - (a^3*(45*e + 45*f*x - 96))/6) + 3*a^3*tan(e/2 + (f*x)/2))/(f*(tan(e/2 + (f*x)/2)^2 + 1)^3)","B"
448,1,3382,143,9.219716,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x)),x)","\frac{\frac{2\,\left(a^3\,c-3\,a^3\,d\right)}{d^2}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{d}-\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{d}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^3\,c-3\,a^3\,d\right)}{d^2}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}-\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)}{d^3}+\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\left(\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)}{d^3}}{\frac{16\,\left(2\,a^9\,c^7-8\,a^9\,c^6\,d+7\,a^9\,c^5\,d^2+21\,a^9\,c^4\,d^3-55\,a^9\,c^3\,d^4+47\,a^9\,c^2\,d^5-14\,a^9\,c\,d^6\right)}{d^5}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,c^8-72\,a^9\,c^7\,d+296\,a^9\,c^6\,d^2-704\,a^9\,c^5\,d^3+1034\,a^9\,c^4\,d^4-926\,a^9\,c^3\,d^5+462\,a^9\,c^2\,d^6-98\,a^9\,c\,d^7\right)}{d^6}-\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}-\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}+\frac{a^3\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\left(\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)\,1{}\mathrm{i}}{d^3}}\right)\,\left(c^2-3\,c\,d+\frac{7\,d^2}{2}\right)}{d^3\,f}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}-\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^3\,\left(c+d\right)}\right)}{d^3\,\left(c+d\right)}\right)\,1{}\mathrm{i}}{d^3\,\left(c+d\right)}+\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^3\,\left(c+d\right)}\right)}{d^3\,\left(c+d\right)}\right)\,1{}\mathrm{i}}{d^3\,\left(c+d\right)}}{\frac{16\,\left(2\,a^9\,c^7-8\,a^9\,c^6\,d+7\,a^9\,c^5\,d^2+21\,a^9\,c^4\,d^3-55\,a^9\,c^3\,d^4+47\,a^9\,c^2\,d^5-14\,a^9\,c\,d^6\right)}{d^5}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,c^8-72\,a^9\,c^7\,d+296\,a^9\,c^6\,d^2-704\,a^9\,c^5\,d^3+1034\,a^9\,c^4\,d^4-926\,a^9\,c^3\,d^5+462\,a^9\,c^2\,d^6-98\,a^9\,c\,d^7\right)}{d^6}-\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}-\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^3\,\left(c+d\right)}\right)}{d^3\,\left(c+d\right)}\right)}{d^3\,\left(c+d\right)}+\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2-24\,a^6\,c^5\,d^3+64\,a^6\,c^4\,d^4-84\,a^6\,c^3\,d^5+49\,a^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+48\,a^6\,c^6\,d^3-116\,a^6\,c^5\,d^4+116\,a^6\,c^4\,d^5+19\,a^6\,c^3\,d^6-144\,a^6\,c^2\,d^7+94\,a^6\,c\,d^8\right)}{d^6}+\frac{a^3\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(2\,a^3\,c^3\,d^6-16\,a^3\,c^2\,d^7+14\,a^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^4\,d^6+24\,a^3\,c^3\,d^7-24\,a^3\,c^2\,d^8+8\,a^3\,c\,d^9\right)}{d^6}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^3\,\left(c+d\right)}\right)}{d^3\,\left(c+d\right)}\right)}{d^3\,\left(c+d\right)}}\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,2{}\mathrm{i}}{d^3\,f\,\left(c+d\right)}","Not used",1,"((2*(a^3*c - 3*a^3*d))/d^2 + (a^3*tan(e/2 + (f*x)/2)^3)/d - (a^3*tan(e/2 + (f*x)/2))/d + (2*tan(e/2 + (f*x)/2)^2*(a^3*c - 3*a^3*d))/d^2)/(f*(2*tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^4 + 1)) + (2*a^3*atan(((a^3*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 - (8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2))/d^3 + (a^3*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*((8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2))/d^3)/((16*(2*a^9*c^7 - 14*a^9*c*d^6 - 8*a^9*c^6*d + 47*a^9*c^2*d^5 - 55*a^9*c^3*d^4 + 21*a^9*c^4*d^3 + 7*a^9*c^5*d^2))/d^5 + (16*tan(e/2 + (f*x)/2)*(8*a^9*c^8 - 98*a^9*c*d^7 - 72*a^9*c^7*d + 462*a^9*c^2*d^6 - 926*a^9*c^3*d^5 + 1034*a^9*c^4*d^4 - 704*a^9*c^5*d^3 + 296*a^9*c^6*d^2))/d^6 - (a^3*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 - (8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3 + (a^3*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*((8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3)*(c^2 - 3*c*d + (7*d^2)/2)*1i)/d^3))*(c^2 - 3*c*d + (7*d^2)/2))/(d^3*f) + (a^3*atan(((a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 - (8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d)^5)^(1/2))/(d^3*(c + d))))/(d^3*(c + d)))*1i)/(d^3*(c + d)) + (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d)^5)^(1/2))/(d^3*(c + d))))/(d^3*(c + d)))*1i)/(d^3*(c + d)))/((16*(2*a^9*c^7 - 14*a^9*c*d^6 - 8*a^9*c^6*d + 47*a^9*c^2*d^5 - 55*a^9*c^3*d^4 + 21*a^9*c^4*d^3 + 7*a^9*c^5*d^2))/d^5 + (16*tan(e/2 + (f*x)/2)*(8*a^9*c^8 - 98*a^9*c*d^7 - 72*a^9*c^7*d + 462*a^9*c^2*d^6 - 926*a^9*c^3*d^5 + 1034*a^9*c^4*d^4 - 704*a^9*c^5*d^3 + 296*a^9*c^6*d^2))/d^6 - (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 - (8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d)^5)^(1/2))/(d^3*(c + d))))/(d^3*(c + d))))/(d^3*(c + d)) + (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*a^6*c^2*d^6 - 84*a^6*c^3*d^5 + 64*a^6*c^4*d^4 - 24*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/d^5 + (8*tan(e/2 + (f*x)/2)*(94*a^6*c*d^8 - 144*a^6*c^2*d^7 + 19*a^6*c^3*d^6 + 116*a^6*c^4*d^5 - 116*a^6*c^5*d^4 + 48*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/d^6 + (a^3*(-(c + d)*(c - d)^5)^(1/2)*((8*(14*a^3*c*d^8 - 16*a^3*c^2*d^7 + 2*a^3*c^3*d^6))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 24*a^3*c^2*d^8 + 24*a^3*c^3*d^7 - 8*a^3*c^4*d^6))/d^6 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d)^5)^(1/2))/(d^3*(c + d))))/(d^3*(c + d))))/(d^3*(c + d))))*(-(c + d)*(c - d)^5)^(1/2)*2i)/(d^3*f*(c + d))","B"
449,1,5079,161,12.954717,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^2,x)","-\frac{\frac{2\,\left(2\,a^3\,c^2-a^3\,c\,d+a^3\,d^2\right)}{d^2\,\left(c+d\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^3\,c^2-a^3\,c\,d+a^3\,d^2\right)}{d^2\,\left(c+d\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^3\,c^2+a^3\,d^2\right)}{c\,d\,\left(c+d\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^3\,c^2-2\,a^3\,c\,d+a^3\,d^2\right)}{c\,d\,\left(c+d\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{2\,a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}-\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(2\,c-3\,d\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}+\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(2\,c-3\,d\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}}{\frac{64\,\left(4\,a^9\,c^6-20\,a^9\,c^5\,d+19\,a^9\,c^4\,d^2+33\,a^9\,c^3\,d^3-63\,a^9\,c^2\,d^4+27\,a^9\,c\,d^5\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-16\,a^9\,c^7+40\,a^9\,c^6\,d+28\,a^9\,c^5\,d^2-130\,a^9\,c^4\,d^3+42\,a^9\,c^3\,d^4+90\,a^9\,c^2\,d^5-54\,a^9\,c\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}-\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(2\,c-3\,d\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}-\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(2\,c-3\,d\right)\,\left(\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(2\,c-3\,d\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}\right)\,\left(2\,c-3\,d\right)}{d^3\,f}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}-\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,1{}\mathrm{i}}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,1{}\mathrm{i}}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}}{\frac{64\,\left(4\,a^9\,c^6-20\,a^9\,c^5\,d+19\,a^9\,c^4\,d^2+33\,a^9\,c^3\,d^3-63\,a^9\,c^2\,d^4+27\,a^9\,c\,d^5\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-16\,a^9\,c^7+40\,a^9\,c^6\,d+28\,a^9\,c^5\,d^2-130\,a^9\,c^4\,d^3+42\,a^9\,c^3\,d^4+90\,a^9\,c^2\,d^5-54\,a^9\,c\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}-\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}-\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\left(4\,a^6\,c^6\,d^2-4\,a^6\,c^5\,d^3-11\,a^6\,c^4\,d^4+6\,a^6\,c^3\,d^5+9\,a^6\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^6\,c^7\,d^2+8\,a^6\,c^6\,d^3+34\,a^6\,c^5\,d^4-34\,a^6\,c^4\,d^5-41\,a^6\,c^3\,d^6+36\,a^6\,c^2\,d^7+9\,a^6\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,\left(\frac{32\,\left(-a^3\,c^4\,d^6-3\,a^3\,c^3\,d^7+a^3\,c^2\,d^8+3\,a^3\,c\,d^9\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^3\,c^5\,d^6+2\,a^3\,c^4\,d^7-10\,a^3\,c^3\,d^8-2\,a^3\,c^2\,d^9+6\,a^3\,c\,d^{10}\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^3\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,c+3\,d\right)\,2{}\mathrm{i}}{f\,\left(c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6\right)}","Not used",1,"- ((2*(2*a^3*c^2 + a^3*d^2 - a^3*c*d))/(d^2*(c + d)) + (2*tan(e/2 + (f*x)/2)^2*(2*a^3*c^2 + a^3*d^2 - a^3*c*d))/(d^2*(c + d)) + (2*tan(e/2 + (f*x)/2)*(3*a^3*c^2 + a^3*d^2))/(c*d*(c + d)) + (2*tan(e/2 + (f*x)/2)^3*(a^3*c^2 + a^3*d^2 - 2*a^3*c*d))/(c*d*(c + d)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + 2*c*tan(e/2 + (f*x)/2)^2 + c*tan(e/2 + (f*x)/2)^4 + 2*d*tan(e/2 + (f*x)/2)^3)) - (2*a^3*atan(((a^3*(2*c - 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(2*c - 3*d)*((32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) - (32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(2*c - 3*d)*1i)/d^3)*1i)/d^3))/d^3 + (a^3*(2*c - 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(2*c - 3*d)*((32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) - (32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(2*c - 3*d)*1i)/d^3)*1i)/d^3))/d^3)/((64*(4*a^9*c^6 + 27*a^9*c*d^5 - 20*a^9*c^5*d - 63*a^9*c^2*d^4 + 33*a^9*c^3*d^3 + 19*a^9*c^4*d^2))/(2*c*d^6 + d^7 + c^2*d^5) - (64*tan(e/2 + (f*x)/2)*(40*a^9*c^6*d - 54*a^9*c*d^6 - 16*a^9*c^7 + 90*a^9*c^2*d^5 + 42*a^9*c^3*d^4 - 130*a^9*c^4*d^3 + 28*a^9*c^5*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(2*c - 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(2*c - 3*d)*((32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) - (32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(2*c - 3*d)*1i)/d^3)*1i)/d^3)*1i)/d^3 - (a^3*(2*c - 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(2*c - 3*d)*((32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) - (32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(2*c - 3*d)*1i)/d^3)*1i)/d^3)*1i)/d^3))*(2*c - 3*d))/(d^3*f) - (a^3*atan(((a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) - (32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*1i)/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) - (32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*1i)/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))/((64*(4*a^9*c^6 + 27*a^9*c*d^5 - 20*a^9*c^5*d - 63*a^9*c^2*d^4 + 33*a^9*c^3*d^3 + 19*a^9*c^4*d^2))/(2*c*d^6 + d^7 + c^2*d^5) - (64*tan(e/2 + (f*x)/2)*(40*a^9*c^6*d - 54*a^9*c*d^6 - 16*a^9*c^7 + 90*a^9*c^2*d^5 + 42*a^9*c^3*d^4 - 130*a^9*c^4*d^3 + 28*a^9*c^5*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) - (32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3) - (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*(9*a^6*c^2*d^6 + 6*a^6*c^3*d^5 - 11*a^6*c^4*d^4 - 4*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(9*a^6*c*d^8 + 36*a^6*c^2*d^7 - 41*a^6*c^3*d^6 - 34*a^6*c^4*d^5 + 34*a^6*c^5*d^4 + 8*a^6*c^6*d^3 - 8*a^6*c^7*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*((32*(3*a^3*c*d^9 + a^3*c^2*d^8 - 3*a^3*c^3*d^7 - a^3*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) - (32*tan(e/2 + (f*x)/2)*(6*a^3*c*d^10 - 2*a^3*c^2*d^9 - 10*a^3*c^3*d^8 + 2*a^3*c^4*d^7 + 4*a^3*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) + (a^3*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*c + 3*d)*2i)/(f*(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))","B"
450,1,6246,187,14.273850,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^3,x)","\frac{\frac{2\,a^3\,c^3+4\,a^3\,c^2\,d-5\,a^3\,c\,d^2-a^3\,d^3}{d^2\,\left(c^2+2\,c\,d+d^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^3\,c^3+5\,a^3\,c^2\,d-4\,a^3\,c\,d^2-2\,a^3\,d^3\right)}{c\,d\,\left(c^2+2\,c\,d+d^2\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(7\,a^3\,c^3+11\,a^3\,c^2\,d-16\,a^3\,c\,d^2-2\,a^3\,d^3\right)}{c\,d\,\left(c^2+2\,c\,d+d^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(2\,a^3\,c^3+4\,a^3\,c^2\,d-5\,a^3\,c\,d^2-a^3\,d^3\right)}{c^2\,d^2\,\left(c^2+2\,c\,d+d^2\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{2\,a^3\,\mathrm{atan}\left(-\frac{\frac{\frac{8\,\left(4\,c^6\,d^2+16\,c^5\,d^3+24\,c^4\,d^4+16\,c^3\,d^5+4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^7\,d^2+32\,c^6\,d^3+36\,c^5\,d^4-36\,c^4\,d^5-99\,c^3\,d^6-46\,c^2\,d^7+41\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^6\,d^6-32\,c^5\,d^7-44\,c^4\,d^8+4\,c^3\,d^9+52\,c^2\,d^{10}+28\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(2\,c^5\,d^6-2\,c^4\,d^7-6\,c^3\,d^8+2\,c^2\,d^9+4\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}{d^3}+\frac{\frac{8\,\left(4\,c^6\,d^2+16\,c^5\,d^3+24\,c^4\,d^4+16\,c^3\,d^5+4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^7\,d^2+32\,c^6\,d^3+36\,c^5\,d^4-36\,c^4\,d^5-99\,c^3\,d^6-46\,c^2\,d^7+41\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\left(2\,c^5\,d^6-2\,c^4\,d^7-6\,c^3\,d^8+2\,c^2\,d^9+4\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^6\,d^6-32\,c^5\,d^7-44\,c^4\,d^8+4\,c^3\,d^9+52\,c^2\,d^{10}+28\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}{d^3}}{\frac{16\,\left(2\,c^5+18\,c^4\,d+29\,c^3\,d^2-49\,c\,d^4\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^6-32\,c^5\,d-44\,c^4\,d^2+4\,c^3\,d^3+52\,c^2\,d^4+28\,c\,d^5\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{\left(\frac{8\,\left(4\,c^6\,d^2+16\,c^5\,d^3+24\,c^4\,d^4+16\,c^3\,d^5+4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^7\,d^2+32\,c^6\,d^3+36\,c^5\,d^4-36\,c^4\,d^5-99\,c^3\,d^6-46\,c^2\,d^7+41\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^6\,d^6-32\,c^5\,d^7-44\,c^4\,d^8+4\,c^3\,d^9+52\,c^2\,d^{10}+28\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(2\,c^5\,d^6-2\,c^4\,d^7-6\,c^3\,d^8+2\,c^2\,d^9+4\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}+\frac{\left(\frac{8\,\left(4\,c^6\,d^2+16\,c^5\,d^3+24\,c^4\,d^4+16\,c^3\,d^5+4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^7\,d^2+32\,c^6\,d^3+36\,c^5\,d^4-36\,c^4\,d^5-99\,c^3\,d^6-46\,c^2\,d^7+41\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\left(2\,c^5\,d^6-2\,c^4\,d^7-6\,c^3\,d^8+2\,c^2\,d^9+4\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^6\,d^6-32\,c^5\,d^7-44\,c^4\,d^8+4\,c^3\,d^9+52\,c^2\,d^{10}+28\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}\right)}{d^3\,f}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2+16\,a^6\,c^5\,d^3+24\,a^6\,c^4\,d^4+16\,a^6\,c^3\,d^5+4\,a^6\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^6\,c^7\,d^2+32\,a^6\,c^6\,d^3+36\,a^6\,c^5\,d^4-36\,a^6\,c^4\,d^5-99\,a^6\,c^3\,d^6-46\,a^6\,c^2\,d^7+41\,a^6\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^6\,d^6-32\,a^3\,c^5\,d^7-44\,a^3\,c^4\,d^8+4\,a^3\,c^3\,d^9+52\,a^3\,c^2\,d^{10}+28\,a^3\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(2\,a^3\,c^5\,d^6-2\,a^3\,c^4\,d^7-6\,a^3\,c^3\,d^8+2\,a^3\,c^2\,d^9+4\,a^3\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)\,1{}\mathrm{i}}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2+16\,a^6\,c^5\,d^3+24\,a^6\,c^4\,d^4+16\,a^6\,c^3\,d^5+4\,a^6\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^6\,c^7\,d^2+32\,a^6\,c^6\,d^3+36\,a^6\,c^5\,d^4-36\,a^6\,c^4\,d^5-99\,a^6\,c^3\,d^6-46\,a^6\,c^2\,d^7+41\,a^6\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\left(2\,a^3\,c^5\,d^6-2\,a^3\,c^4\,d^7-6\,a^3\,c^3\,d^8+2\,a^3\,c^2\,d^9+4\,a^3\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^6\,d^6-32\,a^3\,c^5\,d^7-44\,a^3\,c^4\,d^8+4\,a^3\,c^3\,d^9+52\,a^3\,c^2\,d^{10}+28\,a^3\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)\,1{}\mathrm{i}}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}}{\frac{16\,\left(2\,a^9\,c^5+18\,a^9\,c^4\,d+29\,a^9\,c^3\,d^2-49\,a^9\,c\,d^4\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,c^6+32\,a^9\,c^5\,d+44\,a^9\,c^4\,d^2-4\,a^9\,c^3\,d^3-52\,a^9\,c^2\,d^4-28\,a^9\,c\,d^5\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2+16\,a^6\,c^5\,d^3+24\,a^6\,c^4\,d^4+16\,a^6\,c^3\,d^5+4\,a^6\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^6\,c^7\,d^2+32\,a^6\,c^6\,d^3+36\,a^6\,c^5\,d^4-36\,a^6\,c^4\,d^5-99\,a^6\,c^3\,d^6-46\,a^6\,c^2\,d^7+41\,a^6\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^6\,d^6-32\,a^3\,c^5\,d^7-44\,a^3\,c^4\,d^8+4\,a^3\,c^3\,d^9+52\,a^3\,c^2\,d^{10}+28\,a^3\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(2\,a^3\,c^5\,d^6-2\,a^3\,c^4\,d^7-6\,a^3\,c^3\,d^8+2\,a^3\,c^2\,d^9+4\,a^3\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\left(4\,a^6\,c^6\,d^2+16\,a^6\,c^5\,d^3+24\,a^6\,c^4\,d^4+16\,a^6\,c^3\,d^5+4\,a^6\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^6\,c^7\,d^2+32\,a^6\,c^6\,d^3+36\,a^6\,c^5\,d^4-36\,a^6\,c^4\,d^5-99\,a^6\,c^3\,d^6-46\,a^6\,c^2\,d^7+41\,a^6\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,\left(\frac{8\,\left(2\,a^3\,c^5\,d^6-2\,a^3\,c^4\,d^7-6\,a^3\,c^3\,d^8+2\,a^3\,c^2\,d^9+4\,a^3\,c\,d^{10}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,c^6\,d^6-32\,a^3\,c^5\,d^7-44\,a^3\,c^4\,d^8+4\,a^3\,c^3\,d^9+52\,a^3\,c^2\,d^{10}+28\,a^3\,c\,d^{11}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}\right)}{c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8}}\right)\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(c^2+3\,c\,d+\frac{7\,d^2}{2}\right)\,2{}\mathrm{i}}{f\,\left(c^5\,d^3+5\,c^4\,d^4+10\,c^3\,d^5+10\,c^2\,d^6+5\,c\,d^7+d^8\right)}","Not used",1,"((2*a^3*c^3 - a^3*d^3 - 5*a^3*c*d^2 + 4*a^3*c^2*d)/(d^2*(2*c*d + c^2 + d^2)) + (tan(e/2 + (f*x)/2)^3*(a^3*c^3 - 2*a^3*d^3 - 4*a^3*c*d^2 + 5*a^3*c^2*d))/(c*d*(2*c*d + c^2 + d^2)) + (tan(e/2 + (f*x)/2)*(7*a^3*c^3 - 2*a^3*d^3 - 16*a^3*c*d^2 + 11*a^3*c^2*d))/(c*d*(2*c*d + c^2 + d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(2*a^3*c^3 - a^3*d^3 - 5*a^3*c*d^2 + 4*a^3*c^2*d))/(c^2*d^2*(2*c*d + c^2 + d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) - (2*a^3*atan(-(((((((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 - (8*(4*c*d^10 + 2*c^2*d^9 - 6*c^3*d^8 - 2*c^4*d^7 + 2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(28*c*d^11 + 52*c^2*d^10 + 4*c^3*d^9 - 44*c^4*d^8 - 32*c^5*d^7 - 8*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 + (8*(4*c^2*d^6 + 16*c^3*d^5 + 24*c^4*d^4 + 16*c^5*d^3 + 4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*c*d^8 - 46*c^2*d^7 - 99*c^3*d^6 - 36*c^4*d^5 + 36*c^5*d^4 + 32*c^6*d^3 + 8*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))/d^3 + ((((8*(4*c*d^10 + 2*c^2*d^9 - 6*c^3*d^8 - 2*c^4*d^7 + 2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 - (8*tan(e/2 + (f*x)/2)*(28*c*d^11 + 52*c^2*d^10 + 4*c^3*d^9 - 44*c^4*d^8 - 32*c^5*d^7 - 8*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 + (8*(4*c^2*d^6 + 16*c^3*d^5 + 24*c^4*d^4 + 16*c^5*d^3 + 4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*c*d^8 - 46*c^2*d^7 - 99*c^3*d^6 - 36*c^4*d^5 + 36*c^5*d^4 + 32*c^6*d^3 + 8*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))/d^3)/((16*(18*c^4*d - 49*c*d^4 + 2*c^5 + 29*c^3*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (((((((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 - (8*(4*c*d^10 + 2*c^2*d^9 - 6*c^3*d^8 - 2*c^4*d^7 + 2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(28*c*d^11 + 52*c^2*d^10 + 4*c^3*d^9 - 44*c^4*d^8 - 32*c^5*d^7 - 8*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 + (8*(4*c^2*d^6 + 16*c^3*d^5 + 24*c^4*d^4 + 16*c^5*d^3 + 4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*c*d^8 - 46*c^2*d^7 - 99*c^3*d^6 - 36*c^4*d^5 + 36*c^5*d^4 + 32*c^6*d^3 + 8*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 + (((((8*(4*c*d^10 + 2*c^2*d^9 - 6*c^3*d^8 - 2*c^4*d^7 + 2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 - (8*tan(e/2 + (f*x)/2)*(28*c*d^11 + 52*c^2*d^10 + 4*c^3*d^9 - 44*c^4*d^8 - 32*c^5*d^7 - 8*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 + (8*(4*c^2*d^6 + 16*c^3*d^5 + 24*c^4*d^4 + 16*c^5*d^3 + 4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*c*d^8 - 46*c^2*d^7 - 99*c^3*d^6 - 36*c^4*d^5 + 36*c^5*d^4 + 32*c^6*d^3 + 8*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3 - (16*tan(e/2 + (f*x)/2)*(28*c*d^5 - 32*c^5*d - 8*c^6 + 52*c^2*d^4 + 4*c^3*d^3 - 44*c^4*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))))/(d^3*f) + (a^3*atan(((a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*(4*a^6*c^2*d^6 + 16*a^6*c^3*d^5 + 24*a^6*c^4*d^4 + 16*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*a^6*c*d^8 - 46*a^6*c^2*d^7 - 99*a^6*c^3*d^6 - 36*a^6*c^4*d^5 + 36*a^6*c^5*d^4 + 32*a^6*c^6*d^3 + 8*a^6*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*tan(e/2 + (f*x)/2)*(28*a^3*c*d^11 + 52*a^3*c^2*d^10 + 4*a^3*c^3*d^9 - 44*a^3*c^4*d^8 - 32*a^3*c^5*d^7 - 8*a^3*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (8*(4*a^3*c*d^10 + 2*a^3*c^2*d^9 - 6*a^3*c^3*d^8 - 2*a^3*c^4*d^7 + 2*a^3*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(3*c*d + c^2 + (7*d^2)/2))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3))*1i)/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3) + (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*(4*a^6*c^2*d^6 + 16*a^6*c^3*d^5 + 24*a^6*c^4*d^4 + 16*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*a^6*c*d^8 - 46*a^6*c^2*d^7 - 99*a^6*c^3*d^6 - 36*a^6*c^4*d^5 + 36*a^6*c^5*d^4 + 32*a^6*c^6*d^3 + 8*a^6*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*(4*a^3*c*d^10 + 2*a^3*c^2*d^9 - 6*a^3*c^3*d^8 - 2*a^3*c^4*d^7 + 2*a^3*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(28*a^3*c*d^11 + 52*a^3*c^2*d^10 + 4*a^3*c^3*d^9 - 44*a^3*c^4*d^8 - 32*a^3*c^5*d^7 - 8*a^3*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(3*c*d + c^2 + (7*d^2)/2))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3))*1i)/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3))/((16*(2*a^9*c^5 - 49*a^9*c*d^4 + 18*a^9*c^4*d + 29*a^9*c^3*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (16*tan(e/2 + (f*x)/2)*(8*a^9*c^6 - 28*a^9*c*d^5 + 32*a^9*c^5*d - 52*a^9*c^2*d^4 - 4*a^9*c^3*d^3 + 44*a^9*c^4*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*(4*a^6*c^2*d^6 + 16*a^6*c^3*d^5 + 24*a^6*c^4*d^4 + 16*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*a^6*c*d^8 - 46*a^6*c^2*d^7 - 99*a^6*c^3*d^6 - 36*a^6*c^4*d^5 + 36*a^6*c^5*d^4 + 32*a^6*c^6*d^3 + 8*a^6*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*tan(e/2 + (f*x)/2)*(28*a^3*c*d^11 + 52*a^3*c^2*d^10 + 4*a^3*c^3*d^9 - 44*a^3*c^4*d^8 - 32*a^3*c^5*d^7 - 8*a^3*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (8*(4*a^3*c*d^10 + 2*a^3*c^2*d^9 - 6*a^3*c^3*d^8 - 2*a^3*c^4*d^7 + 2*a^3*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(3*c*d + c^2 + (7*d^2)/2))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3) + (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*(4*a^6*c^2*d^6 + 16*a^6*c^3*d^5 + 24*a^6*c^4*d^4 + 16*a^6*c^5*d^3 + 4*a^6*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(41*a^6*c*d^8 - 46*a^6*c^2*d^7 - 99*a^6*c^3*d^6 - 36*a^6*c^4*d^5 + 36*a^6*c^5*d^4 + 32*a^6*c^6*d^3 + 8*a^6*c^7*d^2))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^3*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*((8*(4*a^3*c*d^10 + 2*a^3*c^2*d^9 - 6*a^3*c^3*d^8 - 2*a^3*c^4*d^7 + 2*a^3*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(28*a^3*c*d^11 + 52*a^3*c^2*d^10 + 4*a^3*c^3*d^9 - 44*a^3*c^4*d^8 - 32*a^3*c^5*d^7 - 8*a^3*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(3*c*d + c^2 + (7*d^2)/2))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))/(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3)))*(-(c + d)^5*(c - d))^(1/2)*(3*c*d + c^2 + (7*d^2)/2)*2i)/(f*(5*c*d^7 + d^8 + 10*c^2*d^6 + 10*c^3*d^5 + 5*c^4*d^4 + c^5*d^3))","B"
451,1,649,207,10.362510,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^4,x)","\frac{5\,a^3\,\mathrm{atan}\left(\frac{\left(\frac{5\,a^3\,\left(2\,c^3\,d+6\,c^2\,d^2+6\,c\,d^3+2\,d^4\right)}{2\,{\left(c+d\right)}^{7/2}\,\sqrt{c-d}\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}+\frac{5\,a^3\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{{\left(c+d\right)}^{7/2}\,\sqrt{c-d}}\right)\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}{5\,a^3}\right)}{f\,{\left(c+d\right)}^{7/2}\,\sqrt{c-d}}-\frac{\frac{22\,a^3\,c^2+9\,a^3\,c\,d+2\,a^3\,d^2}{3\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-3\,c^3+6\,c^2\,d+6\,c\,d^2+2\,d^3\right)}{c\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}+\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c^3+38\,c^2\,d+12\,c\,d^2+2\,d^3\right)}{c\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}+\frac{2\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(8\,c^4+6\,c^3\,d+30\,c^2\,d^2+9\,c\,d^3+2\,d^4\right)}{c^2\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,c^4-3\,c^3\,d+30\,c^2\,d^2+18\,c\,d^3+4\,d^4\right)}{c^2\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}+\frac{2\,a^3\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,c^2+2\,d^2\right)\,\left(22\,c^2+9\,c\,d+2\,d^2\right)}{3\,c^3\,\left(c^3+3\,c^2\,d+3\,c\,d^2+d^3\right)}}{f\,\left(c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^2\,d+8\,d^3\right)+c^3+6\,c^2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,c^2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}","Not used",1,"(5*a^3*atan((((5*a^3*(6*c*d^3 + 2*c^3*d + 2*d^4 + 6*c^2*d^2))/(2*(c + d)^(7/2)*(c - d)^(1/2)*(3*c*d^2 + 3*c^2*d + c^3 + d^3)) + (5*a^3*c*tan(e/2 + (f*x)/2))/((c + d)^(7/2)*(c - d)^(1/2)))*(3*c*d^2 + 3*c^2*d + c^3 + d^3))/(5*a^3)))/(f*(c + d)^(7/2)*(c - d)^(1/2)) - ((22*a^3*c^2 + 2*a^3*d^2 + 9*a^3*c*d)/(3*(3*c*d^2 + 3*c^2*d + c^3 + d^3)) + (a^3*tan(e/2 + (f*x)/2)^5*(6*c*d^2 + 6*c^2*d - 3*c^3 + 2*d^3))/(c*(3*c*d^2 + 3*c^2*d + c^3 + d^3)) + (a^3*tan(e/2 + (f*x)/2)*(12*c*d^2 + 38*c^2*d + 3*c^3 + 2*d^3))/(c*(3*c*d^2 + 3*c^2*d + c^3 + d^3)) + (2*a^3*tan(e/2 + (f*x)/2)^2*(9*c*d^3 + 6*c^3*d + 8*c^4 + 2*d^4 + 30*c^2*d^2))/(c^2*(3*c*d^2 + 3*c^2*d + c^3 + d^3)) + (a^3*tan(e/2 + (f*x)/2)^4*(18*c*d^3 - 3*c^3*d + 6*c^4 + 4*d^4 + 30*c^2*d^2))/(c^2*(3*c*d^2 + 3*c^2*d + c^3 + d^3)) + (2*a^3*d*tan(e/2 + (f*x)/2)^3*(3*c^2 + 2*d^2)*(9*c*d + 22*c^2 + 2*d^2))/(3*c^3*(3*c*d^2 + 3*c^2*d + c^3 + d^3)))/(f*(c^3*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^2*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^4*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^3*(12*c^2*d + 8*d^3) + c^3 + 6*c^2*d*tan(e/2 + (f*x)/2) + 6*c^2*d*tan(e/2 + (f*x)/2)^5))","B"
452,1,1231,289,10.103642,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^5,x)","-\frac{\frac{-88\,a^3\,c^4+36\,a^3\,c^3\,d+37\,a^3\,c^2\,d^2+24\,a^3\,c\,d^3+6\,a^3\,d^4}{12\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(12\,c^5-39\,c^4\,d-16\,c^3\,d^2+16\,c^2\,d^3+24\,c\,d^4+8\,d^5\right)}{4\,c\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(-24\,c^6+44\,c^5\,d-225\,c^4\,d^2+120\,c^2\,d^4+96\,c\,d^5+24\,d^6\right)}{4\,c^2\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-36\,c^5-587\,c^4\,d+336\,c^3\,d^2+248\,c^2\,d^3+120\,c\,d^4+24\,d^5\right)}{12\,c\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(36\,c^7-813\,c^6\,d+288\,c^5\,d^2-892\,c^4\,d^3+552\,c^3\,d^4+664\,c^2\,d^5+384\,c\,d^6+96\,d^7\right)}{12\,c^3\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-36\,c^7-1299\,c^6\,d+576\,c^5\,d^2-1036\,c^4\,d^3+1176\,c^3\,d^4+664\,c^2\,d^5+384\,c\,d^6+96\,d^7\right)}{12\,c^3\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-280\,c^6+12\,c^5\,d-1289\,c^4\,d^2+960\,c^3\,d^3+552\,c^2\,d^4+288\,c\,d^5+72\,d^6\right)}{12\,c^2\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^4+24\,c^2\,d^2+8\,d^4\right)\,\left(-88\,c^4+36\,c^3\,d+37\,c^2\,d^2+24\,c\,d^3+6\,d^4\right)}{12\,c^4\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,c^4+48\,c^2\,d^2+16\,d^4\right)+c^4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+c^4+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,c^4+24\,c^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,c^4+24\,c^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(24\,c^3\,d+32\,c\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(24\,c^3\,d+32\,c\,d^3\right)+8\,c^3\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+8\,c^3\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}-\frac{5\,a^3\,\mathrm{atan}\left(\frac{4\,\left(\frac{5\,a^3\,\left(4\,c-3\,d\right)\,\left(-8\,c^5\,d-24\,c^4\,d^2-16\,c^3\,d^3+16\,c^2\,d^4+24\,c\,d^5+8\,d^6\right)}{32\,{\left(c+d\right)}^{9/2}\,{\left(c-d\right)}^{3/2}\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}+\frac{5\,a^3\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,c-3\,d\right)}{4\,{\left(c+d\right)}^{9/2}\,{\left(c-d\right)}^{3/2}}\right)\,\left(-c^5-3\,c^4\,d-2\,c^3\,d^2+2\,c^2\,d^3+3\,c\,d^4+d^5\right)}{20\,a^3\,c-15\,a^3\,d}\right)\,\left(4\,c-3\,d\right)}{4\,f\,{\left(c+d\right)}^{9/2}\,{\left(c-d\right)}^{3/2}}","Not used",1,"- ((6*a^3*d^4 - 88*a^3*c^4 + 24*a^3*c*d^3 + 36*a^3*c^3*d + 37*a^3*c^2*d^2)/(12*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)^7*(24*c*d^4 - 39*c^4*d + 12*c^5 + 8*d^5 + 16*c^2*d^3 - 16*c^3*d^2))/(4*c*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)^6*(96*c*d^5 + 44*c^5*d - 24*c^6 + 24*d^6 + 120*c^2*d^4 - 225*c^4*d^2))/(4*c^2*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)*(120*c*d^4 - 587*c^4*d - 36*c^5 + 24*d^5 + 248*c^2*d^3 + 336*c^3*d^2))/(12*c*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)^5*(384*c*d^6 - 813*c^6*d + 36*c^7 + 96*d^7 + 664*c^2*d^5 + 552*c^3*d^4 - 892*c^4*d^3 + 288*c^5*d^2))/(12*c^3*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)^3*(384*c*d^6 - 1299*c^6*d - 36*c^7 + 96*d^7 + 664*c^2*d^5 + 1176*c^3*d^4 - 1036*c^4*d^3 + 576*c^5*d^2))/(12*c^3*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)^2*(288*c*d^5 + 12*c^5*d - 280*c^6 + 72*d^6 + 552*c^2*d^4 + 960*c^3*d^3 - 1289*c^4*d^2))/(12*c^2*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (a^3*tan(e/2 + (f*x)/2)^4*(3*c^4 + 8*d^4 + 24*c^2*d^2)*(24*c*d^3 + 36*c^3*d - 88*c^4 + 6*d^4 + 37*c^2*d^2))/(12*c^4*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)))/(f*(tan(e/2 + (f*x)/2)^4*(6*c^4 + 16*d^4 + 48*c^2*d^2) + c^4*tan(e/2 + (f*x)/2)^8 + c^4 + tan(e/2 + (f*x)/2)^2*(4*c^4 + 24*c^2*d^2) + tan(e/2 + (f*x)/2)^6*(4*c^4 + 24*c^2*d^2) + tan(e/2 + (f*x)/2)^3*(32*c*d^3 + 24*c^3*d) + tan(e/2 + (f*x)/2)^5*(32*c*d^3 + 24*c^3*d) + 8*c^3*d*tan(e/2 + (f*x)/2) + 8*c^3*d*tan(e/2 + (f*x)/2)^7)) - (5*a^3*atan((4*((5*a^3*(4*c - 3*d)*(24*c*d^5 - 8*c^5*d + 8*d^6 + 16*c^2*d^4 - 16*c^3*d^3 - 24*c^4*d^2))/(32*(c + d)^(9/2)*(c - d)^(3/2)*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2)) + (5*a^3*c*tan(e/2 + (f*x)/2)*(4*c - 3*d))/(4*(c + d)^(9/2)*(c - d)^(3/2)))*(3*c*d^4 - 3*c^4*d - c^5 + d^5 + 2*c^2*d^3 - 2*c^3*d^2))/(20*a^3*c - 15*a^3*d))*(4*c - 3*d))/(4*f*(c + d)^(9/2)*(c - d)^(3/2))","B"
453,1,451,189,9.786254,"\text{Not used}","int((c + d*sin(e + f*x))^4/(a + a*sin(e + f*x)),x)","\frac{d\,\mathrm{atan}\left(\frac{d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^3-12\,c^2\,d+12\,c\,d^2-3\,d^3\right)}{8\,c^3\,d-12\,c^2\,d^2+12\,c\,d^3-3\,d^4}\right)\,\left(8\,c^3-12\,c^2\,d+12\,c\,d^2-3\,d^3\right)}{a\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c^2\,d^2-4\,c\,d^3+\frac{7\,d^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,c^4-8\,c^3\,d+12\,c^2\,d^2-12\,c\,d^3+3\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,c^4-24\,c^3\,d+48\,c^2\,d^2-32\,c\,d^3+8\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,c^4-24\,c^3\,d+60\,c^2\,d^2-36\,c\,d^3+13\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(12\,c^2\,d^2-12\,c\,d^3+3\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(24\,c^2\,d^2-16\,c\,d^3+8\,d^4\right)-16\,c\,d^3-8\,c^3\,d+2\,c^4+\frac{16\,d^4}{3}+24\,c^2\,d^2}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}","Not used",1,"(d*atan((d*tan(e/2 + (f*x)/2)*(12*c*d^2 - 12*c^2*d + 8*c^3 - 3*d^3))/(12*c*d^3 + 8*c^3*d - 3*d^4 - 12*c^2*d^2))*(12*c*d^2 - 12*c^2*d + 8*c^3 - 3*d^3))/(a*f) - (tan(e/2 + (f*x)/2)*((7*d^4)/3 - 4*c*d^3 + 12*c^2*d^2) + tan(e/2 + (f*x)/2)^6*(2*c^4 - 8*c^3*d - 12*c*d^3 + 3*d^4 + 12*c^2*d^2) + tan(e/2 + (f*x)/2)^4*(6*c^4 - 24*c^3*d - 32*c*d^3 + 8*d^4 + 48*c^2*d^2) + tan(e/2 + (f*x)/2)^2*(6*c^4 - 24*c^3*d - 36*c*d^3 + 13*d^4 + 60*c^2*d^2) + tan(e/2 + (f*x)/2)^5*(3*d^4 - 12*c*d^3 + 12*c^2*d^2) + tan(e/2 + (f*x)/2)^3*(8*d^4 - 16*c*d^3 + 24*c^2*d^2) - 16*c*d^3 - 8*c^3*d + 2*c^4 + (16*d^4)/3 + 24*c^2*d^2)/(f*(a + a*tan(e/2 + (f*x)/2) + 3*a*tan(e/2 + (f*x)/2)^2 + 3*a*tan(e/2 + (f*x)/2)^3 + 3*a*tan(e/2 + (f*x)/2)^4 + 3*a*tan(e/2 + (f*x)/2)^5 + a*tan(e/2 + (f*x)/2)^6 + a*tan(e/2 + (f*x)/2)^7))","B"
454,1,282,121,9.434789,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x)),x)","\frac{3\,d\,\mathrm{atan}\left(\frac{3\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^2-2\,c\,d+d^2\right)}{6\,c^2\,d-6\,c\,d^2+3\,d^3}\right)\,\left(2\,c^2-2\,c\,d+d^2\right)}{a\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,c\,d^2-d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,c^3-6\,c^2\,d+6\,c\,d^2-3\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,c^3-12\,c^2\,d+18\,c\,d^2-5\,d^3\right)+12\,c\,d^2-6\,c^2\,d+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(6\,c\,d^2-3\,d^3\right)+2\,c^3-4\,d^3}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}","Not used",1,"(3*d*atan((3*d*tan(e/2 + (f*x)/2)*(2*c^2 - 2*c*d + d^2))/(6*c^2*d - 6*c*d^2 + 3*d^3))*(2*c^2 - 2*c*d + d^2))/(a*f) - (tan(e/2 + (f*x)/2)*(6*c*d^2 - d^3) + tan(e/2 + (f*x)/2)^4*(6*c*d^2 - 6*c^2*d + 2*c^3 - 3*d^3) + tan(e/2 + (f*x)/2)^2*(18*c*d^2 - 12*c^2*d + 4*c^3 - 5*d^3) + 12*c*d^2 - 6*c^2*d + tan(e/2 + (f*x)/2)^3*(6*c*d^2 - 3*d^3) + 2*c^3 - 4*d^3)/(f*(a + a*tan(e/2 + (f*x)/2) + 2*a*tan(e/2 + (f*x)/2)^2 + 2*a*tan(e/2 + (f*x)/2)^3 + a*tan(e/2 + (f*x)/2)^4 + a*tan(e/2 + (f*x)/2)^5))","B"
455,1,124,62,7.379741,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x)),x)","-\frac{d^2\,f\,x-2\,c\,d\,f\,x}{a\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2-4\,c\,d+2\,d^2\right)-4\,c\,d+2\,c^2+4\,d^2+2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}","Not used",1,"- (d^2*f*x - 2*c*d*f*x)/(a*f) - (tan(e/2 + (f*x)/2)^2*(2*c^2 - 4*c*d + 2*d^2) - 4*c*d + 2*c^2 + 4*d^2 + 2*d^2*tan(e/2 + (f*x)/2))/(f*(a + a*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2 + a*tan(e/2 + (f*x)/2)^3))","B"
456,1,35,35,6.825957,"\text{Not used}","int((c + d*sin(e + f*x))/(a + a*sin(e + f*x)),x)","\frac{d\,x}{a}-\frac{2\,c-2\,d}{a\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}","Not used",1,"(d*x)/a - (2*c - 2*d)/(a*f*(tan(e/2 + (f*x)/2) + 1))","B"
457,1,21,23,6.974983,"\text{Not used}","int(1/(a + a*sin(e + f*x)),x)","-\frac{2}{a\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}","Not used",1,"-2/(a*f*(tan(e/2 + (f*x)/2) + 1))","B"
458,1,121,89,6.986246,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))),x)","\frac{2\,d\,\mathrm{atan}\left(\frac{\frac{d\,\left(2\,a\,d^2-2\,a\,c\,d\right)}{a\,\sqrt{c+d}\,{\left(c-d\right)}^{3/2}}-\frac{2\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c-a\,d\right)}{a\,\sqrt{c+d}\,{\left(c-d\right)}^{3/2}}}{2\,d}\right)}{a\,f\,\sqrt{c+d}\,{\left(c-d\right)}^{3/2}}-\frac{2}{f\,\left(a+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)\,\left(c-d\right)}","Not used",1,"(2*d*atan(((d*(2*a*d^2 - 2*a*c*d))/(a*(c + d)^(1/2)*(c - d)^(3/2)) - (2*c*d*tan(e/2 + (f*x)/2)*(a*c - a*d))/(a*(c + d)^(1/2)*(c - d)^(3/2)))/(2*d)))/(a*f*(c + d)^(1/2)*(c - d)^(3/2)) - 2/(f*(a + a*tan(e/2 + (f*x)/2))*(c - d))","B"
459,1,309,150,8.566419,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^2),x)","-\frac{\frac{2\,\left(c^2+c\,d+d^2\right)}{\left(c+d\right)\,{\left(c-d\right)}^2}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(d^2+2\,c\,d\right)}{c\,{\left(c-d\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^3+c^2\,d+d^3\right)}{c\,\left(c+d\right)\,{\left(c-d\right)}^2}}{f\,\left(a\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\left(a\,c+2\,a\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(a\,c+2\,a\,d\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,c\right)}-\frac{2\,d\,\mathrm{atan}\left(\frac{\frac{d\,\left(2\,c+d\right)\,\left(2\,a\,c^3\,d-2\,a\,c^2\,d^2-2\,a\,c\,d^3+2\,a\,d^4\right)}{a\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{5/2}}+\frac{2\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c+d\right)\,\left(a\,c^3-a\,c^2\,d-a\,c\,d^2+a\,d^3\right)}{a\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{5/2}}}{2\,d^2+4\,c\,d}\right)\,\left(2\,c+d\right)}{a\,f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{5/2}}","Not used",1,"- ((2*(c*d + c^2 + d^2))/((c + d)*(c - d)^2) + (2*tan(e/2 + (f*x)/2)*(2*c*d + d^2))/(c*(c - d)^2) + (2*tan(e/2 + (f*x)/2)^2*(c^2*d + c^3 + d^3))/(c*(c + d)*(c - d)^2))/(f*(a*c + tan(e/2 + (f*x)/2)^2*(a*c + 2*a*d) + tan(e/2 + (f*x)/2)*(a*c + 2*a*d) + a*c*tan(e/2 + (f*x)/2)^3)) - (2*d*atan(((d*(2*c + d)*(2*a*d^4 - 2*a*c^2*d^2 - 2*a*c*d^3 + 2*a*c^3*d))/(a*(c + d)^(3/2)*(c - d)^(5/2)) + (2*c*d*tan(e/2 + (f*x)/2)*(2*c + d)*(a*c^3 + a*d^3 - a*c*d^2 - a*c^2*d))/(a*(c + d)^(3/2)*(c - d)^(5/2)))/(4*c*d + 2*d^2))*(2*c + d))/(a*f*(c + d)^(3/2)*(c - d)^(5/2))","B"
460,1,753,213,10.202927,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^3),x)","\frac{3\,d\,\mathrm{atan}\left(\frac{\frac{3\,d\,\left(2\,c^2+2\,c\,d+d^2\right)\,\left(-2\,a\,c^5\,d+2\,a\,c^4\,d^2+4\,a\,c^3\,d^3-4\,a\,c^2\,d^4-2\,a\,c\,d^5+2\,a\,d^6\right)}{2\,a\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{7/2}}-\frac{3\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^2+2\,c\,d+d^2\right)\,\left(a\,c^5-a\,c^4\,d-2\,a\,c^3\,d^2+2\,a\,c^2\,d^3+a\,c\,d^4-a\,d^5\right)}{a\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{7/2}}}{6\,c^2\,d+6\,c\,d^2+3\,d^3}\right)\,\left(2\,c^2+2\,c\,d+d^2\right)}{a\,f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{7/2}}-\frac{\frac{2\,c^4+4\,c^3\,d+8\,c^2\,d^2+2\,c\,d^3-d^4}{\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^2-2\,c\,d+d^2\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(8\,c^5\,d+22\,c^4\,d^2+17\,c^3\,d^3+13\,c^2\,d^4+2\,c\,d^5-2\,d^6\right)}{c^2\,\left(c^2-2\,c\,d+d^2\right)\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,c^5+4\,c^4\,d+14\,c^3\,d^2+21\,c^2\,d^3+4\,c\,d^4-2\,d^5\right)}{c^2\,\left(c^2-d^2\right)\,\left(c^2-2\,c\,d+d^2\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,c^5+4\,c^4\,d+2\,c^3\,d^2+7\,c^2\,d^3+2\,c\,d^4-2\,d^5\right)}{c\,\left(c^2-2\,c\,d+d^2\right)\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,c^4\,d+22\,c^3\,d^2+27\,c^2\,d^3+5\,c\,d^4-2\,d^5\right)}{c\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^2-2\,c\,d+d^2\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a\,c^2+4\,a\,c\,d+4\,a\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,a\,c^2+4\,a\,c\,d+4\,a\,d^2\right)+a\,c^2+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c^2+4\,a\,d\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(a\,c^2+4\,a\,d\,c\right)+a\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}","Not used",1,"(3*d*atan(((3*d*(2*c*d + 2*c^2 + d^2)*(2*a*d^6 - 4*a*c^2*d^4 + 4*a*c^3*d^3 + 2*a*c^4*d^2 - 2*a*c*d^5 - 2*a*c^5*d))/(2*a*(c + d)^(5/2)*(c - d)^(7/2)) - (3*c*d*tan(e/2 + (f*x)/2)*(2*c*d + 2*c^2 + d^2)*(a*c^5 - a*d^5 + 2*a*c^2*d^3 - 2*a*c^3*d^2 + a*c*d^4 - a*c^4*d))/(a*(c + d)^(5/2)*(c - d)^(7/2)))/(6*c*d^2 + 6*c^2*d + 3*d^3))*(2*c*d + 2*c^2 + d^2))/(a*f*(c + d)^(5/2)*(c - d)^(7/2)) - ((2*c*d^3 + 4*c^3*d + 2*c^4 - d^4 + 8*c^2*d^2)/((c + d)*(c^2 - d^2)*(c^2 - 2*c*d + d^2)) - (tan(e/2 + (f*x)/2)^3*(2*c*d^5 + 8*c^5*d - 2*d^6 + 13*c^2*d^4 + 17*c^3*d^3 + 22*c^4*d^2))/(c^2*(c^2 - 2*c*d + d^2)*(c*d^2 - c^2*d - c^3 + d^3)) + (tan(e/2 + (f*x)/2)^2*(4*c*d^4 + 4*c^4*d + 4*c^5 - 2*d^5 + 21*c^2*d^3 + 14*c^3*d^2))/(c^2*(c^2 - d^2)*(c^2 - 2*c*d + d^2)) - (tan(e/2 + (f*x)/2)^4*(2*c*d^4 + 4*c^4*d + 2*c^5 - 2*d^5 + 7*c^2*d^3 + 2*c^3*d^2))/(c*(c^2 - 2*c*d + d^2)*(c*d^2 - c^2*d - c^3 + d^3)) + (tan(e/2 + (f*x)/2)*(5*c*d^4 + 8*c^4*d - 2*d^5 + 27*c^2*d^3 + 22*c^3*d^2))/(c*(c + d)*(c^2 - d^2)*(c^2 - 2*c*d + d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a*c^2 + 4*a*d^2 + 4*a*c*d) + tan(e/2 + (f*x)/2)^3*(2*a*c^2 + 4*a*d^2 + 4*a*c*d) + a*c^2 + tan(e/2 + (f*x)/2)*(a*c^2 + 4*a*c*d) + tan(e/2 + (f*x)/2)^4*(a*c^2 + 4*a*c*d) + a*c^2*tan(e/2 + (f*x)/2)^5))","B"
461,1,692,260,9.426298,"\text{Not used}","int((c + d*sin(e + f*x))^5/(a + a*sin(e + f*x))^2,x)","\frac{5\,d^2\,\mathrm{atan}\left(\frac{5\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c-d\right)\,\left(2\,c^2-3\,c\,d+2\,d^2\right)}{20\,c^3\,d^2-40\,c^2\,d^3+35\,c\,d^4-10\,d^5}\right)\,\left(2\,c-d\right)\,\left(2\,c^2-3\,c\,d+2\,d^2\right)}{a^2\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,c^5+10\,c^4\,d-60\,c^3\,d^2+120\,c^2\,d^3-105\,c\,d^4+30\,d^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,c^5+10\,c^4\,d-100\,c^3\,d^2+280\,c^2\,d^3-215\,c\,d^4+66\,d^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(10\,c^5+10\,c^4\,d-140\,c^3\,d^2+400\,c^2\,d^3-325\,c\,d^4+102\,d^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(6\,c^5+30\,c^4\,d-180\,c^3\,d^2+400\,c^2\,d^3-315\,c\,d^4+90\,d^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(6\,c^5+30\,c^4\,d-180\,c^3\,d^2+440\,c^2\,d^3-335\,c\,d^4+\frac{310\,d^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{22\,c^5}{3}+\frac{10\,c^4\,d}{3}-\frac{260\,c^3\,d^2}{3}+\frac{680\,c^2\,d^3}{3}-\frac{595\,c\,d^4}{3}+\frac{170\,d^5}{3}\right)-\frac{160\,c\,d^4}{3}+\frac{10\,c^4\,d}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,c^5-20\,c^3\,d^2+40\,c^2\,d^3-35\,c\,d^4+10\,d^5\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^5+10\,c^4\,d-60\,c^3\,d^2+160\,c^2\,d^3-125\,c\,d^4+38\,d^5\right)+\frac{4\,c^5}{3}+16\,d^5+\frac{200\,c^2\,d^3}{3}-\frac{80\,c^3\,d^2}{3}}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+6\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+10\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+12\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+12\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+6\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(5*d^2*atan((5*d^2*tan(e/2 + (f*x)/2)*(2*c - d)*(2*c^2 - 3*c*d + 2*d^2))/(35*c*d^4 - 10*d^5 - 40*c^2*d^3 + 20*c^3*d^2))*(2*c - d)*(2*c^2 - 3*c*d + 2*d^2))/(a^2*f) - (tan(e/2 + (f*x)/2)^7*(10*c^4*d - 105*c*d^4 + 2*c^5 + 30*d^5 + 120*c^2*d^3 - 60*c^3*d^2) + tan(e/2 + (f*x)/2)^2*(10*c^4*d - 215*c*d^4 + 6*c^5 + 66*d^5 + 280*c^2*d^3 - 100*c^3*d^2) + tan(e/2 + (f*x)/2)^4*(10*c^4*d - 325*c*d^4 + 10*c^5 + 102*d^5 + 400*c^2*d^3 - 140*c^3*d^2) + tan(e/2 + (f*x)/2)^5*(30*c^4*d - 315*c*d^4 + 6*c^5 + 90*d^5 + 400*c^2*d^3 - 180*c^3*d^2) + tan(e/2 + (f*x)/2)^3*(30*c^4*d - 335*c*d^4 + 6*c^5 + (310*d^5)/3 + 440*c^2*d^3 - 180*c^3*d^2) + tan(e/2 + (f*x)/2)^6*((10*c^4*d)/3 - (595*c*d^4)/3 + (22*c^5)/3 + (170*d^5)/3 + (680*c^2*d^3)/3 - (260*c^3*d^2)/3) - (160*c*d^4)/3 + (10*c^4*d)/3 + tan(e/2 + (f*x)/2)^8*(2*c^5 - 35*c*d^4 + 10*d^5 + 40*c^2*d^3 - 20*c^3*d^2) + tan(e/2 + (f*x)/2)*(10*c^4*d - 125*c*d^4 + 2*c^5 + 38*d^5 + 160*c^2*d^3 - 60*c^3*d^2) + (4*c^5)/3 + 16*d^5 + (200*c^2*d^3)/3 - (80*c^3*d^2)/3)/(f*(6*a^2*tan(e/2 + (f*x)/2)^2 + 10*a^2*tan(e/2 + (f*x)/2)^3 + 12*a^2*tan(e/2 + (f*x)/2)^4 + 12*a^2*tan(e/2 + (f*x)/2)^5 + 10*a^2*tan(e/2 + (f*x)/2)^6 + 6*a^2*tan(e/2 + (f*x)/2)^7 + 3*a^2*tan(e/2 + (f*x)/2)^8 + a^2*tan(e/2 + (f*x)/2)^9 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
462,1,478,195,9.206673,"\text{Not used}","int((c + d*sin(e + f*x))^4/(a + a*sin(e + f*x))^2,x)","\frac{d^2\,\mathrm{atan}\left(\frac{d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c^2-16\,c\,d+7\,d^2\right)}{12\,c^2\,d^2-16\,c\,d^3+7\,d^4}\right)\,\left(12\,c^2-16\,c\,d+7\,d^2\right)}{a^2\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,c^4+8\,c^3\,d-36\,c^2\,d^2+48\,c\,d^3-21\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,c^4+16\,c^3\,d-72\,c^2\,d^2+112\,c\,d^3-42\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{16\,c^4}{3}+\frac{8\,c^3\,d}{3}-40\,c^2\,d^2+\frac{224\,c\,d^3}{3}-\frac{98\,d^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{14\,c^4}{3}+\frac{16\,c^3\,d}{3}-44\,c^2\,d^2+\frac{256\,c\,d^3}{3}-\frac{97\,d^4}{3}\right)+\frac{80\,c\,d^3}{3}+\frac{8\,c^3\,d}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,c^4-12\,c^2\,d^2+16\,c\,d^3-7\,d^4\right)+\frac{4\,c^4}{3}-\frac{32\,d^4}{3}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^4+8\,c^3\,d-36\,c^2\,d^2+64\,c\,d^3-25\,d^4\right)-16\,c^2\,d^2}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+5\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+5\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(d^2*atan((d^2*tan(e/2 + (f*x)/2)*(12*c^2 - 16*c*d + 7*d^2))/(7*d^4 - 16*c*d^3 + 12*c^2*d^2))*(12*c^2 - 16*c*d + 7*d^2))/(a^2*f) - (tan(e/2 + (f*x)/2)^5*(48*c*d^3 + 8*c^3*d + 2*c^4 - 21*d^4 - 36*c^2*d^2) + tan(e/2 + (f*x)/2)^3*(112*c*d^3 + 16*c^3*d + 4*c^4 - 42*d^4 - 72*c^2*d^2) + tan(e/2 + (f*x)/2)^4*((224*c*d^3)/3 + (8*c^3*d)/3 + (16*c^4)/3 - (98*d^4)/3 - 40*c^2*d^2) + tan(e/2 + (f*x)/2)^2*((256*c*d^3)/3 + (16*c^3*d)/3 + (14*c^4)/3 - (97*d^4)/3 - 44*c^2*d^2) + (80*c*d^3)/3 + (8*c^3*d)/3 + tan(e/2 + (f*x)/2)^6*(16*c*d^3 + 2*c^4 - 7*d^4 - 12*c^2*d^2) + (4*c^4)/3 - (32*d^4)/3 + tan(e/2 + (f*x)/2)*(64*c*d^3 + 8*c^3*d + 2*c^4 - 25*d^4 - 36*c^2*d^2) - 16*c^2*d^2)/(f*(5*a^2*tan(e/2 + (f*x)/2)^2 + 7*a^2*tan(e/2 + (f*x)/2)^3 + 7*a^2*tan(e/2 + (f*x)/2)^4 + 5*a^2*tan(e/2 + (f*x)/2)^5 + 3*a^2*tan(e/2 + (f*x)/2)^6 + a^2*tan(e/2 + (f*x)/2)^7 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
463,1,298,120,8.385229,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^2,x)","\frac{2\,d^2\,\mathrm{atan}\left(\frac{2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c-2\,d\right)}{6\,c\,d^2-4\,d^3}\right)\,\left(3\,c-2\,d\right)}{a^2\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,c^3+6\,c^2\,d-18\,c\,d^2+12\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{10\,c^3}{3}+2\,c^2\,d-14\,c\,d^2+\frac{44\,d^3}{3}\right)-8\,c\,d^2+2\,c^2\,d+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,c^3-6\,c\,d^2+4\,d^3\right)+\frac{4\,c^3}{3}+\frac{20\,d^3}{3}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^3+6\,c^2\,d-18\,c\,d^2+16\,d^3\right)}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(2*d^2*atan((2*d^2*tan(e/2 + (f*x)/2)*(3*c - 2*d))/(6*c*d^2 - 4*d^3))*(3*c - 2*d))/(a^2*f) - (tan(e/2 + (f*x)/2)^3*(6*c^2*d - 18*c*d^2 + 2*c^3 + 12*d^3) + tan(e/2 + (f*x)/2)^2*(2*c^2*d - 14*c*d^2 + (10*c^3)/3 + (44*d^3)/3) - 8*c*d^2 + 2*c^2*d + tan(e/2 + (f*x)/2)^4*(2*c^3 - 6*c*d^2 + 4*d^3) + (4*c^3)/3 + (20*d^3)/3 + tan(e/2 + (f*x)/2)*(6*c^2*d - 18*c*d^2 + 2*c^3 + 16*d^3))/(f*(4*a^2*tan(e/2 + (f*x)/2)^2 + 4*a^2*tan(e/2 + (f*x)/2)^3 + 3*a^2*tan(e/2 + (f*x)/2)^4 + a^2*tan(e/2 + (f*x)/2)^5 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
464,1,93,85,7.432708,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^2,x)","\frac{d^2\,x}{a^2}-\frac{\frac{4\,c\,d}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2-2\,d^2\right)+\frac{4\,c^2}{3}-\frac{8\,d^2}{3}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c^2+4\,c\,d-6\,d^2\right)}{a^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"(d^2*x)/a^2 - ((4*c*d)/3 + tan(e/2 + (f*x)/2)^2*(2*c^2 - 2*d^2) + (4*c^2)/3 - (8*d^2)/3 + tan(e/2 + (f*x)/2)*(4*c*d + 2*c^2 - 6*d^2))/(a^2*f*(tan(e/2 + (f*x)/2) + 1)^3)","B"
465,1,97,65,7.213162,"\text{Not used}","int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^2,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{5\,c}{2}+\frac{d}{2}-\frac{c\,\cos\left(e+f\,x\right)}{2}+\frac{d\,\cos\left(e+f\,x\right)}{2}+\frac{3\,c\,\sin\left(e+f\,x\right)}{2}+\frac{3\,d\,\sin\left(e+f\,x\right)}{2}\right)}{3\,a^2\,f\,\left(\frac{3\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}-\frac{\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{2}\right)}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*((5*c)/2 + d/2 - (c*cos(e + f*x))/2 + (d*cos(e + f*x))/2 + (3*c*sin(e + f*x))/2 + (3*d*sin(e + f*x))/2))/(3*a^2*f*((3*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 - (2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/2))","B"
466,1,76,55,6.980753,"\text{Not used}","int(1/(a + a*sin(e + f*x))^2,x)","-\frac{2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left({\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-3\right)}{3}}{a^2\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^3}","Not used",1,"-(2*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2) - (2*cos(e/2 + (f*x)/2)*(cos(e/2 + (f*x)/2)^2 - 3))/3)/(a^2*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^3)","B"
467,1,250,131,8.019064,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))),x)","\frac{2\,d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(2\,a^2\,c^2\,d-4\,a^2\,c\,d^2+2\,a^2\,d^3\right)}{a^2\,\sqrt{c+d}\,{\left(c-d\right)}^{5/2}}+\frac{2\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,c^2-2\,a^2\,c\,d+a^2\,d^2\right)}{a^2\,\sqrt{c+d}\,{\left(c-d\right)}^{5/2}}}{2\,d^2}\right)}{a^2\,f\,\sqrt{c+d}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{2\,\left(2\,c-5\,d\right)}{3\,{\left(c-d\right)}^2}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(c-3\,d\right)}{{\left(c-d\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c-2\,d\right)}{{\left(c-d\right)}^2}}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(2*d^2*atan(((d^2*(2*a^2*d^3 - 4*a^2*c*d^2 + 2*a^2*c^2*d))/(a^2*(c + d)^(1/2)*(c - d)^(5/2)) + (2*c*d^2*tan(e/2 + (f*x)/2)*(a^2*c^2 + a^2*d^2 - 2*a^2*c*d))/(a^2*(c + d)^(1/2)*(c - d)^(5/2)))/(2*d^2)))/(a^2*f*(c + d)^(1/2)*(c - d)^(5/2)) - ((2*(2*c - 5*d))/(3*(c - d)^2) + (2*tan(e/2 + (f*x)/2)*(c - 3*d))/(c - d)^2 + (2*tan(e/2 + (f*x)/2)^2*(c - 2*d))/(c - d)^2)/(f*(3*a^2*tan(e/2 + (f*x)/2)^2 + a^2*tan(e/2 + (f*x)/2)^3 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
468,1,625,221,10.486755,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^2),x)","\frac{\frac{2\,\left(-2\,c^3+6\,c^2\,d+8\,c\,d^2+3\,d^3\right)}{3\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-5\,c^3+11\,c^2\,d+30\,c\,d^2+9\,d^3\right)}{3\,c\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-3\,c^4+8\,c^3\,d+27\,c^2\,d^2+25\,c\,d^3+3\,d^4\right)}{3\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-c^4+2\,c^3\,d+9\,c^2\,d^2+7\,c\,d^3+3\,d^4\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(-c^4+2\,c^3\,d+3\,c^2\,d^2+d^4\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}}{f\,\left(a^2\,c+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^2\,c+2\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a^2\,c+2\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,a^2\,c+6\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,a^2\,c+6\,a^2\,d\right)+a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}-\frac{2\,d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(3\,c+2\,d\right)\,\left(-2\,a^2\,c^4\,d+4\,a^2\,c^3\,d^2-4\,a^2\,c\,d^4+2\,a^2\,d^5\right)}{a^2\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{7/2}}-\frac{2\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c+2\,d\right)\,\left(a^2\,c^4-2\,a^2\,c^3\,d+2\,a^2\,c\,d^3-a^2\,d^4\right)}{a^2\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{7/2}}}{4\,d^3+6\,c\,d^2}\right)\,\left(3\,c+2\,d\right)}{a^2\,f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{7/2}}","Not used",1,"((2*(8*c*d^2 + 6*c^2*d - 2*c^3 + 3*d^3))/(3*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^2*(30*c*d^2 + 11*c^2*d - 5*c^3 + 9*d^3))/(3*c*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)*(25*c*d^3 + 8*c^3*d - 3*c^4 + 3*d^4 + 27*c^2*d^2))/(3*c*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^3*(7*c*d^3 + 2*c^3*d - c^4 + 3*d^4 + 9*c^2*d^2))/(c*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^4*(2*c^3*d - c^4 + d^4 + 3*c^2*d^2))/(c*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)))/(f*(a^2*c + tan(e/2 + (f*x)/2)*(3*a^2*c + 2*a^2*d) + tan(e/2 + (f*x)/2)^4*(3*a^2*c + 2*a^2*d) + tan(e/2 + (f*x)/2)^2*(4*a^2*c + 6*a^2*d) + tan(e/2 + (f*x)/2)^3*(4*a^2*c + 6*a^2*d) + a^2*c*tan(e/2 + (f*x)/2)^5)) - (2*d^2*atan(((d^2*(3*c + 2*d)*(2*a^2*d^5 - 4*a^2*c*d^4 - 2*a^2*c^4*d + 4*a^2*c^3*d^2))/(a^2*(c + d)^(3/2)*(c - d)^(7/2)) - (2*c*d^2*tan(e/2 + (f*x)/2)*(3*c + 2*d)*(a^2*c^4 - a^2*d^4 + 2*a^2*c*d^3 - 2*a^2*c^3*d))/(a^2*(c + d)^(3/2)*(c - d)^(7/2)))/(6*c*d^2 + 4*d^3))*(3*c + 2*d))/(a^2*f*(c + d)^(3/2)*(c - d)^(7/2))","B"
469,1,1199,294,10.813426,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^3),x)","\frac{\frac{-4\,c^5+14\,c^4\,d+40\,c^3\,d^2+46\,c^2\,d^3+12\,c\,d^4-3\,d^5}{3\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-2\,c^6+4\,c^5\,d+38\,c^4\,d^2+40\,c^3\,d^3+23\,c^2\,d^4+4\,c\,d^5-2\,d^6\right)}{c^2\,\left(c^5-3\,c^4\,d+2\,c^3\,d^2+2\,c^2\,d^3-3\,c\,d^4+d^5\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-6\,c^6+16\,c^5\,d+102\,c^4\,d^2+212\,c^3\,d^3+177\,c^2\,d^4+33\,c\,d^5-9\,d^6\right)}{3\,c^2\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-6\,c^5+20\,c^4\,d+114\,c^3\,d^2+160\,c^2\,d^3+33\,c\,d^4-6\,d^5\right)}{3\,c\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-14\,c^7+16\,c^6\,d+226\,c^5\,d^2+532\,c^4\,d^3+583\,c^3\,d^4+232\,c^2\,d^5+6\,c\,d^6-6\,d^7\right)}{3\,c^2\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(-16\,c^7+14\,c^6\,d+220\,c^5\,d^2+502\,c^4\,d^3+522\,c^3\,d^4+303\,c^2\,d^5+48\,c\,d^6-18\,d^7\right)}{3\,c^2\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(-2\,c^6+4\,c^5\,d+14\,c^4\,d^2+8\,c^3\,d^3+9\,c^2\,d^4+4\,c\,d^5-2\,d^6\right)}{c\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}}{f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^2\,c^2+4\,d\,a^2\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(5\,a^2\,c^2+12\,a^2\,c\,d+4\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(5\,a^2\,c^2+12\,a^2\,c\,d+4\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(7\,a^2\,c^2+16\,a^2\,c\,d+12\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(7\,a^2\,c^2+16\,a^2\,c\,d+12\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(3\,a^2\,c^2+4\,d\,a^2\,c\right)+a^2\,c^2+a^2\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}-\frac{d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(12\,c^2+16\,c\,d+7\,d^2\right)\,\left(-2\,a^2\,c^6\,d+4\,a^2\,c^5\,d^2+2\,a^2\,c^4\,d^3-8\,a^2\,c^3\,d^4+2\,a^2\,c^2\,d^5+4\,a^2\,c\,d^6-2\,a^2\,d^7\right)}{2\,a^2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{9/2}}+\frac{c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c^2+16\,c\,d+7\,d^2\right)\,\left(-a^2\,c^6+2\,a^2\,c^5\,d+a^2\,c^4\,d^2-4\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a^2\,c\,d^5-a^2\,d^6\right)}{a^2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{9/2}}}{12\,c^2\,d^2+16\,c\,d^3+7\,d^4}\right)\,\left(12\,c^2+16\,c\,d+7\,d^2\right)}{a^2\,f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{9/2}}","Not used",1,"((12*c*d^4 + 14*c^4*d - 4*c^5 - 3*d^5 + 46*c^2*d^3 + 40*c^3*d^2)/(3*(c + d)*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^5*(4*c*d^5 + 4*c^5*d - 2*c^6 - 2*d^6 + 23*c^2*d^4 + 40*c^3*d^3 + 38*c^4*d^2))/(c^2*(c^5 - 3*c^4*d - 3*c*d^4 + d^5 + 2*c^2*d^3 + 2*c^3*d^2)) + (2*tan(e/2 + (f*x)/2)^3*(33*c*d^5 + 16*c^5*d - 6*c^6 - 9*d^6 + 177*c^2*d^4 + 212*c^3*d^3 + 102*c^4*d^2))/(3*c^2*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)*(33*c*d^4 + 20*c^4*d - 6*c^5 - 6*d^5 + 160*c^2*d^3 + 114*c^3*d^2))/(3*c*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^2*(6*c*d^6 + 16*c^6*d - 14*c^7 - 6*d^7 + 232*c^2*d^5 + 583*c^3*d^4 + 532*c^4*d^3 + 226*c^5*d^2))/(3*c^2*(c + d)*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^4*(48*c*d^6 + 14*c^6*d - 16*c^7 - 18*d^7 + 303*c^2*d^5 + 522*c^3*d^4 + 502*c^4*d^3 + 220*c^5*d^2))/(3*c^2*(c + d)*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^6*(4*c*d^5 + 4*c^5*d - 2*c^6 - 2*d^6 + 9*c^2*d^4 + 8*c^3*d^3 + 14*c^4*d^2))/(c*(c - d)*(2*c*d + c^2 + d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)))/(f*(tan(e/2 + (f*x)/2)*(3*a^2*c^2 + 4*a^2*c*d) + tan(e/2 + (f*x)/2)^2*(5*a^2*c^2 + 4*a^2*d^2 + 12*a^2*c*d) + tan(e/2 + (f*x)/2)^5*(5*a^2*c^2 + 4*a^2*d^2 + 12*a^2*c*d) + tan(e/2 + (f*x)/2)^3*(7*a^2*c^2 + 12*a^2*d^2 + 16*a^2*c*d) + tan(e/2 + (f*x)/2)^4*(7*a^2*c^2 + 12*a^2*d^2 + 16*a^2*c*d) + tan(e/2 + (f*x)/2)^6*(3*a^2*c^2 + 4*a^2*c*d) + a^2*c^2 + a^2*c^2*tan(e/2 + (f*x)/2)^7)) - (d^2*atan(((d^2*(16*c*d + 12*c^2 + 7*d^2)*(4*a^2*c*d^6 - 2*a^2*d^7 - 2*a^2*c^6*d + 2*a^2*c^2*d^5 - 8*a^2*c^3*d^4 + 2*a^2*c^4*d^3 + 4*a^2*c^5*d^2))/(2*a^2*(c + d)^(5/2)*(c - d)^(9/2)) + (c*d^2*tan(e/2 + (f*x)/2)*(16*c*d + 12*c^2 + 7*d^2)*(2*a^2*c*d^5 - a^2*d^6 - a^2*c^6 + 2*a^2*c^5*d + a^2*c^2*d^4 - 4*a^2*c^3*d^3 + a^2*c^4*d^2))/(a^2*(c + d)^(5/2)*(c - d)^(9/2)))/(16*c*d^3 + 7*d^4 + 12*c^2*d^2))*(16*c*d + 12*c^2 + 7*d^2))/(a^2*f*(c + d)^(5/2)*(c - d)^(9/2))","B"
470,1,898,354,9.713273,"\text{Not used}","int((c + d*sin(e + f*x))^6/(a + a*sin(e + f*x))^3,x)","\frac{d^3\,\mathrm{atan}\left(\frac{d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(40\,c^3-90\,c^2\,d+78\,c\,d^2-23\,d^3\right)}{40\,c^3\,d^3-90\,c^2\,d^4+78\,c\,d^5-23\,d^6}\right)\,\left(40\,c^3-90\,c^2\,d+78\,c\,d^2-23\,d^3\right)}{a^3\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(4\,c^6+12\,c^5\,d-200\,c^3\,d^3+450\,c^2\,d^4-390\,c\,d^5+115\,d^6\right)-\frac{608\,c\,d^5}{5}+\frac{12\,c^5\,d}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(2\,c^6-40\,c^3\,d^3+90\,c^2\,d^4-78\,c\,d^5+23\,d^6\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8\,c^6}{3}+12\,c^5\,d+20\,c^4\,d^2-\frac{760\,c^3\,d^3}{3}+630\,c^2\,d^4-530\,c\,d^5+\frac{475\,d^6}{3}\right)+\frac{14\,c^6}{15}+\frac{544\,d^6}{15}+144\,c^2\,d^4-\frac{176\,c^3\,d^3}{3}+4\,c^4\,d^2+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{34\,c^6}{3}+12\,c^5\,d+40\,c^4\,d^2-\frac{1520\,c^3\,d^3}{3}+1140\,c^2\,d^4-988\,c\,d^5+\frac{874\,d^6}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^6+48\,c^5\,d+60\,c^4\,d^2-960\,c^3\,d^3+2460\,c^2\,d^4-2052\,c\,d^5+\frac{1846\,d^6}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{44\,c^6}{3}+48\,c^5\,d+20\,c^4\,d^2-\frac{2560\,c^3\,d^3}{3}+2100\,c^2\,d^4-1820\,c\,d^5+\frac{1610\,d^6}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(20\,c^6+72\,c^5\,d+60\,c^4\,d^2-1360\,c^3\,d^3+3480\,c^2\,d^4-2952\,c\,d^5+\frac{2668\,d^6}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{122\,c^6}{15}+\frac{96\,c^5\,d}{5}+52\,c^4\,d^2-\frac{1688\,c^3\,d^3}{3}+1422\,c^2\,d^4-\frac{5954\,c\,d^5}{5}+\frac{5347\,d^6}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{104\,c^6}{5}+\frac{216\,c^5\,d}{5}+132\,c^4\,d^2-1376\,c^3\,d^3+3372\,c^2\,d^4-\frac{14004\,c\,d^5}{5}+\frac{12622\,d^6}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{344\,c^6}{15}+\frac{192\,c^5\,d}{5}+124\,c^4\,d^2-\frac{4016\,c^3\,d^3}{3}+3144\,c^2\,d^4-\frac{13208\,c\,d^5}{5}+\frac{11684\,d^6}{15}\right)}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+13\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+25\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+38\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+46\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+46\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+38\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+25\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+13\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(d^3*atan((d^3*tan(e/2 + (f*x)/2)*(78*c*d^2 - 90*c^2*d + 40*c^3 - 23*d^3))/(78*c*d^5 - 23*d^6 - 90*c^2*d^4 + 40*c^3*d^3))*(78*c*d^2 - 90*c^2*d + 40*c^3 - 23*d^3))/(a^3*f) - (tan(e/2 + (f*x)/2)^9*(12*c^5*d - 390*c*d^5 + 4*c^6 + 115*d^6 + 450*c^2*d^4 - 200*c^3*d^3) - (608*c*d^5)/5 + (12*c^5*d)/5 + tan(e/2 + (f*x)/2)^10*(2*c^6 - 78*c*d^5 + 23*d^6 + 90*c^2*d^4 - 40*c^3*d^3) + tan(e/2 + (f*x)/2)*(12*c^5*d - 530*c*d^5 + (8*c^6)/3 + (475*d^6)/3 + 630*c^2*d^4 - (760*c^3*d^3)/3 + 20*c^4*d^2) + (14*c^6)/15 + (544*d^6)/15 + 144*c^2*d^4 - (176*c^3*d^3)/3 + 4*c^4*d^2 + tan(e/2 + (f*x)/2)^8*(12*c^5*d - 988*c*d^5 + (34*c^6)/3 + (874*d^6)/3 + 1140*c^2*d^4 - (1520*c^3*d^3)/3 + 40*c^4*d^2) + tan(e/2 + (f*x)/2)^3*(48*c^5*d - 2052*c*d^5 + 12*c^6 + (1846*d^6)/3 + 2460*c^2*d^4 - 960*c^3*d^3 + 60*c^4*d^2) + tan(e/2 + (f*x)/2)^7*(48*c^5*d - 1820*c*d^5 + (44*c^6)/3 + (1610*d^6)/3 + 2100*c^2*d^4 - (2560*c^3*d^3)/3 + 20*c^4*d^2) + tan(e/2 + (f*x)/2)^5*(72*c^5*d - 2952*c*d^5 + 20*c^6 + (2668*d^6)/3 + 3480*c^2*d^4 - 1360*c^3*d^3 + 60*c^4*d^2) + tan(e/2 + (f*x)/2)^2*((96*c^5*d)/5 - (5954*c*d^5)/5 + (122*c^6)/15 + (5347*d^6)/15 + 1422*c^2*d^4 - (1688*c^3*d^3)/3 + 52*c^4*d^2) + tan(e/2 + (f*x)/2)^4*((216*c^5*d)/5 - (14004*c*d^5)/5 + (104*c^6)/5 + (12622*d^6)/15 + 3372*c^2*d^4 - 1376*c^3*d^3 + 132*c^4*d^2) + tan(e/2 + (f*x)/2)^6*((192*c^5*d)/5 - (13208*c*d^5)/5 + (344*c^6)/15 + (11684*d^6)/15 + 3144*c^2*d^4 - (4016*c^3*d^3)/3 + 124*c^4*d^2))/(f*(13*a^3*tan(e/2 + (f*x)/2)^2 + 25*a^3*tan(e/2 + (f*x)/2)^3 + 38*a^3*tan(e/2 + (f*x)/2)^4 + 46*a^3*tan(e/2 + (f*x)/2)^5 + 46*a^3*tan(e/2 + (f*x)/2)^6 + 38*a^3*tan(e/2 + (f*x)/2)^7 + 25*a^3*tan(e/2 + (f*x)/2)^8 + 13*a^3*tan(e/2 + (f*x)/2)^9 + 5*a^3*tan(e/2 + (f*x)/2)^10 + a^3*tan(e/2 + (f*x)/2)^11 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
471,1,652,278,9.536474,"\text{Not used}","int((c + d*sin(e + f*x))^5/(a + a*sin(e + f*x))^3,x)","\frac{d^3\,\mathrm{atan}\left(\frac{d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(20\,c^2-30\,c\,d+13\,d^2\right)}{20\,c^2\,d^3-30\,c\,d^4+13\,d^5}\right)\,\left(20\,c^2-30\,c\,d+13\,d^2\right)}{a^3\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{28\,c^5}{3}+10\,c^4\,d+\frac{80\,c^3\,d^2}{3}-\frac{700\,c^2\,d^3}{3}+350\,c\,d^4-\frac{455\,d^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{36\,c^5}{5}+14\,c^4\,d+32\,c^3\,d^2-252\,c^2\,d^3+426\,c\,d^4-\frac{891\,d^5}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{32\,c^5}{3}+30\,c^4\,d+\frac{40\,c^3\,d^2}{3}-\frac{980\,c^2\,d^3}{3}+550\,c\,d^4-\frac{715\,d^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{28\,c^5}{3}+30\,c^4\,d+\frac{80\,c^3\,d^2}{3}-\frac{1060\,c^2\,d^3}{3}+610\,c\,d^4-\frac{761\,d^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{68\,c^5}{5}+22\,c^4\,d+56\,c^3\,d^2-436\,c^2\,d^3+698\,c\,d^4-\frac{1443\,d^5}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(4\,c^5+10\,c^4\,d-100\,c^2\,d^3+150\,c\,d^4-65\,d^5\right)+48\,c\,d^4+2\,c^4\,d+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,c^5-20\,c^2\,d^3+30\,c\,d^4-13\,d^5\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8\,c^5}{3}+10\,c^4\,d+\frac{40\,c^3\,d^2}{3}-\frac{380\,c^2\,d^3}{3}+210\,c\,d^4-\frac{265\,d^5}{3}\right)+\frac{14\,c^5}{15}-\frac{304\,d^5}{15}-\frac{88\,c^2\,d^3}{3}+\frac{8\,c^3\,d^2}{3}}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+12\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+20\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+26\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+26\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+20\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+12\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(d^3*atan((d^3*tan(e/2 + (f*x)/2)*(20*c^2 - 30*c*d + 13*d^2))/(13*d^5 - 30*c*d^4 + 20*c^2*d^3))*(20*c^2 - 30*c*d + 13*d^2))/(a^3*f) - (tan(e/2 + (f*x)/2)^6*(350*c*d^4 + 10*c^4*d + (28*c^5)/3 - (455*d^5)/3 - (700*c^2*d^3)/3 + (80*c^3*d^2)/3) + tan(e/2 + (f*x)/2)^2*(426*c*d^4 + 14*c^4*d + (36*c^5)/5 - (891*d^5)/5 - 252*c^2*d^3 + 32*c^3*d^2) + tan(e/2 + (f*x)/2)^5*(550*c*d^4 + 30*c^4*d + (32*c^5)/3 - (715*d^5)/3 - (980*c^2*d^3)/3 + (40*c^3*d^2)/3) + tan(e/2 + (f*x)/2)^3*(610*c*d^4 + 30*c^4*d + (28*c^5)/3 - (761*d^5)/3 - (1060*c^2*d^3)/3 + (80*c^3*d^2)/3) + tan(e/2 + (f*x)/2)^4*(698*c*d^4 + 22*c^4*d + (68*c^5)/5 - (1443*d^5)/5 - 436*c^2*d^3 + 56*c^3*d^2) + tan(e/2 + (f*x)/2)^7*(150*c*d^4 + 10*c^4*d + 4*c^5 - 65*d^5 - 100*c^2*d^3) + 48*c*d^4 + 2*c^4*d + tan(e/2 + (f*x)/2)^8*(30*c*d^4 + 2*c^5 - 13*d^5 - 20*c^2*d^3) + tan(e/2 + (f*x)/2)*(210*c*d^4 + 10*c^4*d + (8*c^5)/3 - (265*d^5)/3 - (380*c^2*d^3)/3 + (40*c^3*d^2)/3) + (14*c^5)/15 - (304*d^5)/15 - (88*c^2*d^3)/3 + (8*c^3*d^2)/3)/(f*(12*a^3*tan(e/2 + (f*x)/2)^2 + 20*a^3*tan(e/2 + (f*x)/2)^3 + 26*a^3*tan(e/2 + (f*x)/2)^4 + 26*a^3*tan(e/2 + (f*x)/2)^5 + 20*a^3*tan(e/2 + (f*x)/2)^6 + 12*a^3*tan(e/2 + (f*x)/2)^7 + 5*a^3*tan(e/2 + (f*x)/2)^8 + a^3*tan(e/2 + (f*x)/2)^9 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
472,1,440,195,9.028337,"\text{Not used}","int((c + d*sin(e + f*x))^4/(a + a*sin(e + f*x))^3,x)","\frac{2\,d^3\,\mathrm{atan}\left(\frac{2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,c-3\,d\right)}{8\,c\,d^3-6\,d^4}\right)\,\left(4\,c-3\,d\right)}{a^3\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{22\,c^4}{3}+8\,c^3\,d+16\,c^2\,d^2-\frac{256\,c\,d^3}{3}+64\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{20\,c^4}{3}+16\,c^3\,d+8\,c^2\,d^2-\frac{272\,c\,d^3}{3}+80\,d^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{94\,c^4}{15}+\frac{48\,c^3\,d}{5}+\frac{88\,c^2\,d^2}{5}-\frac{1336\,c\,d^3}{15}+\frac{378\,d^4}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(4\,c^4+8\,c^3\,d-40\,c\,d^3+30\,d^4\right)-\frac{176\,c\,d^3}{15}+\frac{8\,c^3\,d}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,c^4-8\,c\,d^3+6\,d^4\right)+\frac{14\,c^4}{15}+\frac{48\,d^4}{5}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8\,c^4}{3}+8\,c^3\,d+8\,c^2\,d^2-\frac{152\,c\,d^3}{3}+42\,d^4\right)+\frac{8\,c^2\,d^2}{5}}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+11\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+15\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+15\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+11\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(2*d^3*atan((2*d^3*tan(e/2 + (f*x)/2)*(4*c - 3*d))/(8*c*d^3 - 6*d^4))*(4*c - 3*d))/(a^3*f) - (tan(e/2 + (f*x)/2)^4*(8*c^3*d - (256*c*d^3)/3 + (22*c^4)/3 + 64*d^4 + 16*c^2*d^2) + tan(e/2 + (f*x)/2)^3*(16*c^3*d - (272*c*d^3)/3 + (20*c^4)/3 + 80*d^4 + 8*c^2*d^2) + tan(e/2 + (f*x)/2)^2*((48*c^3*d)/5 - (1336*c*d^3)/15 + (94*c^4)/15 + (378*d^4)/5 + (88*c^2*d^2)/5) + tan(e/2 + (f*x)/2)^5*(8*c^3*d - 40*c*d^3 + 4*c^4 + 30*d^4) - (176*c*d^3)/15 + (8*c^3*d)/5 + tan(e/2 + (f*x)/2)^6*(2*c^4 - 8*c*d^3 + 6*d^4) + (14*c^4)/15 + (48*d^4)/5 + tan(e/2 + (f*x)/2)*(8*c^3*d - (152*c*d^3)/3 + (8*c^4)/3 + 42*d^4 + 8*c^2*d^2) + (8*c^2*d^2)/5)/(f*(11*a^3*tan(e/2 + (f*x)/2)^2 + 15*a^3*tan(e/2 + (f*x)/2)^3 + 15*a^3*tan(e/2 + (f*x)/2)^4 + 11*a^3*tan(e/2 + (f*x)/2)^5 + 5*a^3*tan(e/2 + (f*x)/2)^6 + a^3*tan(e/2 + (f*x)/2)^7 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
473,1,240,142,9.904339,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^3,x)","\frac{d^3\,x}{a^3}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,c^3-2\,d^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{16\,c^3}{3}+6\,c^2\,d+8\,c\,d^2-\frac{58\,d^3}{3}\right)+\frac{4\,c\,d^2}{5}+\frac{6\,c^2\,d}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,c^3+6\,c^2\,d-10\,d^3\right)+\frac{14\,c^3}{15}-\frac{44\,d^3}{15}+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8\,c^3}{3}+6\,c^2\,d+4\,c\,d^2-\frac{38\,d^3}{3}\right)}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(d^3*x)/a^3 - (tan(e/2 + (f*x)/2)^4*(2*c^3 - 2*d^3) + tan(e/2 + (f*x)/2)^2*(8*c*d^2 + 6*c^2*d + (16*c^3)/3 - (58*d^3)/3) + (4*c*d^2)/5 + (6*c^2*d)/5 + tan(e/2 + (f*x)/2)^3*(6*c^2*d + 4*c^3 - 10*d^3) + (14*c^3)/15 - (44*d^3)/15 + tan(e/2 + (f*x)/2)*(4*c*d^2 + 6*c^2*d + (8*c^3)/3 - (38*d^3)/3))/(f*(10*a^3*tan(e/2 + (f*x)/2)^2 + 10*a^3*tan(e/2 + (f*x)/2)^3 + 5*a^3*tan(e/2 + (f*x)/2)^4 + a^3*tan(e/2 + (f*x)/2)^5 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
474,1,218,125,7.485709,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^3,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,c\,d-4\,c^2\,\cos\left(e+f\,x\right)+d^2\,\cos\left(e+f\,x\right)+\frac{25\,c^2\,\sin\left(e+f\,x\right)}{2}+\frac{5\,d^2\,\sin\left(e+f\,x\right)}{2}+\frac{53\,c^2}{4}+\frac{13\,d^2}{4}-\frac{9\,c^2\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{9\,d^2\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{5\,c^2\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{5\,d^2\,\sin\left(2\,e+2\,f\,x\right)}{4}+3\,c\,d\,\cos\left(e+f\,x\right)+15\,c\,d\,\sin\left(e+f\,x\right)-3\,c\,d\,\cos\left(2\,e+2\,f\,x\right)\right)}{15\,a^3\,f\,\left(\frac{5\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{5\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}+\frac{\sqrt{2}\,\cos\left(\frac{5\,e}{2}-\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*(6*c*d - 4*c^2*cos(e + f*x) + d^2*cos(e + f*x) + (25*c^2*sin(e + f*x))/2 + (5*d^2*sin(e + f*x))/2 + (53*c^2)/4 + (13*d^2)/4 - (9*c^2*cos(2*e + 2*f*x))/4 - (9*d^2*cos(2*e + 2*f*x))/4 - (5*c^2*sin(2*e + 2*f*x))/4 + (5*d^2*sin(2*e + 2*f*x))/4 + 3*c*d*cos(e + f*x) + 15*c*d*sin(e + f*x) - 3*c*d*cos(2*e + 2*f*x)))/(15*a^3*f*((5*2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/4 - (5*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 + (2^(1/2)*cos((5*e)/2 - pi/4 + (5*f*x)/2))/4))","B"
475,1,150,102,7.250659,"\text{Not used}","int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^3,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{53\,c}{4}+3\,d-4\,c\,\cos\left(e+f\,x\right)+\frac{3\,d\,\cos\left(e+f\,x\right)}{2}+\frac{25\,c\,\sin\left(e+f\,x\right)}{2}+\frac{15\,d\,\sin\left(e+f\,x\right)}{2}-\frac{9\,c\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{3\,d\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{5\,c\,\sin\left(2\,e+2\,f\,x\right)}{4}\right)}{15\,a^3\,f\,\left(\frac{5\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{5\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}+\frac{\sqrt{2}\,\cos\left(\frac{5\,e}{2}-\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((53*c)/4 + 3*d - 4*c*cos(e + f*x) + (3*d*cos(e + f*x))/2 + (25*c*sin(e + f*x))/2 + (15*d*sin(e + f*x))/2 - (9*c*cos(2*e + 2*f*x))/4 - (3*d*cos(2*e + 2*f*x))/2 - (5*c*sin(2*e + 2*f*x))/4))/(15*a^3*f*((5*2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/4 - (5*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 + (2^(1/2)*cos((5*e)/2 - pi/4 + (5*f*x)/2))/4))","B"
476,1,133,83,6.957166,"\text{Not used}","int(1/(a + a*sin(e + f*x))^3,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(7\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+20\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+40\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+30\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+15\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\right)}{15\,a^3\,f\,{\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}^5}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*(7*cos(e/2 + (f*x)/2)^4 + 15*sin(e/2 + (f*x)/2)^4 + 30*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^3 + 20*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2) + 40*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^2))/(15*a^3*f*(cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))^5)","B"
477,1,466,186,10.069450,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))),x)","\frac{2\,d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\left(-2\,a^3\,c^3\,d+6\,a^3\,c^2\,d^2-6\,a^3\,c\,d^3+2\,a^3\,d^4\right)}{a^3\,\sqrt{c+d}\,{\left(c-d\right)}^{7/2}}-\frac{2\,c\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^3\,c^3-3\,a^3\,c^2\,d+3\,a^3\,c\,d^2-a^3\,d^3\right)}{a^3\,\sqrt{c+d}\,{\left(c-d\right)}^{7/2}}}{2\,d^3}\right)}{a^3\,f\,\sqrt{c+d}\,{\left(c-d\right)}^{7/2}}-\frac{\frac{2\,\left(7\,c^2-24\,c\,d+32\,d^2\right)}{15\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,c^2-15\,c\,d+23\,d^2\right)}{3\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(c^2-3\,c\,d+3\,d^2\right)}{\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,c^2-7\,c\,d+9\,d^2\right)}{\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(8\,c^2-27\,c\,d+37\,d^2\right)}{3\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(2*d^3*atan(((d^3*(2*a^3*d^4 - 6*a^3*c*d^3 - 2*a^3*c^3*d + 6*a^3*c^2*d^2))/(a^3*(c + d)^(1/2)*(c - d)^(7/2)) - (2*c*d^3*tan(e/2 + (f*x)/2)*(a^3*c^3 - a^3*d^3 + 3*a^3*c*d^2 - 3*a^3*c^2*d))/(a^3*(c + d)^(1/2)*(c - d)^(7/2)))/(2*d^3)))/(a^3*f*(c + d)^(1/2)*(c - d)^(7/2)) - ((2*(7*c^2 - 24*c*d + 32*d^2))/(15*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)*(4*c^2 - 15*c*d + 23*d^2))/(3*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^4*(c^2 - 3*c*d + 3*d^2))/((c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^3*(2*c^2 - 7*c*d + 9*d^2))/((c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^2*(8*c^2 - 27*c*d + 37*d^2))/(3*(c - d)*(c^2 - 2*c*d + d^2)))/(f*(10*a^3*tan(e/2 + (f*x)/2)^2 + 10*a^3*tan(e/2 + (f*x)/2)^3 + 5*a^3*tan(e/2 + (f*x)/2)^4 + a^3*tan(e/2 + (f*x)/2)^5 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
478,1,987,298,10.302277,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^2),x)","-\frac{\frac{2\,\left(7\,c^4-27\,c^3\,d+38\,c^2\,d^2+72\,c\,d^3+15\,d^4\right)}{15\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(5\,c^4-18\,c^3\,d+19\,c^2\,d^2+84\,c\,d^3+15\,d^4\right)}{3\,c\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(20\,c^5-76\,c^4\,d+106\,c^3\,d^2+346\,c^2\,d^3+219\,c\,d^4+15\,d^5\right)}{15\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(c^5-3\,c^4\,d+2\,c^3\,d^2+6\,c^2\,d^3+d^5\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,c^5-6\,c^4\,d+4\,c^3\,d^2+24\,c^2\,d^3+13\,c\,d^4+5\,d^5\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(11\,c^5-27\,c^4\,d+4\,c^3\,d^2+162\,c^2\,d^3+135\,c\,d^4+30\,d^5\right)}{3\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(47\,c^5-137\,c^4\,d+88\,c^3\,d^2+812\,c^2\,d^3+690\,c\,d^4+75\,d^5\right)}{15\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}}{f\,\left(a^3\,c+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,a^3\,c+2\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(5\,a^3\,c+2\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(11\,a^3\,c+10\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(11\,a^3\,c+10\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(15\,a^3\,c+20\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(15\,a^3\,c+20\,a^3\,d\right)+a^3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}-\frac{2\,d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\left(4\,c+3\,d\right)\,\left(2\,a^3\,c^5\,d-6\,a^3\,c^4\,d^2+4\,a^3\,c^3\,d^3+4\,a^3\,c^2\,d^4-6\,a^3\,c\,d^5+2\,a^3\,d^6\right)}{a^3\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{9/2}}+\frac{2\,c\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,c+3\,d\right)\,\left(a^3\,c^5-3\,a^3\,c^4\,d+2\,a^3\,c^3\,d^2+2\,a^3\,c^2\,d^3-3\,a^3\,c\,d^4+a^3\,d^5\right)}{a^3\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{9/2}}}{6\,d^4+8\,c\,d^3}\right)\,\left(4\,c+3\,d\right)}{a^3\,f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{9/2}}","Not used",1,"- ((2*(72*c*d^3 - 27*c^3*d + 7*c^4 + 15*d^4 + 38*c^2*d^2))/(15*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (4*tan(e/2 + (f*x)/2)^3*(84*c*d^3 - 18*c^3*d + 5*c^4 + 15*d^4 + 19*c^2*d^2))/(3*c*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)*(219*c*d^4 - 76*c^4*d + 20*c^5 + 15*d^5 + 346*c^2*d^3 + 106*c^3*d^2))/(15*c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^6*(c^5 - 3*c^4*d + d^5 + 6*c^2*d^3 + 2*c^3*d^2))/(c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^5*(13*c*d^4 - 6*c^4*d + 2*c^5 + 5*d^5 + 24*c^2*d^3 + 4*c^3*d^2))/(c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^4*(135*c*d^4 - 27*c^4*d + 11*c^5 + 30*d^5 + 162*c^2*d^3 + 4*c^3*d^2))/(3*c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^2*(690*c*d^4 - 137*c^4*d + 47*c^5 + 75*d^5 + 812*c^2*d^3 + 88*c^3*d^2))/(15*c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)))/(f*(a^3*c + tan(e/2 + (f*x)/2)*(5*a^3*c + 2*a^3*d) + tan(e/2 + (f*x)/2)^6*(5*a^3*c + 2*a^3*d) + tan(e/2 + (f*x)/2)^2*(11*a^3*c + 10*a^3*d) + tan(e/2 + (f*x)/2)^5*(11*a^3*c + 10*a^3*d) + tan(e/2 + (f*x)/2)^3*(15*a^3*c + 20*a^3*d) + tan(e/2 + (f*x)/2)^4*(15*a^3*c + 20*a^3*d) + a^3*c*tan(e/2 + (f*x)/2)^7)) - (2*d^3*atan(((d^3*(4*c + 3*d)*(2*a^3*d^6 - 6*a^3*c*d^5 + 2*a^3*c^5*d + 4*a^3*c^2*d^4 + 4*a^3*c^3*d^3 - 6*a^3*c^4*d^2))/(a^3*(c + d)^(3/2)*(c - d)^(9/2)) + (2*c*d^3*tan(e/2 + (f*x)/2)*(4*c + 3*d)*(a^3*c^5 + a^3*d^5 - 3*a^3*c*d^4 - 3*a^3*c^4*d + 2*a^3*c^2*d^3 + 2*a^3*c^3*d^2))/(a^3*(c + d)^(3/2)*(c - d)^(9/2)))/(8*c*d^3 + 6*d^4))*(4*c + 3*d))/(a^3*f*(c + d)^(3/2)*(c - d)^(9/2))","B"
479,1,1660,378,11.645023,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^3),x)","\frac{d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\left(20\,c^2+30\,c\,d+13\,d^2\right)\,\left(-2\,a^3\,c^7\,d+6\,a^3\,c^6\,d^2-2\,a^3\,c^5\,d^3-10\,a^3\,c^4\,d^4+10\,a^3\,c^3\,d^5+2\,a^3\,c^2\,d^6-6\,a^3\,c\,d^7+2\,a^3\,d^8\right)}{2\,a^3\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{11/2}}-\frac{c\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(20\,c^2+30\,c\,d+13\,d^2\right)\,\left(a^3\,c^7-3\,a^3\,c^6\,d+a^3\,c^5\,d^2+5\,a^3\,c^4\,d^3-5\,a^3\,c^3\,d^4-a^3\,c^2\,d^5+3\,a^3\,c\,d^6-a^3\,d^7\right)}{a^3\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{11/2}}}{20\,c^2\,d^3+30\,c\,d^4+13\,d^5}\right)\,\left(20\,c^2+30\,c\,d+13\,d^2\right)}{a^3\,f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{11/2}}-\frac{\frac{14\,c^6-60\,c^5\,d+92\,c^4\,d^2+420\,c^3\,d^3+404\,c^2\,d^4+90\,c\,d^5-15\,d^6}{15\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(4\,c^8-10\,c^7\,d-2\,c^6\,d^2+122\,c^5\,d^3+200\,c^4\,d^4+141\,c^3\,d^5+49\,c^2\,d^6+2\,c\,d^7-2\,d^8\right)}{c^2\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(28\,c^8-54\,c^7\,d-62\,c^6\,d^2+870\,c^5\,d^3+1960\,c^4\,d^4+1707\,c^3\,d^5+759\,c^2\,d^6+114\,c\,d^7-30\,d^8\right)}{3\,c^2\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(32\,c^8-62\,c^7\,d-70\,c^6\,d^2+1294\,c^5\,d^3+3560\,c^4\,d^4+3763\,c^3\,d^5+1857\,c^2\,d^6+270\,c\,d^7-60\,d^8\right)}{3\,c^2\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,c^7-6\,c^6\,d+2\,c^5\,d^2+30\,c^4\,d^3+20\,c^3\,d^4+11\,c^2\,d^5+6\,c\,d^6-2\,d^7\right)}{c\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(108\,c^8-290\,c^7\,d-10\,c^6\,d^2+4810\,c^5\,d^3+10616\,c^4\,d^4+8725\,c^3\,d^5+2501\,c^2\,d^6+30\,c\,d^7-30\,d^8\right)}{15\,c^2\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(140\,c^8-314\,c^7\,d-210\,c^6\,d^2+6898\,c^5\,d^3+18600\,c^4\,d^4+19441\,c^3\,d^5+7945\,c^2\,d^6+570\,c\,d^7-150\,d^8\right)}{15\,c^2\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(204\,c^7-614\,c^6\,d+316\,c^5\,d^2+7254\,c^4\,d^3+14330\,c^3\,d^4+10235\,c^2\,d^5+1650\,c\,d^6-300\,d^7\right)}{15\,c^2\,\left(c+d\right)\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(40\,c^7-154\,c^6\,d+190\,c^5\,d^2+2018\,c^4\,d^3+3400\,c^3\,d^4+1901\,c^2\,d^5+195\,c\,d^6-30\,d^7\right)}{15\,c\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}}{f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,a^3\,c^2+4\,d\,a^3\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(12\,a^3\,c^2+20\,a^3\,c\,d+4\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(12\,a^3\,c^2+20\,a^3\,c\,d+4\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(20\,a^3\,c^2+44\,a^3\,c\,d+20\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(20\,a^3\,c^2+44\,a^3\,c\,d+20\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(26\,a^3\,c^2+60\,a^3\,c\,d+40\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(26\,a^3\,c^2+60\,a^3\,c\,d+40\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(5\,a^3\,c^2+4\,d\,a^3\,c\right)+a^3\,c^2+a^3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\right)}","Not used",1,"(d^3*atan(((d^3*(30*c*d + 20*c^2 + 13*d^2)*(2*a^3*d^8 - 6*a^3*c*d^7 - 2*a^3*c^7*d + 2*a^3*c^2*d^6 + 10*a^3*c^3*d^5 - 10*a^3*c^4*d^4 - 2*a^3*c^5*d^3 + 6*a^3*c^6*d^2))/(2*a^3*(c + d)^(5/2)*(c - d)^(11/2)) - (c*d^3*tan(e/2 + (f*x)/2)*(30*c*d + 20*c^2 + 13*d^2)*(a^3*c^7 - a^3*d^7 + 3*a^3*c*d^6 - 3*a^3*c^6*d - a^3*c^2*d^5 - 5*a^3*c^3*d^4 + 5*a^3*c^4*d^3 + a^3*c^5*d^2))/(a^3*(c + d)^(5/2)*(c - d)^(11/2)))/(30*c*d^4 + 13*d^5 + 20*c^2*d^3))*(30*c*d + 20*c^2 + 13*d^2))/(a^3*f*(c + d)^(5/2)*(c - d)^(11/2)) - ((90*c*d^5 - 60*c^5*d + 14*c^6 - 15*d^6 + 404*c^2*d^4 + 420*c^3*d^3 + 92*c^4*d^2)/(15*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^7*(2*c*d^7 - 10*c^7*d + 4*c^8 - 2*d^8 + 49*c^2*d^6 + 141*c^3*d^5 + 200*c^4*d^4 + 122*c^5*d^3 - 2*c^6*d^2))/(c^2*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^6*(114*c*d^7 - 54*c^7*d + 28*c^8 - 30*d^8 + 759*c^2*d^6 + 1707*c^3*d^5 + 1960*c^4*d^4 + 870*c^5*d^3 - 62*c^6*d^2))/(3*c^2*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^5*(270*c*d^7 - 62*c^7*d + 32*c^8 - 60*d^8 + 1857*c^2*d^6 + 3763*c^3*d^5 + 3560*c^4*d^4 + 1294*c^5*d^3 - 70*c^6*d^2))/(3*c^2*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^8*(6*c*d^6 - 6*c^6*d + 2*c^7 - 2*d^7 + 11*c^2*d^5 + 20*c^3*d^4 + 30*c^4*d^3 + 2*c^5*d^2))/(c*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^2*(30*c*d^7 - 290*c^7*d + 108*c^8 - 30*d^8 + 2501*c^2*d^6 + 8725*c^3*d^5 + 10616*c^4*d^4 + 4810*c^5*d^3 - 10*c^6*d^2))/(15*c^2*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^3*(570*c*d^7 - 314*c^7*d + 140*c^8 - 150*d^8 + 7945*c^2*d^6 + 19441*c^3*d^5 + 18600*c^4*d^4 + 6898*c^5*d^3 - 210*c^6*d^2))/(15*c^2*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^4*(1650*c*d^6 - 614*c^6*d + 204*c^7 - 300*d^7 + 10235*c^2*d^5 + 14330*c^3*d^4 + 7254*c^4*d^3 + 316*c^5*d^2))/(15*c^2*(c + d)*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)*(195*c*d^6 - 154*c^6*d + 40*c^7 - 30*d^7 + 1901*c^2*d^5 + 3400*c^3*d^4 + 2018*c^4*d^3 + 190*c^5*d^2))/(15*c*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)*(5*a^3*c^2 + 4*a^3*c*d) + tan(e/2 + (f*x)/2)^2*(12*a^3*c^2 + 4*a^3*d^2 + 20*a^3*c*d) + tan(e/2 + (f*x)/2)^7*(12*a^3*c^2 + 4*a^3*d^2 + 20*a^3*c*d) + tan(e/2 + (f*x)/2)^3*(20*a^3*c^2 + 20*a^3*d^2 + 44*a^3*c*d) + tan(e/2 + (f*x)/2)^6*(20*a^3*c^2 + 20*a^3*d^2 + 44*a^3*c*d) + tan(e/2 + (f*x)/2)^4*(26*a^3*c^2 + 40*a^3*d^2 + 60*a^3*c*d) + tan(e/2 + (f*x)/2)^5*(26*a^3*c^2 + 40*a^3*d^2 + 60*a^3*c*d) + tan(e/2 + (f*x)/2)^8*(5*a^3*c^2 + 4*a^3*c*d) + a^3*c^2 + a^3*c^2*tan(e/2 + (f*x)/2)^9))","B"
480,1,94,75,7.065124,"\text{Not used}","int((A + B*sin(x))/(sin(x) + 1)^4,x)","-\frac{2\,A\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+\left(6\,A+2\,B\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\left(12\,A+\frac{10\,B}{3}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+\left(12\,A+\frac{16\,B}{3}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(\frac{42\,A}{5}+\frac{16\,B}{5}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\left(\frac{14\,A}{5}+\frac{26\,B}{15}\right)\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{24\,A}{35}+\frac{26\,B}{105}}{{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^7}","Not used",1,"-((24*A)/35 + (26*B)/105 + 2*A*tan(x/2)^6 + tan(x/2)*((14*A)/5 + (26*B)/15) + tan(x/2)^5*(6*A + 2*B) + tan(x/2)^4*(12*A + (10*B)/3) + tan(x/2)^3*(12*A + (16*B)/3) + tan(x/2)^2*((42*A)/5 + (16*B)/5))/(tan(x/2) + 1)^7","B"
481,1,97,81,7.059439,"\text{Not used}","int((A + B*sin(x))/(sin(x) - 1)^4,x)","-\frac{2\,A\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+\left(2\,B-6\,A\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\left(12\,A-\frac{10\,B}{3}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+\left(\frac{16\,B}{3}-12\,A\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+\left(\frac{42\,A}{5}-\frac{16\,B}{5}\right)\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\left(\frac{26\,B}{15}-\frac{14\,A}{5}\right)\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{24\,A}{35}-\frac{26\,B}{105}}{{\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}^7}","Not used",1,"-((24*A)/35 - (26*B)/105 + 2*A*tan(x/2)^6 - tan(x/2)*((14*A)/5 - (26*B)/15) - tan(x/2)^5*(6*A - 2*B) + tan(x/2)^4*(12*A - (10*B)/3) - tan(x/2)^3*(12*A - (16*B)/3) + tan(x/2)^2*((42*A)/5 - (16*B)/5))/(tan(x/2) - 1)^7","B"
482,0,-1,290,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2), x)","F"
483,0,-1,231,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2), x)","F"
484,0,-1,179,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2), x)","F"
485,1,176,138,7.618772,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(1/2),x)","\frac{a\,\left(2\,c\,\mathrm{F}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|\frac{2\,d}{c+d}\right)-2\,\left(c+d\right)\,\mathrm{E}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|\frac{2\,d}{c+d}\right)\right)\,\sqrt{{\cos\left(e+f\,x\right)}^2}\,\sqrt{\frac{c+d\,\sin\left(e+f\,x\right)}{c+d}}}{d\,f\,\cos\left(e+f\,x\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}-\frac{2\,a\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|\frac{2\,d}{c+d}\right)\,\sqrt{\frac{c+d\,\sin\left(e+f\,x\right)}{c+d}}}{f\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}","Not used",1,"(a*(2*c*ellipticF(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), (2*d)/(c + d)) - 2*(c + d)*ellipticE(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), (2*d)/(c + d)))*(cos(e + f*x)^2)^(1/2)*((c + d*sin(e + f*x))/(c + d))^(1/2))/(d*f*cos(e + f*x)*(c + d*sin(e + f*x))^(1/2)) - (2*a*ellipticF(pi/4 - e/2 - (f*x)/2, (2*d)/(c + d))*((c + d*sin(e + f*x))/(c + d))^(1/2))/(f*(c + d*sin(e + f*x))^(1/2))","B"
486,0,-1,169,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(3/2), x)","F"
487,0,-1,237,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(5/2), x)","F"
488,0,-1,318,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(7/2),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(7/2), x)","F"
489,0,-1,378,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2), x)","F"
490,0,-1,298,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2), x)","F"
491,0,-1,239,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2), x)","F"
492,0,-1,189,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(1/2), x)","F"
493,0,-1,189,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(3/2), x)","F"
494,0,-1,247,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(5/2), x)","F"
495,0,-1,320,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^2/(c + d*sin(e + f*x))^(7/2), x)","F"
496,0,-1,467,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(5/2), x)","F"
497,0,-1,390,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2), x)","F"
498,0,-1,318,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2), x)","F"
499,0,-1,258,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(1/2), x)","F"
500,0,-1,270,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(3/2), x)","F"
501,0,-1,280,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(5/2), x)","F"
502,0,-1,336,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(7/2), x)","F"
503,0,-1,419,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(9/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^3/(c + d*sin(e + f*x))^(9/2), x)","F"
504,0,-1,246,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x)),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x)), x)","F"
505,0,-1,186,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x)),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x)), x)","F"
506,0,-1,170,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x)),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x)), x)","F"
507,0,-1,181,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)), x)","F"
508,0,-1,244,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2)), x)","F"
509,-1,-1,333,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
510,0,-1,256,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^2, x)","F"
511,0,-1,237,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^2, x)","F"
512,0,-1,233,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^2,x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^2, x)","F"
513,0,-1,257,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2)), x)","F"
514,0,-1,326,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2)), x)","F"
515,-1,-1,405,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
516,0,-1,322,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^3, x)","F"
517,0,-1,323,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^3, x)","F"
518,0,-1,334,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^3,x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^3, x)","F"
519,0,-1,344,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2)), x)","F"
520,-1,-1,423,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
521,-1,-1,518,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^(5/2)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
522,0,-1,161,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3,x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3, x)","F"
523,0,-1,112,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2,x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2, x)","F"
524,0,-1,62,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x)),x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x)), x)","F"
525,1,33,26,7.415553,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2),x)","-\frac{2\,\cos\left(e+f\,x\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}}{f\,\left(\sin\left(e+f\,x\right)+1\right)}","Not used",1,"-(2*cos(e + f*x)*(a*(sin(e + f*x) + 1))^(1/2))/(f*(sin(e + f*x) + 1))","B"
526,0,-1,61,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x)),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x)), x)","F"
527,0,-1,105,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^2,x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^2, x)","F"
528,0,-1,154,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^3,x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^3, x)","F"
529,0,-1,231,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3, x)","F"
530,0,-1,157,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2, x)","F"
531,0,-1,101,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x)),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x)), x)","F"
532,0,-1,59,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2), x)","F"
533,0,-1,98,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x)),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x)), x)","F"
534,0,-1,119,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^2,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^2, x)","F"
535,0,-1,179,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^3,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^3, x)","F"
536,0,-1,328,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3, x)","F"
537,0,-1,202,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2, x)","F"
538,0,-1,138,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x)),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x)), x)","F"
539,0,-1,89,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2), x)","F"
540,0,-1,142,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x)),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x)), x)","F"
541,0,-1,166,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^2,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^2, x)","F"
542,0,-1,194,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^3,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^3, x)","F"
543,0,-1,178,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^(1/2), x)","F"
544,0,-1,123,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^(1/2), x)","F"
545,1,151,79,8.961961,"\text{Not used}","int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^(1/2),x)","-\frac{c\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|1\right)\,\sqrt{\frac{2\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{a}}}{f\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}-\frac{d\,\left(4\,\mathrm{E}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|1\right)-2\,\mathrm{F}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|1\right)\right)\,\sqrt{{\cos\left(e+f\,x\right)}^2}\,\sqrt{\frac{a+a\,\sin\left(e+f\,x\right)}{2\,a}}}{f\,\cos\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}","Not used",1,"- (c*ellipticF(pi/4 - e/2 - (f*x)/2, 1)*((2*(a + a*sin(e + f*x)))/a)^(1/2))/(f*(a + a*sin(e + f*x))^(1/2)) - (d*(4*ellipticE(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), 1) - 2*ellipticF(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), 1))*(cos(e + f*x)^2)^(1/2)*((a + a*sin(e + f*x))/(2*a))^(1/2))/(f*cos(e + f*x)*(a + a*sin(e + f*x))^(1/2))","B"
546,1,49,47,7.717822,"\text{Not used}","int(1/(a + a*sin(e + f*x))^(1/2),x)","-\frac{\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|1\right)\,\sqrt{\frac{2\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{a}}}{f\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}","Not used",1,"-(ellipticF(pi/4 - e/2 - (f*x)/2, 1)*((2*(a + a*sin(e + f*x)))/a)^(1/2))/(f*(a + a*sin(e + f*x))^(1/2))","B"
547,0,-1,123,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
548,0,-1,175,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2), x)","F"
549,0,-1,247,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3), x)","F"
550,0,-1,192,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^(3/2), x)","F"
551,0,-1,138,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^(3/2), x)","F"
552,0,-1,87,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{c+d\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^(3/2), x)","F"
553,0,-1,77,0.000000,"\text{Not used}","int(1/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + a*sin(e + f*x))^(3/2), x)","F"
554,0,-1,164,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))), x)","F"
555,0,-1,243,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2), x)","F"
556,0,-1,318,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3), x)","F"
557,0,-1,194,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^3/(a + a*sin(e + f*x))^(5/2), x)","F"
558,0,-1,147,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^2/(a + a*sin(e + f*x))^(5/2), x)","F"
559,0,-1,126,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{c+d\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))/(a + a*sin(e + f*x))^(5/2), x)","F"
560,0,-1,107,0.000000,"\text{Not used}","int(1/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + a*sin(e + f*x))^(5/2), x)","F"
561,0,-1,218,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))), x)","F"
562,0,-1,313,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2), x)","F"
563,0,-1,400,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3), x)","F"
564,0,-1,203,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2),x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2), x)","F"
565,0,-1,156,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2),x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2), x)","F"
566,0,-1,105,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2),x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2), x)","F"
567,0,-1,61,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(1/2), x)","F"
568,1,145,45,9.004328,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(3/2),x)","-\frac{4\,\left(2\,c\,\cos\left(e+f\,x\right)+d\,\sin\left(2\,e+2\,f\,x\right)\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}{f\,\left(c+d\right)\,\left(4\,c\,d+4\,c^2\,\sin\left(e+f\,x\right)+3\,d^2\,\sin\left(e+f\,x\right)+4\,c^2+2\,d^2-2\,d^2\,\cos\left(2\,e+2\,f\,x\right)-d^2\,\sin\left(3\,e+3\,f\,x\right)+8\,c\,d\,\sin\left(e+f\,x\right)-4\,c\,d\,\cos\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"-(4*(2*c*cos(e + f*x) + d*sin(2*e + 2*f*x))*(a*(sin(e + f*x) + 1))^(1/2)*(c + d*sin(e + f*x))^(1/2))/(f*(c + d)*(4*c*d + 4*c^2*sin(e + f*x) + 3*d^2*sin(e + f*x) + 4*c^2 + 2*d^2 - 2*d^2*cos(2*e + 2*f*x) - d^2*sin(3*e + 3*f*x) + 8*c*d*sin(e + f*x) - 4*c*d*cos(2*e + 2*f*x)))","B"
569,1,353,95,13.901574,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(5/2),x)","-\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,8{}\mathrm{i}}{3\,d\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}+\frac{8\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,d\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}+\frac{8\,c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{d^2\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}+\frac{c\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,8{}\mathrm{i}}{d^2\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}\right)}{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}-\frac{{\left(c+d\right)}^2\,1{}\mathrm{i}}{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}-\frac{2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(2\,c^2+2\,c\,d+d^2\right)}{d^2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(4\,c+d\right)}{d}+\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c+d\right)}^2\,\left(2\,c^2+2\,c\,d+d^2\right)\,2{}\mathrm{i}}{d^2\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}-\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c+d\right)}^2\,\left(4\,c+d\right)\,1{}\mathrm{i}}{d\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}}","Not used",1,"-((c + d*sin(e + f*x))^(1/2)*((exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^(1/2)*8i)/(3*d*f*(c*1i + d*1i)^2) + (8*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^(1/2))/(3*d*f*(c*1i + d*1i)^2) + (8*c*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^(1/2))/(d^2*f*(c*1i + d*1i)^2) + (c*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^(1/2)*8i)/(d^2*f*(c*1i + d*1i)^2)))/(exp(e*5i + f*x*5i) - ((c + d)^2*1i)/(c*1i + d*1i)^2 - (2*exp(e*3i + f*x*3i)*(2*c*d + 2*c^2 + d^2))/d^2 + (exp(e*1i + f*x*1i)*(4*c + d))/d + (exp(e*2i + f*x*2i)*(c + d)^2*(2*c*d + 2*c^2 + d^2)*2i)/(d^2*(c*1i + d*1i)^2) - (exp(e*4i + f*x*4i)*(c + d)^2*(4*c + d)*1i)/(d*(c*1i + d*1i)^2))","B"
570,1,501,142,16.351934,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(7/2),x)","-\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,32{}\mathrm{i}}{15\,d\,f\,{\left(c+d\right)}^3}-\frac{32\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d\,f\,{\left(c+d\right)}^3}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(240\,c^2+80\,d^2\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d^3\,f\,{\left(c+d\right)}^3}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(c^2\,240{}\mathrm{i}+d^2\,80{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d^3\,f\,{\left(c+d\right)}^3}+\frac{32\,c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,d^2\,f\,{\left(c+d\right)}^3}-\frac{c\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,32{}\mathrm{i}}{3\,d^2\,f\,{\left(c+d\right)}^3}\right)}{{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+\frac{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3}{{\left(c+d\right)}^3}-\frac{3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(4\,c^2+2\,c\,d+d^2\right)}{d^2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(6\,c+d\right)}{d}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{d^3}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(c\,6{}\mathrm{i}+d\,1{}\mathrm{i}\right)}{d}-\frac{3\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3\,\left(4\,c^2+2\,c\,d+d^2\right)}{d^2\,{\left(c+d\right)}^3}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{d^3\,{\left(c+d\right)}^3}}","Not used",1,"-((c + d*sin(e + f*x))^(1/2)*((exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^(1/2)*32i)/(15*d*f*(c + d)^3) - (32*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2))/(15*d*f*(c + d)^3) + (exp(e*4i + f*x*4i)*(240*c^2 + 80*d^2)*(a + a*sin(e + f*x))^(1/2))/(15*d^3*f*(c + d)^3) - (exp(e*3i + f*x*3i)*(c^2*240i + d^2*80i)*(a + a*sin(e + f*x))^(1/2))/(15*d^3*f*(c + d)^3) + (32*c*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^(1/2))/(3*d^2*f*(c + d)^3) - (c*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2)*32i)/(3*d^2*f*(c + d)^3)))/(exp(e*7i + f*x*7i) + (c*1i + d*1i)^3/(c + d)^3 - (3*exp(e*5i + f*x*5i)*(2*c*d + 4*c^2 + d^2))/d^2 - (exp(e*1i + f*x*1i)*(6*c + d))/d + (exp(e*3i + f*x*3i)*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/d^3 + (exp(e*6i + f*x*6i)*(c*6i + d*1i))/d - (3*exp(e*2i + f*x*2i)*(c*1i + d*1i)^3*(2*c*d + 4*c^2 + d^2))/(d^2*(c + d)^3) + (exp(e*4i + f*x*4i)*(c*1i + d*1i)^3*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/(d^3*(c + d)^3))","B"
571,0,-1,285,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2), x)","F"
572,0,-1,228,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2), x)","F"
573,0,-1,171,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2), x)","F"
574,0,-1,111,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(1/2), x)","F"
575,0,-1,117,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(3/2), x)","F"
576,1,387,115,14.401281,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(5/2),x)","-\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{a\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(c+5\,d\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,4{}\mathrm{i}}{3\,d^2\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}+\frac{a\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(3\,c-d\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,4{}\mathrm{i}}{d^2\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}-\frac{a\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(c\,3{}\mathrm{i}-d\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,4{}\mathrm{i}}{d^2\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}-\frac{a\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(c\,1{}\mathrm{i}+d\,5{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,4{}\mathrm{i}}{3\,d^2\,f\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}\right)}{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}-\frac{{\left(c+d\right)}^2\,1{}\mathrm{i}}{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}-\frac{2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(2\,c^2+2\,c\,d+d^2\right)}{d^2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(4\,c+d\right)}{d}+\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c+d\right)}^2\,\left(2\,c^2+2\,c\,d+d^2\right)\,2{}\mathrm{i}}{d^2\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}-\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c+d\right)}^2\,\left(4\,c+d\right)\,1{}\mathrm{i}}{d\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^2}}","Not used",1,"-((c + d*sin(e + f*x))^(1/2)*((a*exp(e*1i + f*x*1i)*(c + 5*d)*(a + a*sin(e + f*x))^(1/2)*4i)/(3*d^2*f*(c*1i + d*1i)^2) + (a*exp(e*3i + f*x*3i)*(3*c - d)*(a + a*sin(e + f*x))^(1/2)*4i)/(d^2*f*(c*1i + d*1i)^2) - (a*exp(e*2i + f*x*2i)*(c*3i - d*1i)*(a + a*sin(e + f*x))^(1/2)*4i)/(d^2*f*(c*1i + d*1i)^2) - (a*exp(e*4i + f*x*4i)*(c*1i + d*5i)*(a + a*sin(e + f*x))^(1/2)*4i)/(3*d^2*f*(c*1i + d*1i)^2)))/(exp(e*5i + f*x*5i) - ((c + d)^2*1i)/(c*1i + d*1i)^2 - (2*exp(e*3i + f*x*3i)*(2*c*d + 2*c^2 + d^2))/d^2 + (exp(e*1i + f*x*1i)*(4*c + d))/d + (exp(e*2i + f*x*2i)*(c + d)^2*(2*c*d + 2*c^2 + d^2)*2i)/(d^2*(c*1i + d*1i)^2) - (exp(e*4i + f*x*4i)*(c + d)^2*(4*c + d)*1i)/(d*(c*1i + d*1i)^2))","B"
577,1,541,172,17.482550,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(7/2),x)","\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{8\,a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(c+9\,d\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d^2\,f\,{\left(c+d\right)}^3}-\frac{8\,a\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(9\,c^2-4\,c\,d+3\,d^2\right)}{3\,d^3\,f\,{\left(c+d\right)}^3}+\frac{8\,a\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,9{}\mathrm{i}-c\,d\,4{}\mathrm{i}+d^2\,3{}\mathrm{i}\right)}{3\,d^3\,f\,{\left(c+d\right)}^3}-\frac{8\,a\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(c\,1{}\mathrm{i}+d\,9{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d^2\,f\,{\left(c+d\right)}^3}+\frac{8\,a\,c\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(c\,1{}\mathrm{i}+d\,9{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,d^3\,f\,{\left(c+d\right)}^3}-\frac{8\,a\,c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(c+9\,d\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,d^3\,f\,{\left(c+d\right)}^3}\right)}{{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+\frac{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3}{{\left(c+d\right)}^3}-\frac{3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(4\,c^2+2\,c\,d+d^2\right)}{d^2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(6\,c+d\right)}{d}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{d^3}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(c\,6{}\mathrm{i}+d\,1{}\mathrm{i}\right)}{d}-\frac{3\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3\,\left(4\,c^2+2\,c\,d+d^2\right)}{d^2\,{\left(c+d\right)}^3}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{d^3\,{\left(c+d\right)}^3}}","Not used",1,"((c + d*sin(e + f*x))^(1/2)*((8*a*exp(e*6i + f*x*6i)*(c + 9*d)*(a + a*sin(e + f*x))^(1/2))/(15*d^2*f*(c + d)^3) - (8*a*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^(1/2)*(9*c^2 - 4*c*d + 3*d^2))/(3*d^3*f*(c + d)^3) + (8*a*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^(1/2)*(c^2*9i - c*d*4i + d^2*3i))/(3*d^3*f*(c + d)^3) - (8*a*exp(e*1i + f*x*1i)*(c*1i + d*9i)*(a + a*sin(e + f*x))^(1/2))/(15*d^2*f*(c + d)^3) + (8*a*c*exp(e*5i + f*x*5i)*(c*1i + d*9i)*(a + a*sin(e + f*x))^(1/2))/(3*d^3*f*(c + d)^3) - (8*a*c*exp(e*2i + f*x*2i)*(c + 9*d)*(a + a*sin(e + f*x))^(1/2))/(3*d^3*f*(c + d)^3)))/(exp(e*7i + f*x*7i) + (c*1i + d*1i)^3/(c + d)^3 - (3*exp(e*5i + f*x*5i)*(2*c*d + 4*c^2 + d^2))/d^2 - (exp(e*1i + f*x*1i)*(6*c + d))/d + (exp(e*3i + f*x*3i)*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/d^3 + (exp(e*6i + f*x*6i)*(c*6i + d*1i))/d - (3*exp(e*2i + f*x*2i)*(c*1i + d*1i)^3*(2*c*d + 4*c^2 + d^2))/(d^2*(c + d)^3) + (exp(e*4i + f*x*4i)*(c*1i + d*1i)^3*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/(d^3*(c + d)^3))","B"
578,1,807,229,20.213034,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(9/2),x)","\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{32\,a\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\left(c+13\,d\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{105\,d^2\,f\,{\left(c+d\right)}^4}-\frac{16\,a\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(9\,c^3-5\,c^2\,d+9\,c\,d^2-d^3\right)}{3\,d^4\,f\,{\left(c+d\right)}^4}-\frac{16\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^3\,9{}\mathrm{i}-c^2\,d\,5{}\mathrm{i}+c\,d^2\,9{}\mathrm{i}-d^3\,1{}\mathrm{i}\right)}{3\,d^4\,f\,{\left(c+d\right)}^4}-\frac{16\,a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(5\,c^3+65\,c^2\,d+c\,d^2+13\,d^3\right)}{15\,d^4\,f\,{\left(c+d\right)}^4}-\frac{16\,a\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^3\,5{}\mathrm{i}+c^2\,d\,65{}\mathrm{i}+c\,d^2\,1{}\mathrm{i}+d^3\,13{}\mathrm{i}\right)}{15\,d^4\,f\,{\left(c+d\right)}^4}+\frac{32\,a\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(c\,1{}\mathrm{i}+d\,13{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{105\,d^2\,f\,{\left(c+d\right)}^4}+\frac{32\,a\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(c\,1{}\mathrm{i}+d\,13{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d^3\,f\,{\left(c+d\right)}^4}+\frac{32\,a\,c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(c+13\,d\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{15\,d^3\,f\,{\left(c+d\right)}^4}\right)}{{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}+\frac{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,1{}\mathrm{i}}{{\left(c+d\right)}^4}-\frac{4\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(8\,c^3+6\,c^2\,d+6\,c\,d^2+d^3\right)}{d^3}-\frac{4\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(6\,c^2+2\,c\,d+d^2\right)}{d^2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(8\,c+d\right)}{d}+\frac{2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(8\,c^4+16\,c^3\,d+24\,c^2\,d^2+12\,c\,d^3+3\,d^4\right)}{d^4}-\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,\left(8\,c^3+6\,c^2\,d+6\,c\,d^2+d^3\right)\,4{}\mathrm{i}}{d^3\,{\left(c+d\right)}^4}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,\left(6\,c^2+2\,c\,d+d^2\right)\,4{}\mathrm{i}}{d^2\,{\left(c+d\right)}^4}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\left(8\,c+d\right)\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,1{}\mathrm{i}}{d\,{\left(c+d\right)}^4}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,\left(8\,c^4+16\,c^3\,d+24\,c^2\,d^2+12\,c\,d^3+3\,d^4\right)\,2{}\mathrm{i}}{d^4\,{\left(c+d\right)}^4}}","Not used",1,"((c + d*sin(e + f*x))^(1/2)*((32*a*exp(e*8i + f*x*8i)*(c + 13*d)*(a + a*sin(e + f*x))^(1/2))/(105*d^2*f*(c + d)^4) - (16*a*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^(1/2)*(9*c*d^2 - 5*c^2*d + 9*c^3 - d^3))/(3*d^4*f*(c + d)^4) - (16*a*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2)*(c*d^2*9i - c^2*d*5i + c^3*9i - d^3*1i))/(3*d^4*f*(c + d)^4) - (16*a*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*(c*d^2 + 65*c^2*d + 5*c^3 + 13*d^3))/(15*d^4*f*(c + d)^4) - (16*a*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^(1/2)*(c*d^2*1i + c^2*d*65i + c^3*5i + d^3*13i))/(15*d^4*f*(c + d)^4) + (32*a*exp(e*1i + f*x*1i)*(c*1i + d*13i)*(a + a*sin(e + f*x))^(1/2))/(105*d^2*f*(c + d)^4) + (32*a*c*exp(e*7i + f*x*7i)*(c*1i + d*13i)*(a + a*sin(e + f*x))^(1/2))/(15*d^3*f*(c + d)^4) + (32*a*c*exp(e*2i + f*x*2i)*(c + 13*d)*(a + a*sin(e + f*x))^(1/2))/(15*d^3*f*(c + d)^4)))/(exp(e*9i + f*x*9i) + ((c*1i + d*1i)^4*1i)/(c + d)^4 - (4*exp(e*3i + f*x*3i)*(6*c*d^2 + 6*c^2*d + 8*c^3 + d^3))/d^3 - (4*exp(e*7i + f*x*7i)*(2*c*d + 6*c^2 + d^2))/d^2 + (exp(e*1i + f*x*1i)*(8*c + d))/d + (2*exp(e*5i + f*x*5i)*(12*c*d^3 + 16*c^3*d + 8*c^4 + 3*d^4 + 24*c^2*d^2))/d^4 - (exp(e*6i + f*x*6i)*(c*1i + d*1i)^4*(6*c*d^2 + 6*c^2*d + 8*c^3 + d^3)*4i)/(d^3*(c + d)^4) - (exp(e*2i + f*x*2i)*(c*1i + d*1i)^4*(2*c*d + 6*c^2 + d^2)*4i)/(d^2*(c + d)^4) + (exp(e*8i + f*x*8i)*(8*c + d)*(c*1i + d*1i)^4*1i)/(d*(c + d)^4) + (exp(e*4i + f*x*4i)*(c*1i + d*1i)^4*(12*c*d^3 + 16*c^3*d + 8*c^4 + 3*d^4 + 24*c^2*d^2)*2i)/(d^4*(c + d)^4))","B"
579,0,-1,377,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2), x)","F"
580,0,-1,312,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2), x)","F"
581,0,-1,241,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2), x)","F"
582,0,-1,178,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(1/2), x)","F"
583,0,-1,180,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(3/2), x)","F"
584,0,-1,183,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(5/2), x)","F"
585,1,590,189,17.457463,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(7/2),x)","-\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{8\,a^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(15\,c^2-10\,c\,d+7\,d^2\right)}{3\,d^3\,f\,{\left(c+d\right)}^3}+\frac{4\,a^2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(5\,c^2+34\,c\,d-3\,d^2\right)}{3\,d^3\,f\,{\left(c+d\right)}^3}-\frac{8\,a^2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,15{}\mathrm{i}-c\,d\,10{}\mathrm{i}+d^2\,7{}\mathrm{i}\right)}{3\,d^3\,f\,{\left(c+d\right)}^3}-\frac{4\,a^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,5{}\mathrm{i}+c\,d\,34{}\mathrm{i}-d^2\,3{}\mathrm{i}\right)}{3\,d^3\,f\,{\left(c+d\right)}^3}-\frac{4\,a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(3\,c^2+14\,c\,d+43\,d^2\right)}{15\,d^3\,f\,{\left(c+d\right)}^3}+\frac{4\,a^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,3{}\mathrm{i}+c\,d\,14{}\mathrm{i}+d^2\,43{}\mathrm{i}\right)}{15\,d^3\,f\,{\left(c+d\right)}^3}\right)}{{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+\frac{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3}{{\left(c+d\right)}^3}-\frac{3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(4\,c^2+2\,c\,d+d^2\right)}{d^2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(6\,c+d\right)}{d}+\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{d^3}+\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(c\,6{}\mathrm{i}+d\,1{}\mathrm{i}\right)}{d}-\frac{3\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3\,\left(4\,c^2+2\,c\,d+d^2\right)}{d^2\,{\left(c+d\right)}^3}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^3\,\left(8\,c^3+12\,c^2\,d+12\,c\,d^2+3\,d^3\right)}{d^3\,{\left(c+d\right)}^3}}","Not used",1,"-((c + d*sin(e + f*x))^(1/2)*((8*a^2*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^(1/2)*(15*c^2 - 10*c*d + 7*d^2))/(3*d^3*f*(c + d)^3) + (4*a^2*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^(1/2)*(34*c*d + 5*c^2 - 3*d^2))/(3*d^3*f*(c + d)^3) - (8*a^2*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^(1/2)*(c^2*15i - c*d*10i + d^2*7i))/(3*d^3*f*(c + d)^3) - (4*a^2*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2)*(c*d*34i + c^2*5i - d^2*3i))/(3*d^3*f*(c + d)^3) - (4*a^2*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*(14*c*d + 3*c^2 + 43*d^2))/(15*d^3*f*(c + d)^3) + (4*a^2*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^(1/2)*(c*d*14i + c^2*3i + d^2*43i))/(15*d^3*f*(c + d)^3)))/(exp(e*7i + f*x*7i) + (c*1i + d*1i)^3/(c + d)^3 - (3*exp(e*5i + f*x*5i)*(2*c*d + 4*c^2 + d^2))/d^2 - (exp(e*1i + f*x*1i)*(6*c + d))/d + (exp(e*3i + f*x*3i)*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/d^3 + (exp(e*6i + f*x*6i)*(c*6i + d*1i))/d - (3*exp(e*2i + f*x*2i)*(c*1i + d*1i)^3*(2*c*d + 4*c^2 + d^2))/(d^2*(c + d)^3) + (exp(e*4i + f*x*4i)*(c*1i + d*1i)^3*(12*c*d^2 + 12*c^2*d + 8*c^3 + 3*d^3))/(d^3*(c + d)^3))","B"
586,1,862,254,20.608738,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(9/2),x)","\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{8\,a^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(3\,c^2+22\,c\,d+115\,d^2\right)}{105\,d^3\,f\,{\left(c+d\right)}^4}+\frac{8\,a^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,3{}\mathrm{i}+c\,d\,22{}\mathrm{i}+d^2\,115{}\mathrm{i}\right)}{105\,d^3\,f\,{\left(c+d\right)}^4}-\frac{8\,a^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(30\,c^3-25\,c^2\,d+36\,c\,d^2-5\,d^3\right)}{3\,d^4\,f\,{\left(c+d\right)}^4}-\frac{8\,a^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^3\,30{}\mathrm{i}-c^2\,d\,25{}\mathrm{i}+c\,d^2\,36{}\mathrm{i}-d^3\,5{}\mathrm{i}\right)}{3\,d^4\,f\,{\left(c+d\right)}^4}-\frac{8\,a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(25\,c^3+244\,c^2\,d-19\,c\,d^2+50\,d^3\right)}{15\,d^4\,f\,{\left(c+d\right)}^4}-\frac{8\,a^2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^3\,25{}\mathrm{i}+c^2\,d\,244{}\mathrm{i}-c\,d^2\,19{}\mathrm{i}+d^3\,50{}\mathrm{i}\right)}{15\,d^4\,f\,{\left(c+d\right)}^4}+\frac{8\,a^2\,c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(3\,c^2+22\,c\,d+115\,d^2\right)}{15\,d^4\,f\,{\left(c+d\right)}^4}+\frac{8\,a^2\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,3{}\mathrm{i}+c\,d\,22{}\mathrm{i}+d^2\,115{}\mathrm{i}\right)}{15\,d^4\,f\,{\left(c+d\right)}^4}\right)}{{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}+\frac{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,1{}\mathrm{i}}{{\left(c+d\right)}^4}-\frac{4\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(8\,c^3+6\,c^2\,d+6\,c\,d^2+d^3\right)}{d^3}-\frac{4\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(6\,c^2+2\,c\,d+d^2\right)}{d^2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(8\,c+d\right)}{d}+\frac{2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(8\,c^4+16\,c^3\,d+24\,c^2\,d^2+12\,c\,d^3+3\,d^4\right)}{d^4}-\frac{{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,\left(8\,c^3+6\,c^2\,d+6\,c\,d^2+d^3\right)\,4{}\mathrm{i}}{d^3\,{\left(c+d\right)}^4}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,\left(6\,c^2+2\,c\,d+d^2\right)\,4{}\mathrm{i}}{d^2\,{\left(c+d\right)}^4}+\frac{{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\left(8\,c+d\right)\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,1{}\mathrm{i}}{d\,{\left(c+d\right)}^4}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^4\,\left(8\,c^4+16\,c^3\,d+24\,c^2\,d^2+12\,c\,d^3+3\,d^4\right)\,2{}\mathrm{i}}{d^4\,{\left(c+d\right)}^4}}","Not used",1,"((c + d*sin(e + f*x))^(1/2)*((8*a^2*exp(e*8i + f*x*8i)*(a + a*sin(e + f*x))^(1/2)*(22*c*d + 3*c^2 + 115*d^2))/(105*d^3*f*(c + d)^4) + (8*a^2*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^(1/2)*(c*d*22i + c^2*3i + d^2*115i))/(105*d^3*f*(c + d)^4) - (8*a^2*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^(1/2)*(36*c*d^2 - 25*c^2*d + 30*c^3 - 5*d^3))/(3*d^4*f*(c + d)^4) - (8*a^2*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2)*(c*d^2*36i - c^2*d*25i + c^3*30i - d^3*5i))/(3*d^4*f*(c + d)^4) - (8*a^2*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*(244*c^2*d - 19*c*d^2 + 25*c^3 + 50*d^3))/(15*d^4*f*(c + d)^4) - (8*a^2*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^(1/2)*(c^2*d*244i - c*d^2*19i + c^3*25i + d^3*50i))/(15*d^4*f*(c + d)^4) + (8*a^2*c*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^(1/2)*(22*c*d + 3*c^2 + 115*d^2))/(15*d^4*f*(c + d)^4) + (8*a^2*c*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^(1/2)*(c*d*22i + c^2*3i + d^2*115i))/(15*d^4*f*(c + d)^4)))/(exp(e*9i + f*x*9i) + ((c*1i + d*1i)^4*1i)/(c + d)^4 - (4*exp(e*3i + f*x*3i)*(6*c*d^2 + 6*c^2*d + 8*c^3 + d^3))/d^3 - (4*exp(e*7i + f*x*7i)*(2*c*d + 6*c^2 + d^2))/d^2 + (exp(e*1i + f*x*1i)*(8*c + d))/d + (2*exp(e*5i + f*x*5i)*(12*c*d^3 + 16*c^3*d + 8*c^4 + 3*d^4 + 24*c^2*d^2))/d^4 - (exp(e*6i + f*x*6i)*(c*1i + d*1i)^4*(6*c*d^2 + 6*c^2*d + 8*c^3 + d^3)*4i)/(d^3*(c + d)^4) - (exp(e*2i + f*x*2i)*(c*1i + d*1i)^4*(2*c*d + 6*c^2 + d^2)*4i)/(d^2*(c + d)^4) + (exp(e*8i + f*x*8i)*(8*c + d)*(c*1i + d*1i)^4*1i)/(d*(c + d)^4) + (exp(e*4i + f*x*4i)*(c*1i + d*1i)^4*(12*c*d^3 + 16*c^3*d + 8*c^4 + 3*d^4 + 24*c^2*d^2)*2i)/(d^4*(c + d)^4))","B"
587,1,1155,317,26.141840,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(11/2),x)","-\frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(\frac{32\,a^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,1{}\mathrm{i}+c\,d\,10{}\mathrm{i}+d^2\,73{}\mathrm{i}\right)}{315\,d^3\,f\,{\left(c+d\right)}^5}-\frac{32\,a^2\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2+10\,c\,d+73\,d^2\right)}{315\,d^3\,f\,{\left(c+d\right)}^5}-\frac{32\,a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(25\,c^4-25\,c^3\,d+57\,c^2\,d^2-15\,c\,d^3+6\,d^4\right)}{5\,d^5\,f\,{\left(c+d\right)}^5}+\frac{32\,a^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^4\,25{}\mathrm{i}-c^3\,d\,25{}\mathrm{i}+c^2\,d^2\,57{}\mathrm{i}-c\,d^3\,15{}\mathrm{i}+d^4\,6{}\mathrm{i}\right)}{5\,d^5\,f\,{\left(c+d\right)}^5}-\frac{16\,a^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(25\,c^4+318\,c^3\,d-20\,c^2\,d^2+194\,c\,d^3-5\,d^4\right)}{15\,d^5\,f\,{\left(c+d\right)}^5}+\frac{16\,a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^4\,25{}\mathrm{i}+c^3\,d\,318{}\mathrm{i}-c^2\,d^2\,20{}\mathrm{i}+c\,d^3\,194{}\mathrm{i}-d^4\,5{}\mathrm{i}\right)}{15\,d^5\,f\,{\left(c+d\right)}^5}+\frac{16\,a^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(7\,c^4+70\,c^3\,d+512\,c^2\,d^2+10\,c\,d^3+73\,d^4\right)}{35\,d^5\,f\,{\left(c+d\right)}^5}-\frac{16\,a^2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^4\,7{}\mathrm{i}+c^3\,d\,70{}\mathrm{i}+c^2\,d^2\,512{}\mathrm{i}+c\,d^3\,10{}\mathrm{i}+d^4\,73{}\mathrm{i}\right)}{35\,d^5\,f\,{\left(c+d\right)}^5}+\frac{32\,a^2\,c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2+10\,c\,d+73\,d^2\right)}{35\,d^4\,f\,{\left(c+d\right)}^5}-\frac{32\,a^2\,c\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c^2\,1{}\mathrm{i}+c\,d\,10{}\mathrm{i}+d^2\,73{}\mathrm{i}\right)}{35\,d^4\,f\,{\left(c+d\right)}^5}\right)}{{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}-\frac{{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^5}{{\left(c+d\right)}^5}+\frac{10\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(8\,c^4+8\,c^3\,d+12\,c^2\,d^2+4\,c\,d^3+d^4\right)}{d^4}+\frac{5\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(16\,c^3+8\,c^2\,d+8\,c\,d^2+d^3\right)}{d^3}-\frac{5\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\left(8\,c^2+2\,c\,d+d^2\right)}{d^2}-\frac{2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(16\,c^5+40\,c^4\,d+80\,c^3\,d^2+60\,c^2\,d^3+30\,c\,d^4+5\,d^5\right)}{d^5}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(10\,c+d\right)}{d}-\frac{5\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^5\,\left(16\,c^3+8\,c^2\,d+8\,c\,d^2+d^3\right)}{d^3\,{\left(c+d\right)}^5}+\frac{5\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^5\,\left(8\,c^2+2\,c\,d+d^2\right)}{d^2\,{\left(c+d\right)}^5}+\frac{2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^5\,\left(16\,c^5+40\,c^4\,d+80\,c^3\,d^2+60\,c^2\,d^3+30\,c\,d^4+5\,d^5\right)}{d^5\,{\left(c+d\right)}^5}+\frac{{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\left(10\,c+d\right)\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^5}{d\,{\left(c+d\right)}^5}-\frac{10\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(c\,1{}\mathrm{i}+d\,1{}\mathrm{i}\right)}^5\,\left(8\,c^4+8\,c^3\,d+12\,c^2\,d^2+4\,c\,d^3+d^4\right)}{d^4\,{\left(c+d\right)}^5}}","Not used",1,"-((c + d*sin(e + f*x))^(1/2)*((32*a^2*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^(1/2)*(c*d*10i + c^2*1i + d^2*73i))/(315*d^3*f*(c + d)^5) - (32*a^2*exp(e*10i + f*x*10i)*(a + a*sin(e + f*x))^(1/2)*(10*c*d + c^2 + 73*d^2))/(315*d^3*f*(c + d)^5) - (32*a^2*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^(1/2)*(25*c^4 - 25*c^3*d - 15*c*d^3 + 6*d^4 + 57*c^2*d^2))/(5*d^5*f*(c + d)^5) + (32*a^2*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^(1/2)*(c^4*25i - c^3*d*25i - c*d^3*15i + d^4*6i + c^2*d^2*57i))/(5*d^5*f*(c + d)^5) - (16*a^2*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^(1/2)*(194*c*d^3 + 318*c^3*d + 25*c^4 - 5*d^4 - 20*c^2*d^2))/(15*d^5*f*(c + d)^5) + (16*a^2*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^(1/2)*(c*d^3*194i + c^3*d*318i + c^4*25i - d^4*5i - c^2*d^2*20i))/(15*d^5*f*(c + d)^5) + (16*a^2*exp(e*8i + f*x*8i)*(a + a*sin(e + f*x))^(1/2)*(10*c*d^3 + 70*c^3*d + 7*c^4 + 73*d^4 + 512*c^2*d^2))/(35*d^5*f*(c + d)^5) - (16*a^2*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^(1/2)*(c*d^3*10i + c^3*d*70i + c^4*7i + d^4*73i + c^2*d^2*512i))/(35*d^5*f*(c + d)^5) + (32*a^2*c*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^(1/2)*(10*c*d + c^2 + 73*d^2))/(35*d^4*f*(c + d)^5) - (32*a^2*c*exp(e*9i + f*x*9i)*(a + a*sin(e + f*x))^(1/2)*(c*d*10i + c^2*1i + d^2*73i))/(35*d^4*f*(c + d)^5)))/(exp(e*11i + f*x*11i) - (c*1i + d*1i)^5/(c + d)^5 + (10*exp(e*7i + f*x*7i)*(4*c*d^3 + 8*c^3*d + 8*c^4 + d^4 + 12*c^2*d^2))/d^4 + (5*exp(e*3i + f*x*3i)*(8*c*d^2 + 8*c^2*d + 16*c^3 + d^3))/d^3 - (5*exp(e*9i + f*x*9i)*(2*c*d + 8*c^2 + d^2))/d^2 - (2*exp(e*5i + f*x*5i)*(30*c*d^4 + 40*c^4*d + 16*c^5 + 5*d^5 + 60*c^2*d^3 + 80*c^3*d^2))/d^5 - (exp(e*1i + f*x*1i)*(10*c + d))/d - (5*exp(e*8i + f*x*8i)*(c*1i + d*1i)^5*(8*c*d^2 + 8*c^2*d + 16*c^3 + d^3))/(d^3*(c + d)^5) + (5*exp(e*2i + f*x*2i)*(c*1i + d*1i)^5*(2*c*d + 8*c^2 + d^2))/(d^2*(c + d)^5) + (2*exp(e*6i + f*x*6i)*(c*1i + d*1i)^5*(30*c*d^4 + 40*c^4*d + 16*c^5 + 5*d^5 + 60*c^2*d^3 + 80*c^3*d^2))/(d^5*(c + d)^5) + (exp(e*10i + f*x*10i)*(10*c + d)*(c*1i + d*1i)^5)/(d*(c + d)^5) - (10*exp(e*4i + f*x*4i)*(c*1i + d*1i)^5*(4*c*d^3 + 8*c^3*d + 8*c^4 + d^4 + 12*c^2*d^2))/(d^4*(c + d)^5))","B"
588,0,-1,249,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(1/2), x)","F"
589,0,-1,188,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(1/2), x)","F"
590,0,-1,141,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(1/2), x)","F"
591,0,-1,79,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
592,0,-1,131,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
593,0,-1,191,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
594,0,-1,251,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(3/2), x)","F"
595,0,-1,194,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(3/2), x)","F"
596,0,-1,126,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(3/2), x)","F"
597,0,-1,135,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
598,0,-1,197,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
599,0,-1,271,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
600,0,-1,260,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + a*sin(e + f*x))^(5/2), x)","F"
601,0,-1,184,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + a*sin(e + f*x))^(5/2), x)","F"
602,0,-1,191,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + a*sin(e + f*x))^(5/2), x)","F"
603,0,-1,201,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
604,0,-1,270,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
605,0,-1,355,0.000000,"\text{Not used}","int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
606,0,-1,129,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
607,0,-1,320,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^3,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^3, x)","F"
608,0,-1,193,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^2,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^2, x)","F"
609,0,-1,117,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x)),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x)), x)","F"
610,0,-1,74,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((a + a*sin(e + f*x))^m, x)","F"
611,0,-1,100,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x)),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x)), x)","F"
612,0,-1,100,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^2,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^2, x)","F"
613,0,-1,100,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^3,x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^3, x)","F"
614,0,-1,138,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(5/2), x)","F"
615,0,-1,136,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2), x)","F"
616,0,-1,131,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2), x)","F"
617,0,-1,131,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(1/2), x)","F"
618,0,-1,138,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(3/2), x)","F"
619,0,-1,138,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(5/2), x)","F"
620,0,-1,62,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(5*sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(5\,\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(5*sin(e + f*x) + 3)^(m + 1), x)","F"
621,0,-1,64,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(4*sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(4\,\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(4*sin(e + f*x) + 3)^(m + 1), x)","F"
622,1,41,28,0.432292,"\text{Not used}","int((sin(e + f*x) + 1)^m/(3*sin(e + f*x) + 3)^(m + 1),x)","\frac{\frac{1}{3^{m+1}}\,\left(-\cos\left(e+f\,x\right)+\sin\left(e+f\,x\right)\,1{}\mathrm{i}+1{}\mathrm{i}\right)}{f\,\left(\sin\left(e+f\,x\right)+1\right)}","Not used",1,"(1/3^(m + 1)*(sin(e + f*x)*1i - cos(e + f*x) + 1i))/(f*(sin(e + f*x) + 1))","B"
623,0,-1,122,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(2*sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(2\,\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(2*sin(e + f*x) + 3)^(m + 1), x)","F"
624,0,-1,106,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(sin(e + f*x) + 3)^(m + 1), x)","F"
625,0,-1,65,0.000000,"\text{Not used}","int(1/3^(m + 1)*(sin(e + f*x) + 1)^m,x)","\int \frac{1}{3^{m+1}}\,{\left(\sin\left(e+f\,x\right)+1\right)}^m \,d x","Not used",1,"int(1/3^(m + 1)*(sin(e + f*x) + 1)^m, x)","F"
626,0,-1,94,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(3 - sin(e + f*x))^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(3-\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(3 - sin(e + f*x))^(m + 1), x)","F"
627,0,-1,114,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(3 - 2*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(3-2\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(3 - 2*sin(e + f*x))^(m + 1), x)","F"
628,1,43,43,7.848787,"\text{Not used}","int((sin(e + f*x) + 1)^m/(3 - 3*sin(e + f*x))^(m + 1),x)","\frac{\cos\left(e+f\,x\right)\,{\left(\sin\left(e+f\,x\right)+1\right)}^m}{f\,\left(2\,m+1\right)\,{\left(3-3\,\sin\left(e+f\,x\right)\right)}^{m+1}}","Not used",1,"(cos(e + f*x)*(sin(e + f*x) + 1)^m)/(f*(2*m + 1)*(3 - 3*sin(e + f*x))^(m + 1))","B"
629,0,-1,83,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(3 - 4*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(3-4\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(3 - 4*sin(e + f*x))^(m + 1), x)","F"
630,0,-1,78,0.000000,"\text{Not used}","int((sin(e + f*x) + 1)^m/(3 - 5*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(\sin\left(e+f\,x\right)+1\right)}^m}{{\left(3-5\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((sin(e + f*x) + 1)^m/(3 - 5*sin(e + f*x))^(m + 1), x)","F"
631,0,-1,81,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(5*sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(5\,\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(5*sin(e + f*x) + 3)^(m + 1), x)","F"
632,0,-1,83,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(4*sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(4\,\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(4*sin(e + f*x) + 3)^(m + 1), x)","F"
633,1,52,39,0.426393,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3*sin(e + f*x) + 3)^(m + 1),x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(-\cos\left(e+f\,x\right)+\sin\left(e+f\,x\right)\,1{}\mathrm{i}+1{}\mathrm{i}\right)}{f\,{\left(3\,\sin\left(e+f\,x\right)+3\right)}^{m+1}}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(sin(e + f*x)*1i - cos(e + f*x) + 1i))/(f*(3*sin(e + f*x) + 3)^(m + 1))","B"
634,0,-1,83,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(2*sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(2\,\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(2*sin(e + f*x) + 3)^(m + 1), x)","F"
635,0,-1,81,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(sin(e + f*x) + 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(\sin\left(e+f\,x\right)+3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(sin(e + f*x) + 3)^(m + 1), x)","F"
636,0,-1,81,0.000000,"\text{Not used}","int(1/3^(m + 1)*(a + a*sin(e + f*x))^m,x)","\int \frac{1}{3^{m+1}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(1/3^(m + 1)*(a + a*sin(e + f*x))^m, x)","F"
637,0,-1,72,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3 - sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(3-\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(3 - sin(e + f*x))^(m + 1), x)","F"
638,0,-1,77,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3 - 2*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(3-2\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(3 - 2*sin(e + f*x))^(m + 1), x)","F"
639,1,45,45,0.371207,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3 - 3*sin(e + f*x))^(m + 1),x)","\frac{\cos\left(e+f\,x\right)\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m}{f\,\left(2\,m+1\right)\,{\left(3-3\,\sin\left(e+f\,x\right)\right)}^{m+1}}","Not used",1,"(cos(e + f*x)*(a*(sin(e + f*x) + 1))^m)/(f*(2*m + 1)*(3 - 3*sin(e + f*x))^(m + 1))","B"
640,0,-1,115,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3 - 4*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(3-4\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(3 - 4*sin(e + f*x))^(m + 1), x)","F"
641,0,-1,113,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3 - 5*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(3-5\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(3 - 5*sin(e + f*x))^(m + 1), x)","F"
642,0,-1,72,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(5*sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(5\,\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(5*sin(e + f*x) - 3)^(m + 1), x)","F"
643,0,-1,77,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(4*sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(4\,\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(4*sin(e + f*x) - 3)^(m + 1), x)","F"
644,1,45,45,7.828969,"\text{Not used}","int((a + a*sin(e + f*x))^m/(3*sin(e + f*x) - 3)^(m + 1),x)","\frac{\cos\left(e+f\,x\right)\,{\left(\frac{a\,\left(\sin\left(e+f\,x\right)+1\right)}{3}\right)}^m}{3\,f\,\left(2\,m+1\right)\,{\left(\sin\left(e+f\,x\right)-1\right)}^{m+1}}","Not used",1,"(cos(e + f*x)*((a*(sin(e + f*x) + 1))/3)^m)/(3*f*(2*m + 1)*(sin(e + f*x) - 1)^(m + 1))","B"
645,0,-1,117,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(2*sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(2\,\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(2*sin(e + f*x) - 3)^(m + 1), x)","F"
646,0,-1,116,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(sin(e + f*x) - 3)^(m + 1), x)","F"
647,0,-1,81,0.000000,"\text{Not used}","int(1/(-3)^(m + 1)*(a + a*sin(e + f*x))^m,x)","\int \frac{1}{{\left(-3\right)}^{m+1}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(1/(-3)^(m + 1)*(a + a*sin(e + f*x))^m, x)","F"
648,0,-1,119,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(- sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(-\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(- sin(e + f*x) - 3)^(m + 1), x)","F"
649,0,-1,119,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(- 2*sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(-2\,\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(- 2*sin(e + f*x) - 3)^(m + 1), x)","F"
650,1,52,39,0.394003,"\text{Not used}","int((a + a*sin(e + f*x))^m/(- 3*sin(e + f*x) - 3)^(m + 1),x)","\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(-\cos\left(e+f\,x\right)+\sin\left(e+f\,x\right)\,1{}\mathrm{i}+1{}\mathrm{i}\right)}{f\,{\left(-3\,\sin\left(e+f\,x\right)-3\right)}^{m+1}}","Not used",1,"((a*(sin(e + f*x) + 1))^m*(sin(e + f*x)*1i - cos(e + f*x) + 1i))/(f*(- 3*sin(e + f*x) - 3)^(m + 1))","B"
651,0,-1,117,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(- 4*sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(-4\,\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(- 4*sin(e + f*x) - 3)^(m + 1), x)","F"
652,0,-1,115,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(- 5*sin(e + f*x) - 3)^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(-5\,\sin\left(e+f\,x\right)-3\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(- 5*sin(e + f*x) - 3)^(m + 1), x)","F"
653,0,-1,116,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(d*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(d\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(d*sin(e + f*x))^(m + 1), x)","F"
654,0,-1,129,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int((a + a*sin(e + f*x))^m/(c + d*sin(e + f*x))^(m + 1), x)","F"
655,0,-1,107,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^n, x)","F"
656,0,-1,107,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n, x)","F"
657,0,-1,105,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
658,0,-1,104,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n,x)","\int {\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((c + d*sin(e + f*x))^n, x)","F"
659,0,-1,107,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x)),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x)), x)","F"
660,0,-1,109,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^2, x)","F"
661,0,-1,109,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^3, x)","F"
662,0,-1,257,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^n, x)","F"
663,0,-1,160,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^n, x)","F"
664,0,-1,85,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^n,x)","\int \sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^n, x)","F"
665,0,-1,99,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(1/2), x)","F"
666,0,-1,104,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(3/2), x)","F"
667,0,-1,104,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^n/(a + a*sin(e + f*x))^(5/2), x)","F"
668,0,-1,107,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(1/3),x)","\int \left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{1/3} \,d x","Not used",1,"int((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^(1/3), x)","F"
669,0,-1,107,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(1/3),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(1/3), x)","F"
670,0,-1,112,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(4/3),x)","\int \frac{a+a\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((a + a*sin(e + f*x))/(c + d*sin(e + f*x))^(4/3), x)","F"
671,1,183,171,8.080426,"\text{Not used}","int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^3,x)","\frac{2\,a\,d^3\,\cos\left(3\,e+3\,f\,x\right)-6\,b\,d^3\,\sin\left(2\,e+2\,f\,x\right)+\frac{3\,b\,d^3\,\sin\left(4\,e+4\,f\,x\right)}{4}-18\,a\,d^3\,\cos\left(e+f\,x\right)-24\,b\,c^3\,\cos\left(e+f\,x\right)-72\,a\,c^2\,d\,\cos\left(e+f\,x\right)-54\,b\,c\,d^2\,\cos\left(e+f\,x\right)+24\,a\,c^3\,f\,x+9\,b\,d^3\,f\,x+6\,b\,c\,d^2\,\cos\left(3\,e+3\,f\,x\right)-18\,a\,c\,d^2\,\sin\left(2\,e+2\,f\,x\right)-18\,b\,c^2\,d\,\sin\left(2\,e+2\,f\,x\right)+36\,a\,c\,d^2\,f\,x+36\,b\,c^2\,d\,f\,x}{24\,f}","Not used",1,"(2*a*d^3*cos(3*e + 3*f*x) - 6*b*d^3*sin(2*e + 2*f*x) + (3*b*d^3*sin(4*e + 4*f*x))/4 - 18*a*d^3*cos(e + f*x) - 24*b*c^3*cos(e + f*x) - 72*a*c^2*d*cos(e + f*x) - 54*b*c*d^2*cos(e + f*x) + 24*a*c^3*f*x + 9*b*d^3*f*x + 6*b*c*d^2*cos(3*e + 3*f*x) - 18*a*c*d^2*sin(2*e + 2*f*x) - 18*b*c^2*d*sin(2*e + 2*f*x) + 36*a*c*d^2*f*x + 36*b*c^2*d*f*x)/(24*f)","B"
672,1,108,106,7.894183,"\text{Not used}","int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^2,x)","-\frac{\frac{3\,a\,d^2\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{b\,d^2\,\cos\left(3\,e+3\,f\,x\right)}{2}+6\,b\,c^2\,\cos\left(e+f\,x\right)+\frac{9\,b\,d^2\,\cos\left(e+f\,x\right)}{2}+3\,b\,c\,d\,\sin\left(2\,e+2\,f\,x\right)-6\,a\,c^2\,f\,x-3\,a\,d^2\,f\,x+12\,a\,c\,d\,\cos\left(e+f\,x\right)-6\,b\,c\,d\,f\,x}{6\,f}","Not used",1,"-((3*a*d^2*sin(2*e + 2*f*x))/2 - (b*d^2*cos(3*e + 3*f*x))/2 + 6*b*c^2*cos(e + f*x) + (9*b*d^2*cos(e + f*x))/2 + 3*b*c*d*sin(2*e + 2*f*x) - 6*a*c^2*f*x - 3*a*d^2*f*x + 12*a*c*d*cos(e + f*x) - 6*b*c*d*f*x)/(6*f)","B"
673,1,52,53,7.720359,"\text{Not used}","int((a + b*sin(e + f*x))*(c + d*sin(e + f*x)),x)","a\,c\,x+\frac{b\,d\,x}{2}-\frac{a\,d\,\cos\left(e+f\,x\right)}{f}-\frac{b\,c\,\cos\left(e+f\,x\right)}{f}-\frac{b\,d\,\sin\left(2\,e+2\,f\,x\right)}{4\,f}","Not used",1,"a*c*x + (b*d*x)/2 - (a*d*cos(e + f*x))/f - (b*c*cos(e + f*x))/f - (b*d*sin(2*e + 2*f*x))/(4*f)","B"
674,1,25,16,7.635876,"\text{Not used}","int(a + b*sin(e + f*x),x)","a\,x-\frac{2\,b}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x - (2*b)/(f*(tan(e/2 + (f*x)/2)^2 + 1))","B"
675,1,342,65,9.682738,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x)),x)","\frac{2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{d\,f}+\frac{c\,\left(b\,\ln\left(\frac{d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}-b\,\ln\left(\frac{d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{d^2-c^2}\right)-a\,d\,\ln\left(\frac{d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}+a\,d\,\ln\left(\frac{d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{d^2-c^2}}{d\,f\,\left(c^2-d^2\right)}","Not used",1,"(2*b*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(d*f) + (c*(b*log((d*cos(e/2 + (f*x)/2) + c*sin(e/2 + (f*x)/2) - cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2))/cos(e/2 + (f*x)/2))*(-(c + d)*(c - d))^(1/2) - b*log((d*cos(e/2 + (f*x)/2) + c*sin(e/2 + (f*x)/2) + cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2))/cos(e/2 + (f*x)/2))*(d^2 - c^2)^(1/2)) - a*d*log((d*cos(e/2 + (f*x)/2) + c*sin(e/2 + (f*x)/2) - cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2))/cos(e/2 + (f*x)/2))*(-(c + d)*(c - d))^(1/2) + a*d*log((d*cos(e/2 + (f*x)/2) + c*sin(e/2 + (f*x)/2) + cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2))/cos(e/2 + (f*x)/2))*(d^2 - c^2)^(1/2))/(d*f*(c^2 - d^2))","B"
676,1,214,98,7.919885,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(a\,d-b\,c\right)}{c^2-d^2}+\frac{2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,d-b\,c\right)}{c\,\left(c^2-d^2\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}+\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{2\,\left(c^2\,d-d^3\right)\,\left(a\,c-b\,d\right)}{{\left(c+d\right)}^{3/2}\,\left(c^2-d^2\right)\,{\left(c-d\right)}^{3/2}}+\frac{2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c-b\,d\right)}{{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{3/2}}\right)\,\left(c^2-d^2\right)}{2\,\left(a\,c-b\,d\right)}\right)\,\left(a\,c-b\,d\right)}{f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{3/2}}","Not used",1,"((2*(a*d - b*c))/(c^2 - d^2) + (2*d*tan(e/2 + (f*x)/2)*(a*d - b*c))/(c*(c^2 - d^2)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2)) + (2*atan((((2*(c^2*d - d^3)*(a*c - b*d))/((c + d)^(3/2)*(c^2 - d^2)*(c - d)^(3/2)) + (2*c*tan(e/2 + (f*x)/2)*(a*c - b*d))/((c + d)^(3/2)*(c - d)^(3/2)))*(c^2 - d^2))/(2*(a*c - b*d)))*(a*c - b*d))/(f*(c + d)^(3/2)*(c - d)^(3/2))","B"
677,1,477,164,9.607876,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,c^4\,d-4\,c^2\,d^3+2\,d^5\right)\,\left(2\,a\,c^2-3\,b\,c\,d+a\,d^2\right)}{2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{5/2}\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a\,c^2-3\,b\,c\,d+a\,d^2\right)}{{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{5/2}}\right)\,\left(c^4-2\,c^2\,d^2+d^4\right)}{2\,a\,c^2-3\,b\,c\,d+a\,d^2}\right)\,\left(2\,a\,c^2-3\,b\,c\,d+a\,d^2\right)}{f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{2\,b\,c^3-4\,a\,c^2\,d+b\,c\,d^2+a\,d^3}{c^4-2\,c^2\,d^2+d^4}+\frac{d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,b\,c^3-5\,a\,c^2\,d+2\,a\,d^3\right)}{c\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,b\,c^3-11\,a\,c^2\,d+4\,b\,c\,d^2+2\,a\,d^3\right)}{c\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(2\,b\,c^3-4\,a\,c^2\,d+b\,c\,d^2+a\,d^3\right)}{c^2\,\left(c^4-2\,c^2\,d^2+d^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}","Not used",1,"(atan(((((2*c^4*d + 2*d^5 - 4*c^2*d^3)*(2*a*c^2 + a*d^2 - 3*b*c*d))/(2*(c + d)^(5/2)*(c - d)^(5/2)*(c^4 + d^4 - 2*c^2*d^2)) + (c*tan(e/2 + (f*x)/2)*(2*a*c^2 + a*d^2 - 3*b*c*d))/((c + d)^(5/2)*(c - d)^(5/2)))*(c^4 + d^4 - 2*c^2*d^2))/(2*a*c^2 + a*d^2 - 3*b*c*d))*(2*a*c^2 + a*d^2 - 3*b*c*d))/(f*(c + d)^(5/2)*(c - d)^(5/2)) - ((a*d^3 + 2*b*c^3 - 4*a*c^2*d + b*c*d^2)/(c^4 + d^4 - 2*c^2*d^2) + (d*tan(e/2 + (f*x)/2)^3*(2*a*d^3 + 3*b*c^3 - 5*a*c^2*d))/(c*(c^4 + d^4 - 2*c^2*d^2)) + (d*tan(e/2 + (f*x)/2)*(2*a*d^3 + 5*b*c^3 - 11*a*c^2*d + 4*b*c*d^2))/(c*(c^4 + d^4 - 2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(a*d^3 + 2*b*c^3 - 4*a*c^2*d + b*c*d^2))/(c^2*(c^4 + d^4 - 2*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2)))","B"
678,1,358,314,8.443688,"\text{Not used}","int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^3,x)","-\frac{90\,a^2\,d^3\,\cos\left(e+f\,x\right)+75\,b^2\,d^3\,\cos\left(e+f\,x\right)-10\,a^2\,d^3\,\cos\left(3\,e+3\,f\,x\right)-\frac{25\,b^2\,d^3\,\cos\left(3\,e+3\,f\,x\right)}{2}+\frac{3\,b^2\,d^3\,\cos\left(5\,e+5\,f\,x\right)}{2}+30\,b^2\,c^3\,\sin\left(2\,e+2\,f\,x\right)-30\,b^2\,c^2\,d\,\cos\left(3\,e+3\,f\,x\right)+90\,a^2\,c\,d^2\,\sin\left(2\,e+2\,f\,x\right)+90\,b^2\,c\,d^2\,\sin\left(2\,e+2\,f\,x\right)-\frac{45\,b^2\,c\,d^2\,\sin\left(4\,e+4\,f\,x\right)}{4}+240\,a\,b\,c^3\,\cos\left(e+f\,x\right)+360\,a^2\,c^2\,d\,\cos\left(e+f\,x\right)+270\,b^2\,c^2\,d\,\cos\left(e+f\,x\right)+60\,a\,b\,d^3\,\sin\left(2\,e+2\,f\,x\right)-\frac{15\,a\,b\,d^3\,\sin\left(4\,e+4\,f\,x\right)}{2}-120\,a^2\,c^3\,f\,x-60\,b^2\,c^3\,f\,x-60\,a\,b\,c\,d^2\,\cos\left(3\,e+3\,f\,x\right)+180\,a\,b\,c^2\,d\,\sin\left(2\,e+2\,f\,x\right)-180\,a^2\,c\,d^2\,f\,x-135\,b^2\,c\,d^2\,f\,x+540\,a\,b\,c\,d^2\,\cos\left(e+f\,x\right)-90\,a\,b\,d^3\,f\,x-360\,a\,b\,c^2\,d\,f\,x}{120\,f}","Not used",1,"-(90*a^2*d^3*cos(e + f*x) + 75*b^2*d^3*cos(e + f*x) - 10*a^2*d^3*cos(3*e + 3*f*x) - (25*b^2*d^3*cos(3*e + 3*f*x))/2 + (3*b^2*d^3*cos(5*e + 5*f*x))/2 + 30*b^2*c^3*sin(2*e + 2*f*x) - 30*b^2*c^2*d*cos(3*e + 3*f*x) + 90*a^2*c*d^2*sin(2*e + 2*f*x) + 90*b^2*c*d^2*sin(2*e + 2*f*x) - (45*b^2*c*d^2*sin(4*e + 4*f*x))/4 + 240*a*b*c^3*cos(e + f*x) + 360*a^2*c^2*d*cos(e + f*x) + 270*b^2*c^2*d*cos(e + f*x) + 60*a*b*d^3*sin(2*e + 2*f*x) - (15*a*b*d^3*sin(4*e + 4*f*x))/2 - 120*a^2*c^3*f*x - 60*b^2*c^3*f*x - 60*a*b*c*d^2*cos(3*e + 3*f*x) + 180*a*b*c^2*d*sin(2*e + 2*f*x) - 180*a^2*c*d^2*f*x - 135*b^2*c*d^2*f*x + 540*a*b*c*d^2*cos(e + f*x) - 90*a*b*d^3*f*x - 360*a*b*c^2*d*f*x)/(120*f)","B"
679,1,221,217,8.139746,"\text{Not used}","int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^2,x)","-\frac{6\,a^2\,d^2\,\sin\left(2\,e+2\,f\,x\right)+6\,b^2\,c^2\,\sin\left(2\,e+2\,f\,x\right)+6\,b^2\,d^2\,\sin\left(2\,e+2\,f\,x\right)-\frac{3\,b^2\,d^2\,\sin\left(4\,e+4\,f\,x\right)}{4}+48\,a\,b\,c^2\,\cos\left(e+f\,x\right)+36\,a\,b\,d^2\,\cos\left(e+f\,x\right)+48\,a^2\,c\,d\,\cos\left(e+f\,x\right)+36\,b^2\,c\,d\,\cos\left(e+f\,x\right)-4\,a\,b\,d^2\,\cos\left(3\,e+3\,f\,x\right)-4\,b^2\,c\,d\,\cos\left(3\,e+3\,f\,x\right)-24\,a^2\,c^2\,f\,x-12\,a^2\,d^2\,f\,x-12\,b^2\,c^2\,f\,x-9\,b^2\,d^2\,f\,x+24\,a\,b\,c\,d\,\sin\left(2\,e+2\,f\,x\right)-48\,a\,b\,c\,d\,f\,x}{24\,f}","Not used",1,"-(6*a^2*d^2*sin(2*e + 2*f*x) + 6*b^2*c^2*sin(2*e + 2*f*x) + 6*b^2*d^2*sin(2*e + 2*f*x) - (3*b^2*d^2*sin(4*e + 4*f*x))/4 + 48*a*b*c^2*cos(e + f*x) + 36*a*b*d^2*cos(e + f*x) + 48*a^2*c*d*cos(e + f*x) + 36*b^2*c*d*cos(e + f*x) - 4*a*b*d^2*cos(3*e + 3*f*x) - 4*b^2*c*d*cos(3*e + 3*f*x) - 24*a^2*c^2*f*x - 12*a^2*d^2*f*x - 12*b^2*c^2*f*x - 9*b^2*d^2*f*x + 24*a*b*c*d*sin(2*e + 2*f*x) - 48*a*b*c*d*f*x)/(24*f)","B"
680,1,108,107,7.765423,"\text{Not used}","int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x)),x)","-\frac{\frac{3\,b^2\,c\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{b^2\,d\,\cos\left(3\,e+3\,f\,x\right)}{2}+6\,a^2\,d\,\cos\left(e+f\,x\right)+\frac{9\,b^2\,d\,\cos\left(e+f\,x\right)}{2}+3\,a\,b\,d\,\sin\left(2\,e+2\,f\,x\right)-6\,a^2\,c\,f\,x-3\,b^2\,c\,f\,x+12\,a\,b\,c\,\cos\left(e+f\,x\right)-6\,a\,b\,d\,f\,x}{6\,f}","Not used",1,"-((3*b^2*c*sin(2*e + 2*f*x))/2 - (b^2*d*cos(3*e + 3*f*x))/2 + 6*a^2*d*cos(e + f*x) + (9*b^2*d*cos(e + f*x))/2 + 3*a*b*d*sin(2*e + 2*f*x) - 6*a^2*c*f*x - 3*b^2*c*f*x + 12*a*b*c*cos(e + f*x) - 6*a*b*d*f*x)/(6*f)","B"
681,1,44,50,7.610811,"\text{Not used}","int((a + b*sin(e + f*x))^2,x)","-\frac{\frac{b^2\,\sin\left(2\,e+2\,f\,x\right)}{2}+4\,a\,b\,\cos\left(e+f\,x\right)-2\,a^2\,f\,x-b^2\,f\,x}{2\,f}","Not used",1,"-((b^2*sin(2*e + 2*f*x))/2 + 4*a*b*cos(e + f*x) - 2*a^2*f*x - b^2*f*x)/(2*f)","B"
682,1,2629,93,12.431821,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x)),x)","\frac{2\,b\,\mathrm{atan}\left(\frac{64\,b^6\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{-128\,a^5\,b\,c\,d^3+576\,a^4\,b^2\,c^2\,d^2-512\,a^3\,b^3\,c^3\,d-512\,a^3\,b^3\,c\,d^3+128\,a^2\,b^4\,c^4+768\,a^2\,b^4\,c^2\,d^2-384\,a\,b^5\,c^3\,d+64\,b^6\,c^4}+\frac{384\,a\,b^5\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{384\,a\,b^5\,c^3+512\,a^3\,b^3\,c^3-\frac{64\,b^6\,c^4}{d}-768\,a^2\,b^4\,c^2\,d+512\,a^3\,b^3\,c\,d^2-576\,a^4\,b^2\,c^2\,d-\frac{128\,a^2\,b^4\,c^4}{d}+128\,a^5\,b\,c\,d^2}+\frac{768\,a^2\,b^4\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{768\,a^2\,b^4\,c^2+576\,a^4\,b^2\,c^2+\frac{64\,b^6\,c^4}{d^2}-\frac{384\,a\,b^5\,c^3}{d}-128\,a^5\,b\,c\,d-\frac{512\,a^3\,b^3\,c^3}{d}+\frac{128\,a^2\,b^4\,c^4}{d^2}-512\,a^3\,b^3\,c\,d}+\frac{576\,a^4\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{768\,a^2\,b^4\,c^2+576\,a^4\,b^2\,c^2+\frac{64\,b^6\,c^4}{d^2}-\frac{384\,a\,b^5\,c^3}{d}-128\,a^5\,b\,c\,d-\frac{512\,a^3\,b^3\,c^3}{d}+\frac{128\,a^2\,b^4\,c^4}{d^2}-512\,a^3\,b^3\,c\,d}+\frac{512\,a^3\,b^3\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{384\,a\,b^5\,c^3+512\,a^3\,b^3\,c^3-\frac{64\,b^6\,c^4}{d}-768\,a^2\,b^4\,c^2\,d+512\,a^3\,b^3\,c\,d^2-576\,a^4\,b^2\,c^2\,d-\frac{128\,a^2\,b^4\,c^4}{d}+128\,a^5\,b\,c\,d^2}+\frac{128\,a^2\,b^4\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{-128\,a^5\,b\,c\,d^3+576\,a^4\,b^2\,c^2\,d^2-512\,a^3\,b^3\,c^3\,d-512\,a^3\,b^3\,c\,d^3+128\,a^2\,b^4\,c^4+768\,a^2\,b^4\,c^2\,d^2-384\,a\,b^5\,c^3\,d+64\,b^6\,c^4}-\frac{128\,a^5\,b\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{768\,a^2\,b^4\,c^2+576\,a^4\,b^2\,c^2+\frac{64\,b^6\,c^4}{d^2}-\frac{384\,a\,b^5\,c^3}{d}-128\,a^5\,b\,c\,d-\frac{512\,a^3\,b^3\,c^3}{d}+\frac{128\,a^2\,b^4\,c^4}{d^2}-512\,a^3\,b^3\,c\,d}-\frac{512\,a^3\,b^3\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{768\,a^2\,b^4\,c^2+576\,a^4\,b^2\,c^2+\frac{64\,b^6\,c^4}{d^2}-\frac{384\,a\,b^5\,c^3}{d}-128\,a^5\,b\,c\,d-\frac{512\,a^3\,b^3\,c^3}{d}+\frac{128\,a^2\,b^4\,c^4}{d^2}-512\,a^3\,b^3\,c\,d}\right)\,\left(2\,a\,d-b\,c\right)}{d^2\,f}-\frac{2\,b^2}{d\,f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(4\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}{d^2}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+10\,a^2\,b^2\,c^3\,d^3-8\,a^2\,b^2\,c\,d^5-8\,a\,b^3\,c^4\,d^2+8\,a\,b^3\,c^2\,d^4+2\,b^4\,c^5\,d-2\,b^4\,c^3\,d^3\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,c^2\,d^4-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4\right)}{d^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c\,d^6-4\,a\,b\,c^2\,d^5+2\,b^2\,c^3\,d^4\right)}{d^3}+\frac{\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2}{d^4-c^2\,d^2}\right)}{d^4-c^2\,d^2}\right)\,1{}\mathrm{i}}{d^4-c^2\,d^2}-\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+10\,a^2\,b^2\,c^3\,d^3-8\,a^2\,b^2\,c\,d^5-8\,a\,b^3\,c^4\,d^2+8\,a\,b^3\,c^2\,d^4+2\,b^4\,c^5\,d-2\,b^4\,c^3\,d^3\right)}{d^3}-\frac{32\,\left(4\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}{d^2}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,c^2\,d^4-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4\right)}{d^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c\,d^6-4\,a\,b\,c^2\,d^5+2\,b^2\,c^3\,d^4\right)}{d^3}-\frac{\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2}{d^4-c^2\,d^2}\right)}{d^4-c^2\,d^2}\right)\,1{}\mathrm{i}}{d^4-c^2\,d^2}}{\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^4\,b^2\,c\,d^4-24\,a^3\,b^3\,c^2\,d^3+26\,a^2\,b^4\,c^3\,d^2-12\,a\,b^5\,c^4\,d+2\,b^6\,c^5\right)}{d^3}-\frac{64\,\left(-2\,a^5\,b\,c\,d^3+5\,a^4\,b^2\,c^2\,d^2-4\,a^3\,b^3\,c^3\,d+a^2\,b^4\,c^4\right)}{d^2}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(4\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}{d^2}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+10\,a^2\,b^2\,c^3\,d^3-8\,a^2\,b^2\,c\,d^5-8\,a\,b^3\,c^4\,d^2+8\,a\,b^3\,c^2\,d^4+2\,b^4\,c^5\,d-2\,b^4\,c^3\,d^3\right)}{d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,c^2\,d^4-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4\right)}{d^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c\,d^6-4\,a\,b\,c^2\,d^5+2\,b^2\,c^3\,d^4\right)}{d^3}+\frac{\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2}{d^4-c^2\,d^2}\right)}{d^4-c^2\,d^2}\right)}{d^4-c^2\,d^2}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+10\,a^2\,b^2\,c^3\,d^3-8\,a^2\,b^2\,c\,d^5-8\,a\,b^3\,c^4\,d^2+8\,a\,b^3\,c^2\,d^4+2\,b^4\,c^5\,d-2\,b^4\,c^3\,d^3\right)}{d^3}-\frac{32\,\left(4\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}{d^2}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,c^2\,d^4-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4\right)}{d^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c\,d^6-4\,a\,b\,c^2\,d^5+2\,b^2\,c^3\,d^4\right)}{d^3}-\frac{\left(32\,c^2\,d^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,c\,d^7-2\,c^3\,d^5\right)}{d^3}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2}{d^4-c^2\,d^2}\right)}{d^4-c^2\,d^2}\right)}{d^4-c^2\,d^2}}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^2\,2{}\mathrm{i}}{f\,\left(d^4-c^2\,d^2\right)}","Not used",1,"(2*b*atan((64*b^6*c^4*tan(e/2 + (f*x)/2))/(64*b^6*c^4 + 128*a^2*b^4*c^4 - 512*a^3*b^3*c*d^3 - 512*a^3*b^3*c^3*d + 768*a^2*b^4*c^2*d^2 + 576*a^4*b^2*c^2*d^2 - 384*a*b^5*c^3*d - 128*a^5*b*c*d^3) + (384*a*b^5*c^3*tan(e/2 + (f*x)/2))/(384*a*b^5*c^3 + 512*a^3*b^3*c^3 - (64*b^6*c^4)/d - 768*a^2*b^4*c^2*d + 512*a^3*b^3*c*d^2 - 576*a^4*b^2*c^2*d - (128*a^2*b^4*c^4)/d + 128*a^5*b*c*d^2) + (768*a^2*b^4*c^2*tan(e/2 + (f*x)/2))/(768*a^2*b^4*c^2 + 576*a^4*b^2*c^2 + (64*b^6*c^4)/d^2 - (384*a*b^5*c^3)/d - 128*a^5*b*c*d - (512*a^3*b^3*c^3)/d + (128*a^2*b^4*c^4)/d^2 - 512*a^3*b^3*c*d) + (576*a^4*b^2*c^2*tan(e/2 + (f*x)/2))/(768*a^2*b^4*c^2 + 576*a^4*b^2*c^2 + (64*b^6*c^4)/d^2 - (384*a*b^5*c^3)/d - 128*a^5*b*c*d - (512*a^3*b^3*c^3)/d + (128*a^2*b^4*c^4)/d^2 - 512*a^3*b^3*c*d) + (512*a^3*b^3*c^3*tan(e/2 + (f*x)/2))/(384*a*b^5*c^3 + 512*a^3*b^3*c^3 - (64*b^6*c^4)/d - 768*a^2*b^4*c^2*d + 512*a^3*b^3*c*d^2 - 576*a^4*b^2*c^2*d - (128*a^2*b^4*c^4)/d + 128*a^5*b*c*d^2) + (128*a^2*b^4*c^4*tan(e/2 + (f*x)/2))/(64*b^6*c^4 + 128*a^2*b^4*c^4 - 512*a^3*b^3*c*d^3 - 512*a^3*b^3*c^3*d + 768*a^2*b^4*c^2*d^2 + 576*a^4*b^2*c^2*d^2 - 384*a*b^5*c^3*d - 128*a^5*b*c*d^3) - (128*a^5*b*c*d*tan(e/2 + (f*x)/2))/(768*a^2*b^4*c^2 + 576*a^4*b^2*c^2 + (64*b^6*c^4)/d^2 - (384*a*b^5*c^3)/d - 128*a^5*b*c*d - (512*a^3*b^3*c^3)/d + (128*a^2*b^4*c^4)/d^2 - 512*a^3*b^3*c*d) - (512*a^3*b^3*c*d*tan(e/2 + (f*x)/2))/(768*a^2*b^4*c^2 + 576*a^4*b^2*c^2 + (64*b^6*c^4)/d^2 - (384*a*b^5*c^3)/d - 128*a^5*b*c*d - (512*a^3*b^3*c^3)/d + (128*a^2*b^4*c^4)/d^2 - 512*a^3*b^3*c*d))*(2*a*d - b*c))/(d^2*f) - (2*b^2)/(d*f*(tan(e/2 + (f*x)/2)^2 + 1)) - (atan((((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 4*a^2*b^2*c^2*d^3))/d^2 - (32*tan(e/2 + (f*x)/2)*(a^4*c*d^5 + 2*b^4*c^5*d - 2*b^4*c^3*d^3 + 8*a*b^3*c^2*d^4 - 8*a*b^3*c^4*d^2 - 8*a^2*b^2*c*d^5 - 4*a^3*b*c^2*d^4 + 10*a^2*b^2*c^3*d^3))/d^3 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*(a^2*c^2*d^4 + b^2*c^2*d^4 - 2*a*b*c*d^5))/d^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*c*d^6 + 2*b^2*c^3*d^4 - 4*a*b*c^2*d^5))/d^3 + ((32*c^2*d^3 + (32*tan(e/2 + (f*x)/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2)/(d^4 - c^2*d^2)))/(d^4 - c^2*d^2))*1i)/(d^4 - c^2*d^2) - ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*tan(e/2 + (f*x)/2)*(a^4*c*d^5 + 2*b^4*c^5*d - 2*b^4*c^3*d^3 + 8*a*b^3*c^2*d^4 - 8*a*b^3*c^4*d^2 - 8*a^2*b^2*c*d^5 - 4*a^3*b*c^2*d^4 + 10*a^2*b^2*c^3*d^3))/d^3 - (32*(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 4*a^2*b^2*c^2*d^3))/d^2 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*(a^2*c^2*d^4 + b^2*c^2*d^4 - 2*a*b*c*d^5))/d^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*c*d^6 + 2*b^2*c^3*d^4 - 4*a*b*c^2*d^5))/d^3 - ((32*c^2*d^3 + (32*tan(e/2 + (f*x)/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2)/(d^4 - c^2*d^2)))/(d^4 - c^2*d^2))*1i)/(d^4 - c^2*d^2))/((64*tan(e/2 + (f*x)/2)*(2*b^6*c^5 + 8*a^4*b^2*c*d^4 + 26*a^2*b^4*c^3*d^2 - 24*a^3*b^3*c^2*d^3 - 12*a*b^5*c^4*d))/d^3 - (64*(a^2*b^4*c^4 - 4*a^3*b^3*c^3*d + 5*a^4*b^2*c^2*d^2 - 2*a^5*b*c*d^3))/d^2 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 4*a^2*b^2*c^2*d^3))/d^2 - (32*tan(e/2 + (f*x)/2)*(a^4*c*d^5 + 2*b^4*c^5*d - 2*b^4*c^3*d^3 + 8*a*b^3*c^2*d^4 - 8*a*b^3*c^4*d^2 - 8*a^2*b^2*c*d^5 - 4*a^3*b*c^2*d^4 + 10*a^2*b^2*c^3*d^3))/d^3 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*(a^2*c^2*d^4 + b^2*c^2*d^4 - 2*a*b*c*d^5))/d^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*c*d^6 + 2*b^2*c^3*d^4 - 4*a*b*c^2*d^5))/d^3 + ((32*c^2*d^3 + (32*tan(e/2 + (f*x)/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2)/(d^4 - c^2*d^2)))/(d^4 - c^2*d^2)))/(d^4 - c^2*d^2) + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*tan(e/2 + (f*x)/2)*(a^4*c*d^5 + 2*b^4*c^5*d - 2*b^4*c^3*d^3 + 8*a*b^3*c^2*d^4 - 8*a*b^3*c^4*d^2 - 8*a^2*b^2*c*d^5 - 4*a^3*b*c^2*d^4 + 10*a^2*b^2*c^3*d^3))/d^3 - (32*(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 4*a^2*b^2*c^2*d^3))/d^2 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*((32*(a^2*c^2*d^4 + b^2*c^2*d^4 - 2*a*b*c*d^5))/d^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*c*d^6 + 2*b^2*c^3*d^4 - 4*a*b*c^2*d^5))/d^3 - ((32*c^2*d^3 + (32*tan(e/2 + (f*x)/2)*(3*c*d^7 - 2*c^3*d^5))/d^3)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2)/(d^4 - c^2*d^2)))/(d^4 - c^2*d^2)))/(d^4 - c^2*d^2)))*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^2*2i)/(f*(d^4 - c^2*d^2))","B"
683,1,5776,129,15.469325,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{d\,\left(c^2-d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{c\,\left(c^2-d^2\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{b^2\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{b^2\,\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)}{d^2}-\frac{b^2\,\left(\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{b^2\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{b^2\,\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)}{d^2}}{\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,b^4\,c^4\,d^2+2\,a^2\,b^4\,c^2\,d^4+4\,a\,b^5\,c^3\,d^3-4\,a\,b^5\,c\,d^5+2\,b^6\,c^6-6\,b^6\,c^4\,d^2+4\,b^6\,c^2\,d^4\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{64\,\left(a^4\,b^2\,c^3\,d^2-4\,a^3\,b^3\,c^2\,d^3-a^2\,b^4\,c^5+3\,a^2\,b^4\,c^3\,d^2+4\,a^2\,b^4\,c\,d^4+2\,a\,b^5\,c^4\,d-6\,a\,b^5\,c^2\,d^3-b^6\,c^5+2\,b^6\,c^3\,d^2\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{b^2\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{b^2\,\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}+\frac{b^2\,\left(\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{b^2\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{b^2\,\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}}\right)}{d^2\,f}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)\,1{}\mathrm{i}}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}-\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)\,1{}\mathrm{i}}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}}{\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,b^4\,c^4\,d^2+2\,a^2\,b^4\,c^2\,d^4+4\,a\,b^5\,c^3\,d^3-4\,a\,b^5\,c\,d^5+2\,b^6\,c^6-6\,b^6\,c^4\,d^2+4\,b^6\,c^2\,d^4\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{64\,\left(a^4\,b^2\,c^3\,d^2-4\,a^3\,b^3\,c^2\,d^3-a^2\,b^4\,c^5+3\,a^2\,b^4\,c^3\,d^2+4\,a^2\,b^4\,c\,d^4+2\,a\,b^5\,c^4\,d-6\,a\,b^5\,c^2\,d^3-b^6\,c^5+2\,b^6\,c^3\,d^2\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}+\frac{\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,c^3\,d^5-4\,a^3\,b\,c^2\,d^6-2\,a^2\,b^2\,c^5\,d^3+4\,a^2\,b^2\,c^3\,d^5+4\,a^2\,b^2\,c\,d^7+4\,a\,b^3\,c^4\,d^4-8\,a\,b^3\,c^2\,d^6+2\,b^4\,c^7\,d-8\,b^4\,c^5\,d^3+9\,b^4\,c^3\,d^5-2\,b^4\,c\,d^7\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{32\,\left(b^4\,c^6\,d-2\,b^4\,c^4\,d^3+b^4\,c^2\,d^5\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^2\,c^5\,d^4+a^2\,c^3\,d^6+2\,a\,b\,c^4\,d^5-2\,a\,b\,c^2\,d^7-b^2\,c^3\,d^6+b^2\,c\,d^8\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^2\,c^4\,d^6+2\,a^2\,c^2\,d^8+4\,a\,b\,c^3\,d^7-4\,a\,b\,c\,d^9+2\,b^2\,c^6\,d^4-6\,b^2\,c^4\,d^6+4\,b^2\,c^2\,d^8\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}-\frac{\left(\frac{32\,\left(c^6\,d^5-2\,c^4\,d^7+c^2\,d^9\right)}{c^4\,d^2-2\,c^2\,d^4+d^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^5+7\,c^5\,d^7-8\,c^3\,d^9+3\,c\,d^{11}\right)}{c^4\,d^3-2\,c^2\,d^5+d^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}\right)\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)}{-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(b\,c^2+a\,c\,d-2\,b\,d^2\right)\,2{}\mathrm{i}}{f\,\left(-c^6\,d^2+3\,c^4\,d^4-3\,c^2\,d^6+d^8\right)}","Not used",1,"((2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(d*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(c*(c^2 - d^2)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2)) - (2*b^2*atan(((b^2*((b^2*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (b^2*((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*1i)/d^2)*1i)/d^2 - (32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3)))/d^2 - (b^2*((32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (b^2*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) + (b^2*((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*1i)/d^2)*1i)/d^2 - (32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3)))/d^2)/((b^2*((b^2*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (b^2*((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*1i)/d^2)*1i)/d^2 - (32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3))*1i)/d^2 - (64*(2*b^6*c^3*d^2 - a^2*b^4*c^5 - b^6*c^5 - 6*a*b^5*c^2*d^3 + 4*a^2*b^4*c*d^4 + 3*a^2*b^4*c^3*d^2 - 4*a^3*b^3*c^2*d^3 + a^4*b^2*c^3*d^2 + 2*a*b^5*c^4*d))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (b^2*((32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (b^2*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) + (b^2*((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*1i)/d^2)*1i)/d^2 - (32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3))*1i)/d^2 + (64*tan(e/2 + (f*x)/2)*(2*b^6*c^6 + 4*b^6*c^2*d^4 - 6*b^6*c^4*d^2 + 4*a*b^5*c^3*d^3 + 2*a^2*b^4*c^2*d^4 - 2*a^2*b^4*c^4*d^2 - 4*a*b^5*c*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))))/(d^2*f) + (atan((((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) - (32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) + (((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d)*1i)/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2) - ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d)*1i)/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))/((64*tan(e/2 + (f*x)/2)*(2*b^6*c^6 + 4*b^6*c^2*d^4 - 6*b^6*c^4*d^2 + 4*a*b^5*c^3*d^3 + 2*a^2*b^4*c^2*d^4 - 2*a^2*b^4*c^4*d^2 - 4*a*b^5*c*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (64*(2*b^6*c^3*d^2 - a^2*b^4*c^5 - b^6*c^5 - 6*a*b^5*c^2*d^3 + 4*a^2*b^4*c*d^4 + 3*a^2*b^4*c^3*d^2 - 4*a^3*b^3*c^2*d^3 + a^4*b^2*c^3*d^2 + 2*a*b^5*c^4*d))/(d^6 - 2*c^2*d^4 + c^4*d^2) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) - (32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) + (((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*b^4*c^7*d - 2*b^4*c*d^7 + a^4*c^3*d^5 + 9*b^4*c^3*d^5 - 8*b^4*c^5*d^3 - 8*a*b^3*c^2*d^6 + 4*a*b^3*c^4*d^4 + 4*a^2*b^2*c*d^7 - 4*a^3*b*c^2*d^6 + 4*a^2*b^2*c^3*d^5 - 2*a^2*b^2*c^5*d^3))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (32*(b^4*c^6*d + b^4*c^2*d^5 - 2*b^4*c^4*d^3))/(d^6 - 2*c^2*d^4 + c^4*d^2) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(b^2*c*d^8 + a^2*c^3*d^6 - a^2*c^5*d^4 - b^2*c^3*d^6 - 2*a*b*c^2*d^7 + 2*a*b*c^4*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*c^2*d^8 - 2*a^2*c^4*d^6 + 4*b^2*c^2*d^8 - 6*b^2*c^4*d^6 + 2*b^2*c^6*d^4 - 4*a*b*c*d^9 + 4*a*b*c^3*d^7))/(d^7 - 2*c^2*d^5 + c^4*d^3) - (((32*(c^2*d^9 - 2*c^4*d^7 + c^6*d^5))/(d^6 - 2*c^2*d^4 + c^4*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^11 - 8*c^3*d^9 + 7*c^5*d^7 - 2*c^7*d^5))/(d^7 - 2*c^2*d^5 + c^4*d^3))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))*(b*c^2 - 2*b*d^2 + a*c*d))/(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2)))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(b*c^2 - 2*b*d^2 + a*c*d)*2i)/(f*(d^8 - 3*c^2*d^6 + 3*c^4*d^4 - c^6*d^2))","B"
684,1,641,196,10.264755,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,c^4\,d-4\,c^2\,d^3+2\,d^5\right)\,\left(2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2\right)}{2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{5/2}\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2\right)}{{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{5/2}}\right)\,\left(c^4-2\,c^2\,d^2+d^4\right)}{2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2}\right)\,\left(2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2\right)}{f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{-4\,a^2\,c^2\,d+a^2\,d^3+4\,a\,b\,c^3+2\,a\,b\,c\,d^2-3\,b^2\,c^2\,d}{c^4-2\,c^2\,d^2+d^4}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-11\,a^2\,c^2\,d^2+2\,a^2\,d^4+10\,a\,b\,c^3\,d+8\,a\,b\,c\,d^3+b^2\,c^4-10\,b^2\,c^2\,d^2\right)}{c\,\left(c^4-2\,c^2\,d^2+d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(5\,a^2\,c^2\,d^2-2\,a^2\,d^4-6\,a\,b\,c^3\,d+b^2\,c^4+2\,b^2\,c^2\,d^2\right)}{c\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(-4\,a^2\,c^2\,d+a^2\,d^3+4\,a\,b\,c^3+2\,a\,b\,c\,d^2-3\,b^2\,c^2\,d\right)}{c^2\,\left(c^4-2\,c^2\,d^2+d^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}","Not used",1,"(atan(((((2*c^4*d + 2*d^5 - 4*c^2*d^3)*(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))/(2*(c + d)^(5/2)*(c - d)^(5/2)*(c^4 + d^4 - 2*c^2*d^2)) + (c*tan(e/2 + (f*x)/2)*(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))/((c + d)^(5/2)*(c - d)^(5/2)))*(c^4 + d^4 - 2*c^2*d^2))/(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))*(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))/(f*(c + d)^(5/2)*(c - d)^(5/2)) - ((a^2*d^3 - 4*a^2*c^2*d - 3*b^2*c^2*d + 4*a*b*c^3 + 2*a*b*c*d^2)/(c^4 + d^4 - 2*c^2*d^2) + (tan(e/2 + (f*x)/2)*(2*a^2*d^4 + b^2*c^4 - 11*a^2*c^2*d^2 - 10*b^2*c^2*d^2 + 8*a*b*c*d^3 + 10*a*b*c^3*d))/(c*(c^4 + d^4 - 2*c^2*d^2)) - (tan(e/2 + (f*x)/2)^3*(b^2*c^4 - 2*a^2*d^4 + 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(c*(c^4 + d^4 - 2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(a^2*d^3 - 4*a^2*c^2*d - 3*b^2*c^2*d + 4*a*b*c^3 + 2*a*b*c*d^2))/(c^2*(c^4 + d^4 - 2*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2)))","B"
685,1,1220,305,11.155337,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^4,x)","\frac{\frac{18\,a^2\,c^4\,d-5\,a^2\,c^2\,d^3+2\,a^2\,d^5-12\,a\,b\,c^5-20\,a\,b\,c^3\,d^2+2\,a\,b\,c\,d^4+13\,b^2\,c^4\,d+2\,b^2\,c^2\,d^3}{3\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a^2\,c^6\,d+27\,a^2\,c^4\,d^3-12\,a^2\,c^2\,d^5+4\,a^2\,d^7-4\,a\,b\,c^7-28\,a\,b\,c^5\,d^2-22\,a\,b\,c^3\,d^4+4\,a\,b\,c\,d^6+5\,b^2\,c^6\,d+20\,b^2\,c^4\,d^3\right)}{c^2\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(27\,a^2\,c^4\,d^2-4\,a^2\,c^2\,d^4+2\,a^2\,d^6-16\,a\,b\,c^5\,d-38\,a\,b\,c^3\,d^3+4\,a\,b\,c\,d^5-b^2\,c^6+22\,b^2\,c^4\,d^2+4\,b^2\,c^2\,d^4\right)}{c\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,a^2\,c^6\,d+20\,a^2\,c^4\,d^3-3\,a^2\,c^2\,d^5+2\,a^2\,d^7-4\,a\,b\,c^7-20\,a\,b\,c^5\,d^2-28\,a\,b\,c^3\,d^4+2\,a\,b\,c\,d^6+4\,b^2\,c^6\,d+17\,b^2\,c^4\,d^3+4\,b^2\,c^2\,d^5\right)}{c^2\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(9\,a^2\,c^4\,d^2-6\,a^2\,c^2\,d^4+2\,a^2\,d^6-8\,a\,b\,c^5\,d-2\,a\,b\,c^3\,d^3+b^2\,c^6+4\,b^2\,c^4\,d^2\right)}{c\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,c^2+2\,d^2\right)\,\left(18\,a^2\,c^4\,d-5\,a^2\,c^2\,d^3+2\,a^2\,d^5-12\,a\,b\,c^5-20\,a\,b\,c^3\,d^2+2\,a\,b\,c\,d^4+13\,b^2\,c^4\,d+2\,b^2\,c^2\,d^3\right)}{3\,c^3\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}}{f\,\left(c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^2\,d+8\,d^3\right)+c^3+6\,c^2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,c^2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}+\frac{\mathrm{atan}\left(\frac{\left(\frac{c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c^3+3\,a^2\,c\,d^2-8\,a\,b\,c^2\,d-2\,a\,b\,d^3+b^2\,c^3+4\,b^2\,c\,d^2\right)}{{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{7/2}}+\frac{\left(2\,c^6\,d-6\,c^4\,d^3+6\,c^2\,d^5-2\,d^7\right)\,\left(2\,a^2\,c^3+3\,a^2\,c\,d^2-8\,a\,b\,c^2\,d-2\,a\,b\,d^3+b^2\,c^3+4\,b^2\,c\,d^2\right)}{2\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{7/2}\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}\right)\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}{2\,a^2\,c^3+3\,a^2\,c\,d^2-8\,a\,b\,c^2\,d-2\,a\,b\,d^3+b^2\,c^3+4\,b^2\,c\,d^2}\right)\,\left(2\,a^2\,c^3+3\,a^2\,c\,d^2-8\,a\,b\,c^2\,d-2\,a\,b\,d^3+b^2\,c^3+4\,b^2\,c\,d^2\right)}{f\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{7/2}}","Not used",1,"((2*a^2*d^5 + 18*a^2*c^4*d + 13*b^2*c^4*d - 5*a^2*c^2*d^3 + 2*b^2*c^2*d^3 - 12*a*b*c^5 + 2*a*b*c*d^4 - 20*a*b*c^3*d^2)/(3*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (tan(e/2 + (f*x)/2)^4*(4*a^2*d^7 + 6*a^2*c^6*d + 5*b^2*c^6*d - 12*a^2*c^2*d^5 + 27*a^2*c^4*d^3 + 20*b^2*c^4*d^3 - 4*a*b*c^7 + 4*a*b*c*d^6 - 22*a*b*c^3*d^4 - 28*a*b*c^5*d^2))/(c^2*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (tan(e/2 + (f*x)/2)*(2*a^2*d^6 - b^2*c^6 - 4*a^2*c^2*d^4 + 27*a^2*c^4*d^2 + 4*b^2*c^2*d^4 + 22*b^2*c^4*d^2 + 4*a*b*c*d^5 - 16*a*b*c^5*d - 38*a*b*c^3*d^3))/(c*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (2*tan(e/2 + (f*x)/2)^2*(2*a^2*d^7 + 6*a^2*c^6*d + 4*b^2*c^6*d - 3*a^2*c^2*d^5 + 20*a^2*c^4*d^3 + 4*b^2*c^2*d^5 + 17*b^2*c^4*d^3 - 4*a*b*c^7 + 2*a*b*c*d^6 - 28*a*b*c^3*d^4 - 20*a*b*c^5*d^2))/(c^2*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (tan(e/2 + (f*x)/2)^5*(2*a^2*d^6 + b^2*c^6 - 6*a^2*c^2*d^4 + 9*a^2*c^4*d^2 + 4*b^2*c^4*d^2 - 8*a*b*c^5*d - 2*a*b*c^3*d^3))/(c*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (2*d*tan(e/2 + (f*x)/2)^3*(3*c^2 + 2*d^2)*(2*a^2*d^5 + 18*a^2*c^4*d + 13*b^2*c^4*d - 5*a^2*c^2*d^3 + 2*b^2*c^2*d^3 - 12*a*b*c^5 + 2*a*b*c*d^4 - 20*a*b*c^3*d^2))/(3*c^3*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)))/(f*(c^3*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^2*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^4*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^3*(12*c^2*d + 8*d^3) + c^3 + 6*c^2*d*tan(e/2 + (f*x)/2) + 6*c^2*d*tan(e/2 + (f*x)/2)^5)) + (atan((((c*tan(e/2 + (f*x)/2)*(2*a^2*c^3 + b^2*c^3 + 3*a^2*c*d^2 + 4*b^2*c*d^2 - 2*a*b*d^3 - 8*a*b*c^2*d))/((c + d)^(7/2)*(c - d)^(7/2)) + ((2*c^6*d - 2*d^7 + 6*c^2*d^5 - 6*c^4*d^3)*(2*a^2*c^3 + b^2*c^3 + 3*a^2*c*d^2 + 4*b^2*c*d^2 - 2*a*b*d^3 - 8*a*b*c^2*d))/(2*(c + d)^(7/2)*(c - d)^(7/2)*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)))*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2))/(2*a^2*c^3 + b^2*c^3 + 3*a^2*c*d^2 + 4*b^2*c*d^2 - 2*a*b*d^3 - 8*a*b*c^2*d))*(2*a^2*c^3 + b^2*c^3 + 3*a^2*c*d^2 + 4*b^2*c*d^2 - 2*a*b*d^3 - 8*a*b*c^2*d))/(f*(c + d)^(7/2)*(c - d)^(7/2))","B"
686,1,574,400,8.916377,"\text{Not used}","int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^3,x)","-\frac{180\,a^3\,d^3\,\cos\left(e+f\,x\right)+180\,b^3\,c^3\,\cos\left(e+f\,x\right)-20\,a^3\,d^3\,\cos\left(3\,e+3\,f\,x\right)-20\,b^3\,c^3\,\cos\left(3\,e+3\,f\,x\right)+\frac{225\,b^3\,d^3\,\sin\left(2\,e+2\,f\,x\right)}{4}-\frac{45\,b^3\,d^3\,\sin\left(4\,e+4\,f\,x\right)}{4}+\frac{5\,b^3\,d^3\,\sin\left(6\,e+6\,f\,x\right)}{4}-75\,a\,b^2\,d^3\,\cos\left(3\,e+3\,f\,x\right)+9\,a\,b^2\,d^3\,\cos\left(5\,e+5\,f\,x\right)-75\,b^3\,c\,d^2\,\cos\left(3\,e+3\,f\,x\right)+9\,b^3\,c\,d^2\,\cos\left(5\,e+5\,f\,x\right)+180\,a\,b^2\,c^3\,\sin\left(2\,e+2\,f\,x\right)+180\,a^2\,b\,d^3\,\sin\left(2\,e+2\,f\,x\right)-\frac{45\,a^2\,b\,d^3\,\sin\left(4\,e+4\,f\,x\right)}{2}+180\,a^3\,c\,d^2\,\sin\left(2\,e+2\,f\,x\right)+180\,b^3\,c^2\,d\,\sin\left(2\,e+2\,f\,x\right)-\frac{45\,b^3\,c^2\,d\,\sin\left(4\,e+4\,f\,x\right)}{2}+720\,a^2\,b\,c^3\,\cos\left(e+f\,x\right)+450\,a\,b^2\,d^3\,\cos\left(e+f\,x\right)+720\,a^3\,c^2\,d\,\cos\left(e+f\,x\right)+450\,b^3\,c\,d^2\,\cos\left(e+f\,x\right)-240\,a^3\,c^3\,f\,x-75\,b^3\,d^3\,f\,x+1620\,a\,b^2\,c^2\,d\,\cos\left(e+f\,x\right)+1620\,a^2\,b\,c\,d^2\,\cos\left(e+f\,x\right)-360\,a\,b^2\,c^3\,f\,x-270\,a^2\,b\,d^3\,f\,x-360\,a^3\,c\,d^2\,f\,x-270\,b^3\,c^2\,d\,f\,x-180\,a\,b^2\,c^2\,d\,\cos\left(3\,e+3\,f\,x\right)-180\,a^2\,b\,c\,d^2\,\cos\left(3\,e+3\,f\,x\right)+540\,a\,b^2\,c\,d^2\,\sin\left(2\,e+2\,f\,x\right)+540\,a^2\,b\,c^2\,d\,\sin\left(2\,e+2\,f\,x\right)-\frac{135\,a\,b^2\,c\,d^2\,\sin\left(4\,e+4\,f\,x\right)}{2}-810\,a\,b^2\,c\,d^2\,f\,x-1080\,a^2\,b\,c^2\,d\,f\,x}{240\,f}","Not used",1,"-(180*a^3*d^3*cos(e + f*x) + 180*b^3*c^3*cos(e + f*x) - 20*a^3*d^3*cos(3*e + 3*f*x) - 20*b^3*c^3*cos(3*e + 3*f*x) + (225*b^3*d^3*sin(2*e + 2*f*x))/4 - (45*b^3*d^3*sin(4*e + 4*f*x))/4 + (5*b^3*d^3*sin(6*e + 6*f*x))/4 - 75*a*b^2*d^3*cos(3*e + 3*f*x) + 9*a*b^2*d^3*cos(5*e + 5*f*x) - 75*b^3*c*d^2*cos(3*e + 3*f*x) + 9*b^3*c*d^2*cos(5*e + 5*f*x) + 180*a*b^2*c^3*sin(2*e + 2*f*x) + 180*a^2*b*d^3*sin(2*e + 2*f*x) - (45*a^2*b*d^3*sin(4*e + 4*f*x))/2 + 180*a^3*c*d^2*sin(2*e + 2*f*x) + 180*b^3*c^2*d*sin(2*e + 2*f*x) - (45*b^3*c^2*d*sin(4*e + 4*f*x))/2 + 720*a^2*b*c^3*cos(e + f*x) + 450*a*b^2*d^3*cos(e + f*x) + 720*a^3*c^2*d*cos(e + f*x) + 450*b^3*c*d^2*cos(e + f*x) - 240*a^3*c^3*f*x - 75*b^3*d^3*f*x + 1620*a*b^2*c^2*d*cos(e + f*x) + 1620*a^2*b*c*d^2*cos(e + f*x) - 360*a*b^2*c^3*f*x - 270*a^2*b*d^3*f*x - 360*a^3*c*d^2*f*x - 270*b^3*c^2*d*f*x - 180*a*b^2*c^2*d*cos(3*e + 3*f*x) - 180*a^2*b*c*d^2*cos(3*e + 3*f*x) + 540*a*b^2*c*d^2*sin(2*e + 2*f*x) + 540*a^2*b*c^2*d*sin(2*e + 2*f*x) - (135*a*b^2*c*d^2*sin(4*e + 4*f*x))/2 - 810*a*b^2*c*d^2*f*x - 1080*a^2*b*c^2*d*f*x)/(240*f)","B"
687,1,358,315,8.520756,"\text{Not used}","int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^2,x)","-\frac{90\,b^3\,c^2\,\cos\left(e+f\,x\right)+75\,b^3\,d^2\,\cos\left(e+f\,x\right)-10\,b^3\,c^2\,\cos\left(3\,e+3\,f\,x\right)-\frac{25\,b^3\,d^2\,\cos\left(3\,e+3\,f\,x\right)}{2}+\frac{3\,b^3\,d^2\,\cos\left(5\,e+5\,f\,x\right)}{2}+30\,a^3\,d^2\,\sin\left(2\,e+2\,f\,x\right)-30\,a^2\,b\,d^2\,\cos\left(3\,e+3\,f\,x\right)+90\,a\,b^2\,c^2\,\sin\left(2\,e+2\,f\,x\right)+90\,a\,b^2\,d^2\,\sin\left(2\,e+2\,f\,x\right)-\frac{45\,a\,b^2\,d^2\,\sin\left(4\,e+4\,f\,x\right)}{4}+240\,a^3\,c\,d\,\cos\left(e+f\,x\right)+360\,a^2\,b\,c^2\,\cos\left(e+f\,x\right)+270\,a^2\,b\,d^2\,\cos\left(e+f\,x\right)+60\,b^3\,c\,d\,\sin\left(2\,e+2\,f\,x\right)-\frac{15\,b^3\,c\,d\,\sin\left(4\,e+4\,f\,x\right)}{2}-120\,a^3\,c^2\,f\,x-60\,a^3\,d^2\,f\,x-60\,a\,b^2\,c\,d\,\cos\left(3\,e+3\,f\,x\right)+180\,a^2\,b\,c\,d\,\sin\left(2\,e+2\,f\,x\right)-180\,a\,b^2\,c^2\,f\,x-135\,a\,b^2\,d^2\,f\,x+540\,a\,b^2\,c\,d\,\cos\left(e+f\,x\right)-90\,b^3\,c\,d\,f\,x-360\,a^2\,b\,c\,d\,f\,x}{120\,f}","Not used",1,"-(90*b^3*c^2*cos(e + f*x) + 75*b^3*d^2*cos(e + f*x) - 10*b^3*c^2*cos(3*e + 3*f*x) - (25*b^3*d^2*cos(3*e + 3*f*x))/2 + (3*b^3*d^2*cos(5*e + 5*f*x))/2 + 30*a^3*d^2*sin(2*e + 2*f*x) - 30*a^2*b*d^2*cos(3*e + 3*f*x) + 90*a*b^2*c^2*sin(2*e + 2*f*x) + 90*a*b^2*d^2*sin(2*e + 2*f*x) - (45*a*b^2*d^2*sin(4*e + 4*f*x))/4 + 240*a^3*c*d*cos(e + f*x) + 360*a^2*b*c^2*cos(e + f*x) + 270*a^2*b*d^2*cos(e + f*x) + 60*b^3*c*d*sin(2*e + 2*f*x) - (15*b^3*c*d*sin(4*e + 4*f*x))/2 - 120*a^3*c^2*f*x - 60*a^3*d^2*f*x - 60*a*b^2*c*d*cos(3*e + 3*f*x) + 180*a^2*b*c*d*sin(2*e + 2*f*x) - 180*a*b^2*c^2*f*x - 135*a*b^2*d^2*f*x + 540*a*b^2*c*d*cos(e + f*x) - 90*b^3*c*d*f*x - 360*a^2*b*c*d*f*x)/(120*f)","B"
688,1,183,171,7.953265,"\text{Not used}","int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x)),x)","\frac{2\,b^3\,c\,\cos\left(3\,e+3\,f\,x\right)-6\,b^3\,d\,\sin\left(2\,e+2\,f\,x\right)+\frac{3\,b^3\,d\,\sin\left(4\,e+4\,f\,x\right)}{4}-24\,a^3\,d\,\cos\left(e+f\,x\right)-18\,b^3\,c\,\cos\left(e+f\,x\right)-72\,a^2\,b\,c\,\cos\left(e+f\,x\right)-54\,a\,b^2\,d\,\cos\left(e+f\,x\right)+24\,a^3\,c\,f\,x+9\,b^3\,d\,f\,x+6\,a\,b^2\,d\,\cos\left(3\,e+3\,f\,x\right)-18\,a\,b^2\,c\,\sin\left(2\,e+2\,f\,x\right)-18\,a^2\,b\,d\,\sin\left(2\,e+2\,f\,x\right)+36\,a\,b^2\,c\,f\,x+36\,a^2\,b\,d\,f\,x}{24\,f}","Not used",1,"(2*b^3*c*cos(3*e + 3*f*x) - 6*b^3*d*sin(2*e + 2*f*x) + (3*b^3*d*sin(4*e + 4*f*x))/4 - 24*a^3*d*cos(e + f*x) - 18*b^3*c*cos(e + f*x) - 72*a^2*b*c*cos(e + f*x) - 54*a*b^2*d*cos(e + f*x) + 24*a^3*c*f*x + 9*b^3*d*f*x + 6*a*b^2*d*cos(3*e + 3*f*x) - 18*a*b^2*c*sin(2*e + 2*f*x) - 18*a^2*b*d*sin(2*e + 2*f*x) + 36*a*b^2*c*f*x + 36*a^2*b*d*f*x)/(24*f)","B"
689,1,127,90,7.686383,"\text{Not used}","int((a + b*sin(e + f*x))^3,x)","a^3\,x-\frac{4\,b^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{f}+\frac{8\,b^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6}{3\,f}+\frac{3\,a\,b^2\,x}{2}-\frac{6\,a^2\,b\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{f}-\frac{6\,a\,b^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f}+\frac{3\,a\,b^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f}","Not used",1,"a^3*x - (4*b^3*cos(e/2 + (f*x)/2)^4)/f + (8*b^3*cos(e/2 + (f*x)/2)^6)/(3*f) + (3*a*b^2*x)/2 - (6*a^2*b*cos(e/2 + (f*x)/2)^2)/f - (6*a*b^2*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2))/f + (3*a*b^2*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2))/f","B"
690,1,5902,156,14.561203,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x)),x)","\frac{\frac{2\,\left(b^3\,c-3\,a\,b^2\,d\right)}{d^2}+\frac{b^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{d}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(b^3\,c-3\,a\,b^2\,d\right)}{d^2}-\frac{b^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{d}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}-\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)}{d^3}\right)}{d^3}\right)\,1{}\mathrm{i}}{d^3}+\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)}{d^3}\right)}{d^3}\right)\,1{}\mathrm{i}}{d^3}}{\frac{16\,\left(-12\,a^8\,b\,c\,d^6+48\,a^7\,b^2\,c^2\,d^5-76\,a^6\,b^3\,c^3\,d^4-2\,a^6\,b^3\,c\,d^6+60\,a^5\,b^4\,c^4\,d^3-24\,a^4\,b^5\,c^5\,d^2+18\,a^4\,b^5\,c^3\,d^4+4\,a^3\,b^6\,c^6\,d-36\,a^3\,b^6\,c^4\,d^3-a^3\,b^6\,c^2\,d^5+30\,a^2\,b^7\,c^5\,d^2+3\,a^2\,b^7\,c^3\,d^4-12\,a\,b^8\,c^6\,d-3\,a\,b^8\,c^4\,d^3+2\,b^9\,c^7+b^9\,c^5\,d^2\right)}{d^5}-\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}-\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)}{d^3}\right)}{d^3}\right)}{d^3}+\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)}{d^3}\right)}{d^3}\right)}{d^3}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^7\,b^2\,c\,d^7+360\,a^6\,b^3\,c^2\,d^6-768\,a^5\,b^4\,c^3\,d^5-24\,a^5\,b^4\,c\,d^7+912\,a^4\,b^5\,c^4\,d^4+96\,a^4\,b^5\,c^2\,d^6-656\,a^3\,b^6\,c^5\,d^3-152\,a^3\,b^6\,c^3\,d^5-2\,a^3\,b^6\,c\,d^7+288\,a^2\,b^7\,c^6\,d^2+120\,a^2\,b^7\,c^4\,d^4+6\,a^2\,b^7\,c^2\,d^6-72\,a\,b^8\,c^7\,d-48\,a\,b^8\,c^5\,d^3-6\,a\,b^8\,c^3\,d^5+8\,b^9\,c^8+8\,b^9\,c^6\,d^2+2\,b^9\,c^4\,d^4\right)}{d^6}}\right)\,\left(b^3\,c^2\,1{}\mathrm{i}+\frac{b\,d^2\,\left(6\,a^2+b^2\right)\,1{}\mathrm{i}}{2}-a\,b^2\,c\,d\,3{}\mathrm{i}\right)\,2{}\mathrm{i}}{d^3\,f}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}-\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3}{d^5-c^2\,d^3}\right)}{d^5-c^2\,d^3}\right)\,1{}\mathrm{i}}{d^5-c^2\,d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3}{d^5-c^2\,d^3}\right)}{d^5-c^2\,d^3}\right)\,1{}\mathrm{i}}{d^5-c^2\,d^3}}{\frac{16\,\left(-12\,a^8\,b\,c\,d^6+48\,a^7\,b^2\,c^2\,d^5-76\,a^6\,b^3\,c^3\,d^4-2\,a^6\,b^3\,c\,d^6+60\,a^5\,b^4\,c^4\,d^3-24\,a^4\,b^5\,c^5\,d^2+18\,a^4\,b^5\,c^3\,d^4+4\,a^3\,b^6\,c^6\,d-36\,a^3\,b^6\,c^4\,d^3-a^3\,b^6\,c^2\,d^5+30\,a^2\,b^7\,c^5\,d^2+3\,a^2\,b^7\,c^3\,d^4-12\,a\,b^8\,c^6\,d-3\,a\,b^8\,c^4\,d^3+2\,b^9\,c^7+b^9\,c^5\,d^2\right)}{d^5}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^7\,b^2\,c\,d^7+360\,a^6\,b^3\,c^2\,d^6-768\,a^5\,b^4\,c^3\,d^5-24\,a^5\,b^4\,c\,d^7+912\,a^4\,b^5\,c^4\,d^4+96\,a^4\,b^5\,c^2\,d^6-656\,a^3\,b^6\,c^5\,d^3-152\,a^3\,b^6\,c^3\,d^5-2\,a^3\,b^6\,c\,d^7+288\,a^2\,b^7\,c^6\,d^2+120\,a^2\,b^7\,c^4\,d^4+6\,a^2\,b^7\,c^2\,d^6-72\,a\,b^8\,c^7\,d-48\,a\,b^8\,c^5\,d^3-6\,a\,b^8\,c^3\,d^5+8\,b^9\,c^8+8\,b^9\,c^6\,d^2+2\,b^9\,c^4\,d^4\right)}{d^6}-\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}-\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3}{d^5-c^2\,d^3}\right)}{d^5-c^2\,d^3}\right)}{d^5-c^2\,d^3}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(36\,a^4\,b^2\,c^2\,d^6-72\,a^3\,b^3\,c^3\,d^5+60\,a^2\,b^4\,c^4\,d^4+12\,a^2\,b^4\,c^2\,d^6-24\,a\,b^5\,c^5\,d^3-12\,a\,b^5\,c^3\,d^5+4\,b^6\,c^6\,d^2+4\,b^6\,c^4\,d^4+b^6\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^6\,c\,d^8+24\,a^5\,b\,c^2\,d^7-96\,a^4\,b^2\,c^3\,d^6+72\,a^4\,b^2\,c\,d^8+152\,a^3\,b^3\,c^4\,d^5-144\,a^3\,b^3\,c^2\,d^7-120\,a^2\,b^4\,c^5\,d^4+108\,a^2\,b^4\,c^3\,d^6+24\,a^2\,b^4\,c\,d^8+48\,a\,b^5\,c^6\,d^3-36\,a\,b^5\,c^4\,d^5-24\,a\,b^5\,c^2\,d^7-8\,b^6\,c^7\,d^2+4\,b^6\,c^5\,d^4+7\,b^6\,c^3\,d^6+2\,b^6\,c\,d^8\right)}{d^6}+\frac{\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(-4\,a^3\,c^2\,d^7+12\,a^2\,b\,c\,d^8-12\,a\,b^2\,c^2\,d^7+2\,b^3\,c^3\,d^6+2\,b^3\,c\,d^8\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c\,d^9-24\,a^2\,b\,c^2\,d^8+24\,a\,b^2\,c^3\,d^7-8\,b^3\,c^4\,d^6\right)}{d^6}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3}{d^5-c^2\,d^3}\right)}{d^5-c^2\,d^3}\right)}{d^5-c^2\,d^3}}\right)\,\sqrt{-\left(c+d\right)\,\left(c-d\right)}\,{\left(a\,d-b\,c\right)}^3\,2{}\mathrm{i}}{f\,\left(d^5-c^2\,d^3\right)}","Not used",1,"((2*(b^3*c - 3*a*b^2*d))/d^2 + (b^3*tan(e/2 + (f*x)/2)^3)/d + (2*tan(e/2 + (f*x)/2)^2*(b^3*c - 3*a*b^2*d))/d^2 - (b^3*tan(e/2 + (f*x)/2))/d)/(f*(2*tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^4 + 1)) + (atan((((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 - (8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i))/d^3))/d^3)*1i)/d^3 + ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i))/d^3))/d^3)*1i)/d^3)/((16*(2*b^9*c^7 + b^9*c^5*d^2 - 3*a*b^8*c^4*d^3 + 4*a^3*b^6*c^6*d - 2*a^6*b^3*c*d^6 + 3*a^2*b^7*c^3*d^4 + 30*a^2*b^7*c^5*d^2 - a^3*b^6*c^2*d^5 - 36*a^3*b^6*c^4*d^3 + 18*a^4*b^5*c^3*d^4 - 24*a^4*b^5*c^5*d^2 + 60*a^5*b^4*c^4*d^3 - 76*a^6*b^3*c^3*d^4 + 48*a^7*b^2*c^2*d^5 - 12*a*b^8*c^6*d - 12*a^8*b*c*d^6))/d^5 - ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 - (8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i))/d^3))/d^3))/d^3 + ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*((8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i))/d^3))/d^3))/d^3 + (16*tan(e/2 + (f*x)/2)*(8*b^9*c^8 + 2*b^9*c^4*d^4 + 8*b^9*c^6*d^2 - 6*a*b^8*c^3*d^5 - 48*a*b^8*c^5*d^3 - 2*a^3*b^6*c*d^7 - 24*a^5*b^4*c*d^7 - 72*a^7*b^2*c*d^7 + 6*a^2*b^7*c^2*d^6 + 120*a^2*b^7*c^4*d^4 + 288*a^2*b^7*c^6*d^2 - 152*a^3*b^6*c^3*d^5 - 656*a^3*b^6*c^5*d^3 + 96*a^4*b^5*c^2*d^6 + 912*a^4*b^5*c^4*d^4 - 768*a^5*b^4*c^3*d^5 + 360*a^6*b^3*c^2*d^6 - 72*a*b^8*c^7*d))/d^6))*(b^3*c^2*1i + (b*d^2*(6*a^2 + b^2)*1i)/2 - a*b^2*c*d*3i)*2i)/(d^3*f) + (atan((((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 - (8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3)/(d^5 - c^2*d^3)))/(d^5 - c^2*d^3))*1i)/(d^5 - c^2*d^3) + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3)/(d^5 - c^2*d^3)))/(d^5 - c^2*d^3))*1i)/(d^5 - c^2*d^3))/((16*(2*b^9*c^7 + b^9*c^5*d^2 - 3*a*b^8*c^4*d^3 + 4*a^3*b^6*c^6*d - 2*a^6*b^3*c*d^6 + 3*a^2*b^7*c^3*d^4 + 30*a^2*b^7*c^5*d^2 - a^3*b^6*c^2*d^5 - 36*a^3*b^6*c^4*d^3 + 18*a^4*b^5*c^3*d^4 - 24*a^4*b^5*c^5*d^2 + 60*a^5*b^4*c^4*d^3 - 76*a^6*b^3*c^3*d^4 + 48*a^7*b^2*c^2*d^5 - 12*a*b^8*c^6*d - 12*a^8*b*c*d^6))/d^5 + (16*tan(e/2 + (f*x)/2)*(8*b^9*c^8 + 2*b^9*c^4*d^4 + 8*b^9*c^6*d^2 - 6*a*b^8*c^3*d^5 - 48*a*b^8*c^5*d^3 - 2*a^3*b^6*c*d^7 - 24*a^5*b^4*c*d^7 - 72*a^7*b^2*c*d^7 + 6*a^2*b^7*c^2*d^6 + 120*a^2*b^7*c^4*d^4 + 288*a^2*b^7*c^6*d^2 - 152*a^3*b^6*c^3*d^5 - 656*a^3*b^6*c^5*d^3 + 96*a^4*b^5*c^2*d^6 + 912*a^4*b^5*c^4*d^4 - 768*a^5*b^4*c^3*d^5 + 360*a^6*b^3*c^2*d^6 - 72*a*b^8*c^7*d))/d^6 - ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 - (8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3)/(d^5 - c^2*d^3)))/(d^5 - c^2*d^3)))/(d^5 - c^2*d^3) + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*(b^6*c^2*d^6 + 4*b^6*c^4*d^4 + 4*b^6*c^6*d^2 - 12*a*b^5*c^3*d^5 - 24*a*b^5*c^5*d^3 + 12*a^2*b^4*c^2*d^6 + 60*a^2*b^4*c^4*d^4 - 72*a^3*b^3*c^3*d^5 + 36*a^4*b^2*c^2*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(2*b^6*c*d^8 - 4*a^6*c*d^8 + 7*b^6*c^3*d^6 + 4*b^6*c^5*d^4 - 8*b^6*c^7*d^2 - 24*a*b^5*c^2*d^7 - 36*a*b^5*c^4*d^5 + 48*a*b^5*c^6*d^3 + 24*a^2*b^4*c*d^8 + 72*a^4*b^2*c*d^8 + 24*a^5*b*c^2*d^7 + 108*a^2*b^4*c^3*d^6 - 120*a^2*b^4*c^5*d^4 - 144*a^3*b^3*c^2*d^7 + 152*a^3*b^3*c^4*d^5 - 96*a^4*b^2*c^3*d^6))/d^6 + ((-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*((8*(2*b^3*c*d^8 - 4*a^3*c^2*d^7 + 2*b^3*c^3*d^6 - 12*a*b^2*c^2*d^7 + 12*a^2*b*c*d^8))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*a^3*c*d^9 - 8*b^3*c^4*d^6 + 24*a*b^2*c^3*d^7 - 24*a^2*b*c^2*d^8))/d^6 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3)/(d^5 - c^2*d^3)))/(d^5 - c^2*d^3)))/(d^5 - c^2*d^3)))*(-(c + d)*(c - d))^(1/2)*(a*d - b*c)^3*2i)/(f*(d^5 - c^2*d^3))","B"
691,1,8953,208,17.637279,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-2\,b^3\,c^3+b^3\,c\,d^2\right)}{d^2\,\left(c^2-d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-2\,b^3\,c^3+b^3\,c\,d^2\right)}{d^2\,\left(c^2-d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-3\,b^3\,c^3+2\,b^3\,c\,d^2\right)}{c\,d\,\left(c^2-d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{c\,d\,\left(c^2-d^2\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}+\frac{2\,b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}-\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{b^2\,\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(3\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}+\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(3\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}}{\frac{64\,\left(-3\,a^7\,b^2\,c^3\,d^5+2\,a^6\,b^3\,c^4\,d^4+18\,a^6\,b^3\,c^2\,d^6+9\,a^5\,b^4\,c^5\,d^3-39\,a^5\,b^4\,c^3\,d^5-27\,a^5\,b^4\,c\,d^7-12\,a^4\,b^5\,c^6\,d^2+3\,a^4\,b^5\,c^4\,d^4+99\,a^4\,b^5\,c^2\,d^6+4\,a^3\,b^6\,c^7\,d+55\,a^3\,b^6\,c^5\,d^3-144\,a^3\,b^6\,c^3\,d^5-57\,a^2\,b^7\,c^6\,d^2+105\,a^2\,b^7\,c^4\,d^4+24\,a\,b^8\,c^7\,d-39\,a\,b^8\,c^5\,d^3-4\,b^9\,c^8+6\,b^9\,c^6\,d^2\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-18\,a^5\,b^4\,c^4\,d^5+18\,a^5\,b^4\,c^2\,d^7+24\,a^4\,b^5\,c^5\,d^4+30\,a^4\,b^5\,c^3\,d^6-54\,a^4\,b^5\,c\,d^8+46\,a^3\,b^6\,c^6\,d^3-226\,a^3\,b^6\,c^4\,d^5+180\,a^3\,b^6\,c^2\,d^7-108\,a^2\,b^7\,c^7\,d^2+330\,a^2\,b^7\,c^5\,d^4-222\,a^2\,b^7\,c^3\,d^6+72\,a\,b^8\,c^8\,d-192\,a\,b^8\,c^6\,d^3+120\,a\,b^8\,c^4\,d^5-16\,b^9\,c^9+40\,b^9\,c^7\,d^2-24\,b^9\,c^5\,d^4\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}-\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{b^2\,\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(3\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}-\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(3\,a\,d-2\,b\,c\right)\,\left(\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{b^2\,\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(3\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}\right)\,\left(3\,a\,d-2\,b\,c\right)}{d^3\,f}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}-\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)\,1{}\mathrm{i}}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)\,1{}\mathrm{i}}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}}{\frac{64\,\left(-3\,a^7\,b^2\,c^3\,d^5+2\,a^6\,b^3\,c^4\,d^4+18\,a^6\,b^3\,c^2\,d^6+9\,a^5\,b^4\,c^5\,d^3-39\,a^5\,b^4\,c^3\,d^5-27\,a^5\,b^4\,c\,d^7-12\,a^4\,b^5\,c^6\,d^2+3\,a^4\,b^5\,c^4\,d^4+99\,a^4\,b^5\,c^2\,d^6+4\,a^3\,b^6\,c^7\,d+55\,a^3\,b^6\,c^5\,d^3-144\,a^3\,b^6\,c^3\,d^5-57\,a^2\,b^7\,c^6\,d^2+105\,a^2\,b^7\,c^4\,d^4+24\,a\,b^8\,c^7\,d-39\,a\,b^8\,c^5\,d^3-4\,b^9\,c^8+6\,b^9\,c^6\,d^2\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-18\,a^5\,b^4\,c^4\,d^5+18\,a^5\,b^4\,c^2\,d^7+24\,a^4\,b^5\,c^5\,d^4+30\,a^4\,b^5\,c^3\,d^6-54\,a^4\,b^5\,c\,d^8+46\,a^3\,b^6\,c^6\,d^3-226\,a^3\,b^6\,c^4\,d^5+180\,a^3\,b^6\,c^2\,d^7-108\,a^2\,b^7\,c^7\,d^2+330\,a^2\,b^7\,c^5\,d^4-222\,a^2\,b^7\,c^3\,d^6+72\,a\,b^8\,c^8\,d-192\,a\,b^8\,c^6\,d^3+120\,a\,b^8\,c^4\,d^5-16\,b^9\,c^9+40\,b^9\,c^7\,d^2-24\,b^9\,c^5\,d^4\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}-\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}-\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(9\,a^2\,b^4\,c^6\,d^4-18\,a^2\,b^4\,c^4\,d^6+9\,a^2\,b^4\,c^2\,d^8-12\,a\,b^5\,c^7\,d^3+24\,a\,b^5\,c^5\,d^5-12\,a\,b^5\,c^3\,d^7+4\,b^6\,c^8\,d^2-8\,b^6\,c^6\,d^4+4\,b^6\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^8-6\,a^5\,b\,c^2\,d^9-6\,a^4\,b^2\,c^5\,d^6+12\,a^4\,b^2\,c^3\,d^8+9\,a^4\,b^2\,c\,d^{10}+4\,a^3\,b^3\,c^6\,d^5+12\,a^3\,b^3\,c^4\,d^7-36\,a^3\,b^3\,c^2\,d^9+18\,a^2\,b^4\,c^7\,d^4-84\,a^2\,b^4\,c^5\,d^6+99\,a^2\,b^4\,c^3\,d^8-18\,a^2\,b^4\,c\,d^{10}-24\,a\,b^5\,c^8\,d^3+90\,a\,b^5\,c^6\,d^5-96\,a\,b^5\,c^4\,d^7+24\,a\,b^5\,c^2\,d^9+8\,b^6\,c^9\,d^2-28\,b^6\,c^7\,d^4+29\,b^6\,c^5\,d^6-8\,b^6\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^3\,c^5\,d^7-a^3\,c^3\,d^9-3\,a^2\,b\,c^4\,d^8+3\,a^2\,b\,c^2\,d^{10}+3\,a\,b^2\,c^3\,d^9-3\,a\,b^2\,c\,d^{11}+b^3\,c^6\,d^6-3\,b^3\,c^4\,d^8+2\,b^3\,c^2\,d^{10}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^3\,c^4\,d^9+2\,a^3\,c^2\,d^{11}+6\,a^2\,b\,c^3\,d^{10}-6\,a^2\,b\,c\,d^{12}+6\,a\,b^2\,c^6\,d^7-18\,a\,b^2\,c^4\,d^9+12\,a\,b^2\,c^2\,d^{11}-4\,b^3\,c^7\,d^6+10\,b^3\,c^5\,d^8-6\,b^3\,c^3\,d^{10}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,b\,c^2+a\,c\,d-3\,b\,d^2\right)\,2{}\mathrm{i}}{f\,\left(-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9\right)}","Not used",1,"((2*(a^3*d^3 - 2*b^3*c^3 + b^3*c*d^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(d^2*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)^2*(a^3*d^3 - 2*b^3*c^3 + b^3*c*d^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(d^2*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)*(a^3*d^3 - 3*b^3*c^3 + 2*b^3*c*d^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(c*d*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(c*d*(c^2 - d^2)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + 2*c*tan(e/2 + (f*x)/2)^2 + c*tan(e/2 + (f*x)/2)^4 + 2*d*tan(e/2 + (f*x)/2)^3)) + (2*b^2*atan(((b^2*(3*a*d - 2*b*c)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*(3*a*d - 2*b*c)*((32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) - (32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (b^2*((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(3*a*d - 2*b*c)*1i)/d^3)*1i)/d^3))/d^3 + (b^2*(3*a*d - 2*b*c)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*(3*a*d - 2*b*c)*((32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(3*a*d - 2*b*c)*1i)/d^3)*1i)/d^3))/d^3)/((64*(6*b^9*c^6*d^2 - 4*b^9*c^8 - 39*a*b^8*c^5*d^3 + 4*a^3*b^6*c^7*d - 27*a^5*b^4*c*d^7 + 105*a^2*b^7*c^4*d^4 - 57*a^2*b^7*c^6*d^2 - 144*a^3*b^6*c^3*d^5 + 55*a^3*b^6*c^5*d^3 + 99*a^4*b^5*c^2*d^6 + 3*a^4*b^5*c^4*d^4 - 12*a^4*b^5*c^6*d^2 - 39*a^5*b^4*c^3*d^5 + 9*a^5*b^4*c^5*d^3 + 18*a^6*b^3*c^2*d^6 + 2*a^6*b^3*c^4*d^4 - 3*a^7*b^2*c^3*d^5 + 24*a*b^8*c^7*d))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (64*tan(e/2 + (f*x)/2)*(40*b^9*c^7*d^2 - 24*b^9*c^5*d^4 - 16*b^9*c^9 + 120*a*b^8*c^4*d^5 - 192*a*b^8*c^6*d^3 - 54*a^4*b^5*c*d^8 - 222*a^2*b^7*c^3*d^6 + 330*a^2*b^7*c^5*d^4 - 108*a^2*b^7*c^7*d^2 + 180*a^3*b^6*c^2*d^7 - 226*a^3*b^6*c^4*d^5 + 46*a^3*b^6*c^6*d^3 + 30*a^4*b^5*c^3*d^6 + 24*a^4*b^5*c^5*d^4 + 18*a^5*b^4*c^2*d^7 - 18*a^5*b^4*c^4*d^5 + 72*a*b^8*c^8*d))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*(3*a*d - 2*b*c)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*(3*a*d - 2*b*c)*((32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) - (32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (b^2*((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(3*a*d - 2*b*c)*1i)/d^3)*1i)/d^3)*1i)/d^3 - (b^2*(3*a*d - 2*b*c)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*(3*a*d - 2*b*c)*((32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (b^2*((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(3*a*d - 2*b*c)*1i)/d^3)*1i)/d^3)*1i)/d^3))*(3*a*d - 2*b*c))/(d^3*f) + (atan((((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) - (32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d)*1i)/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3) + ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d)*1i)/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))/((64*(6*b^9*c^6*d^2 - 4*b^9*c^8 - 39*a*b^8*c^5*d^3 + 4*a^3*b^6*c^7*d - 27*a^5*b^4*c*d^7 + 105*a^2*b^7*c^4*d^4 - 57*a^2*b^7*c^6*d^2 - 144*a^3*b^6*c^3*d^5 + 55*a^3*b^6*c^5*d^3 + 99*a^4*b^5*c^2*d^6 + 3*a^4*b^5*c^4*d^4 - 12*a^4*b^5*c^6*d^2 - 39*a^5*b^4*c^3*d^5 + 9*a^5*b^4*c^5*d^3 + 18*a^6*b^3*c^2*d^6 + 2*a^6*b^3*c^4*d^4 - 3*a^7*b^2*c^3*d^5 + 24*a*b^8*c^7*d))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (64*tan(e/2 + (f*x)/2)*(40*b^9*c^7*d^2 - 24*b^9*c^5*d^4 - 16*b^9*c^9 + 120*a*b^8*c^4*d^5 - 192*a*b^8*c^6*d^3 - 54*a^4*b^5*c*d^8 - 222*a^2*b^7*c^3*d^6 + 330*a^2*b^7*c^5*d^4 - 108*a^2*b^7*c^7*d^2 + 180*a^3*b^6*c^2*d^7 - 226*a^3*b^6*c^4*d^5 + 46*a^3*b^6*c^6*d^3 + 30*a^4*b^5*c^3*d^6 + 24*a^4*b^5*c^5*d^4 + 18*a^5*b^4*c^2*d^7 - 18*a^5*b^4*c^4*d^5 + 72*a*b^8*c^8*d))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) - (32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3) - ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*b^6*c^4*d^6 - 8*b^6*c^6*d^4 + 4*b^6*c^8*d^2 - 12*a*b^5*c^3*d^7 + 24*a*b^5*c^5*d^5 - 12*a*b^5*c^7*d^3 + 9*a^2*b^4*c^2*d^8 - 18*a^2*b^4*c^4*d^6 + 9*a^2*b^4*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^8 - 8*b^6*c^3*d^8 + 29*b^6*c^5*d^6 - 28*b^6*c^7*d^4 + 8*b^6*c^9*d^2 + 24*a*b^5*c^2*d^9 - 96*a*b^5*c^4*d^7 + 90*a*b^5*c^6*d^5 - 24*a*b^5*c^8*d^3 - 18*a^2*b^4*c*d^10 + 9*a^4*b^2*c*d^10 - 6*a^5*b*c^2*d^9 + 99*a^2*b^4*c^3*d^8 - 84*a^2*b^4*c^5*d^6 + 18*a^2*b^4*c^7*d^4 - 36*a^3*b^3*c^2*d^9 + 12*a^3*b^3*c^4*d^7 + 4*a^3*b^3*c^6*d^5 + 12*a^4*b^2*c^3*d^8 - 6*a^4*b^2*c^5*d^6))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^3*c^5*d^7 - a^3*c^3*d^9 + 2*b^3*c^2*d^10 - 3*b^3*c^4*d^8 + b^3*c^6*d^6 + 3*a*b^2*c^3*d^9 + 3*a^2*b*c^2*d^10 - 3*a^2*b*c^4*d^8 - 3*a*b^2*c*d^11))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(2*a^3*c^2*d^11 - 2*a^3*c^4*d^9 - 6*b^3*c^3*d^10 + 10*b^3*c^5*d^8 - 4*b^3*c^7*d^6 + 12*a*b^2*c^2*d^11 - 18*a*b^2*c^4*d^9 + 6*a*b^2*c^6*d^7 + 6*a^2*b*c^3*d^10 - 6*a^2*b*c*d^12))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*b*c^2 - 3*b*d^2 + a*c*d))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3)))*(a*d - b*c)^2*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*c^2 - 3*b*d^2 + a*c*d)*2i)/(f*(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))","B"
692,1,11848,255,20.457660,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^3,x)","-\frac{\frac{-4\,a^3\,c^2\,d^3+a^3\,d^5+6\,a^2\,b\,c^3\,d^2+3\,a^2\,b\,c\,d^4-9\,a\,b^2\,c^2\,d^3-2\,b^3\,c^5+5\,b^3\,c^3\,d^2}{d^2\,\left(c^4-2\,c^2\,d^2+d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(5\,a^3\,c^2\,d^3-2\,a^3\,d^5-9\,a^2\,b\,c^3\,d^2+3\,a\,b^2\,c^4\,d+6\,a\,b^2\,c^2\,d^3+b^3\,c^5-4\,b^3\,c^3\,d^2\right)}{c\,d\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-11\,a^3\,c^2\,d^3+2\,a^3\,d^5+15\,a^2\,b\,c^3\,d^2+12\,a^2\,b\,c\,d^4+3\,a\,b^2\,c^4\,d-30\,a\,b^2\,c^2\,d^3-7\,b^3\,c^5+16\,b^3\,c^3\,d^2\right)}{c\,d\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(-4\,a^3\,c^2\,d^3+a^3\,d^5+6\,a^2\,b\,c^3\,d^2+3\,a^2\,b\,c\,d^4-9\,a\,b^2\,c^2\,d^3-2\,b^3\,c^5+5\,b^3\,c^3\,d^2\right)}{c^2\,d^2\,\left(c^4-2\,c^2\,d^2+d^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{2\,b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}-\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{b^3\,\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}+\frac{b^3\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}}{\frac{16\,\left(4\,a^6\,b^3\,c^5\,d^4+4\,a^6\,b^3\,c^3\,d^6+a^6\,b^3\,c\,d^8-36\,a^5\,b^4\,c^4\,d^5-18\,a^5\,b^4\,c^2\,d^7+12\,a^4\,b^5\,c^5\,d^4+111\,a^4\,b^5\,c^3\,d^6+12\,a^4\,b^5\,c\,d^8-4\,a^3\,b^6\,c^8\,d+10\,a^3\,b^6\,c^6\,d^3-68\,a^3\,b^6\,c^4\,d^5-118\,a^3\,b^6\,c^2\,d^7+18\,a^2\,b^7\,c^7\,d^2-45\,a^2\,b^7\,c^5\,d^4+126\,a^2\,b^7\,c^3\,d^6+36\,a^2\,b^7\,c\,d^8-6\,a\,b^8\,c^8\,d+6\,a\,b^8\,c^6\,d^3+6\,a\,b^8\,c^4\,d^5-60\,a\,b^8\,c^2\,d^7-2\,b^9\,c^9+13\,b^9\,c^7\,d^2-26\,b^9\,c^5\,d^4+24\,b^9\,c^3\,d^6\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,b^6\,c^7\,d^3+12\,a^3\,b^6\,c^5\,d^5-4\,a^3\,b^6\,c\,d^9+36\,a^2\,b^7\,c^6\,d^4-72\,a^2\,b^7\,c^4\,d^6+36\,a^2\,b^7\,c^2\,d^8-12\,a\,b^8\,c^7\,d^3+36\,a\,b^8\,c^3\,d^7-24\,a\,b^8\,c\,d^9+8\,b^9\,c^{10}-36\,b^9\,c^8\,d^2+72\,b^9\,c^6\,d^4-68\,b^9\,c^4\,d^6+24\,b^9\,c^2\,d^8\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}-\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{b^3\,\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}-\frac{b^3\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{b^3\,\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}\right)}{d^3\,f}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}-\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)\,1{}\mathrm{i}}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)\,1{}\mathrm{i}}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}}{\frac{16\,\left(4\,a^6\,b^3\,c^5\,d^4+4\,a^6\,b^3\,c^3\,d^6+a^6\,b^3\,c\,d^8-36\,a^5\,b^4\,c^4\,d^5-18\,a^5\,b^4\,c^2\,d^7+12\,a^4\,b^5\,c^5\,d^4+111\,a^4\,b^5\,c^3\,d^6+12\,a^4\,b^5\,c\,d^8-4\,a^3\,b^6\,c^8\,d+10\,a^3\,b^6\,c^6\,d^3-68\,a^3\,b^6\,c^4\,d^5-118\,a^3\,b^6\,c^2\,d^7+18\,a^2\,b^7\,c^7\,d^2-45\,a^2\,b^7\,c^5\,d^4+126\,a^2\,b^7\,c^3\,d^6+36\,a^2\,b^7\,c\,d^8-6\,a\,b^8\,c^8\,d+6\,a\,b^8\,c^6\,d^3+6\,a\,b^8\,c^4\,d^5-60\,a\,b^8\,c^2\,d^7-2\,b^9\,c^9+13\,b^9\,c^7\,d^2-26\,b^9\,c^5\,d^4+24\,b^9\,c^3\,d^6\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^3\,b^6\,c^7\,d^3+12\,a^3\,b^6\,c^5\,d^5-4\,a^3\,b^6\,c\,d^9+36\,a^2\,b^7\,c^6\,d^4-72\,a^2\,b^7\,c^4\,d^6+36\,a^2\,b^7\,c^2\,d^8-12\,a\,b^8\,c^7\,d^3+36\,a\,b^8\,c^3\,d^7-24\,a\,b^8\,c\,d^9+8\,b^9\,c^{10}-36\,b^9\,c^8\,d^2+72\,b^9\,c^6\,d^4-68\,b^9\,c^4\,d^6+24\,b^9\,c^2\,d^8\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}-\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}-\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,b^6\,c^{10}\,d^2-16\,b^6\,c^8\,d^4+24\,b^6\,c^6\,d^6-16\,b^6\,c^4\,d^8+4\,b^6\,c^2\,d^{10}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^6\,c^5\,d^8+4\,a^6\,c^3\,d^{10}+a^6\,c\,d^{12}-36\,a^5\,b\,c^4\,d^9-18\,a^5\,b\,c^2\,d^{11}+12\,a^4\,b^2\,c^5\,d^8+111\,a^4\,b^2\,c^3\,d^{10}+12\,a^4\,b^2\,c\,d^{12}-8\,a^3\,b^3\,c^8\,d^5+16\,a^3\,b^3\,c^6\,d^7-68\,a^3\,b^3\,c^4\,d^9-120\,a^3\,b^3\,c^2\,d^{11}+36\,a^2\,b^4\,c^7\,d^6-81\,a^2\,b^4\,c^5\,d^8+144\,a^2\,b^4\,c^3\,d^{10}+36\,a^2\,b^4\,c\,d^{12}-12\,a\,b^5\,c^8\,d^5+6\,a\,b^5\,c^6\,d^7+24\,a\,b^5\,c^4\,d^9-72\,a\,b^5\,c^2\,d^{11}+8\,b^6\,c^{11}\,d^2-44\,b^6\,c^9\,d^4+105\,b^6\,c^7\,d^6-124\,b^6\,c^5\,d^8+72\,b^6\,c^3\,d^{10}-8\,b^6\,c\,d^{12}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(-4\,a^3\,c^8\,d^7+6\,a^3\,c^6\,d^9-2\,a^3\,c^2\,d^{13}+18\,a^2\,b\,c^7\,d^8-36\,a^2\,b\,c^5\,d^{10}+18\,a^2\,b\,c^3\,d^{12}-6\,a\,b^2\,c^8\,d^7+18\,a\,b^2\,c^4\,d^{11}-12\,a\,b^2\,c^2\,d^{13}+2\,b^3\,c^9\,d^6-4\,b^3\,c^7\,d^8+6\,b^3\,c^5\,d^{10}-8\,b^3\,c^3\,d^{12}+4\,b^3\,c\,d^{14}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^3\,c^7\,d^9-12\,a^3\,c^5\,d^{11}+4\,a^3\,c\,d^{15}-36\,a^2\,b\,c^6\,d^{10}+72\,a^2\,b\,c^4\,d^{12}-36\,a^2\,b\,c^2\,d^{14}+12\,a\,b^2\,c^7\,d^9-36\,a\,b^2\,c^3\,d^{13}+24\,a\,b^2\,c\,d^{15}-8\,b^3\,c^{10}\,d^6+36\,b^3\,c^8\,d^8-72\,b^3\,c^6\,d^{10}+68\,b^3\,c^4\,d^{12}-24\,b^3\,c^2\,d^{14}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}+\frac{\left(\frac{8\,\left(4\,c^{10}\,d^8-16\,c^8\,d^{10}+24\,c^6\,d^{12}-16\,c^4\,d^{14}+4\,c^2\,d^{16}\right)}{c^8\,d^5-4\,c^6\,d^7+6\,c^4\,d^9-4\,c^2\,d^{11}+d^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^{11}\,d^8+44\,c^9\,d^{10}-96\,c^7\,d^{12}+104\,c^5\,d^{14}-56\,c^3\,d^{16}+12\,c\,d^{18}\right)}{c^8\,d^6-4\,c^6\,d^8+6\,c^4\,d^{10}-4\,c^2\,d^{12}+d^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-8\,a\,b\,c\,d^3+2\,b^2\,c^4-5\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)\,1{}\mathrm{i}}{f\,\left(-c^{10}\,d^3+5\,c^8\,d^5-10\,c^6\,d^7+10\,c^4\,d^9-5\,c^2\,d^{11}+d^{13}\right)}","Not used",1,"- ((a^3*d^5 - 2*b^3*c^5 - 4*a^3*c^2*d^3 + 5*b^3*c^3*d^2 - 9*a*b^2*c^2*d^3 + 6*a^2*b*c^3*d^2 + 3*a^2*b*c*d^4)/(d^2*(c^4 + d^4 - 2*c^2*d^2)) - (tan(e/2 + (f*x)/2)^3*(b^3*c^5 - 2*a^3*d^5 + 5*a^3*c^2*d^3 - 4*b^3*c^3*d^2 + 6*a*b^2*c^2*d^3 - 9*a^2*b*c^3*d^2 + 3*a*b^2*c^4*d))/(c*d*(c^4 + d^4 - 2*c^2*d^2)) + (tan(e/2 + (f*x)/2)*(2*a^3*d^5 - 7*b^3*c^5 - 11*a^3*c^2*d^3 + 16*b^3*c^3*d^2 - 30*a*b^2*c^2*d^3 + 15*a^2*b*c^3*d^2 + 3*a*b^2*c^4*d + 12*a^2*b*c*d^4))/(c*d*(c^4 + d^4 - 2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(a^3*d^5 - 2*b^3*c^5 - 4*a^3*c^2*d^3 + 5*b^3*c^3*d^2 - 9*a*b^2*c^2*d^3 + 6*a^2*b*c^3*d^2 + 3*a^2*b*c*d^4))/(c^2*d^2*(c^4 + d^4 - 2*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) - (2*b^3*atan(((b^3*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + (b^3*((b^3*((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3 - (8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3))/d^3 + (b^3*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + (b^3*((8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (b^3*((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3 - (8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3))/d^3)/((16*(24*b^9*c^3*d^6 - 2*b^9*c^9 - 26*b^9*c^5*d^4 + 13*b^9*c^7*d^2 - 60*a*b^8*c^2*d^7 + 6*a*b^8*c^4*d^5 + 6*a*b^8*c^6*d^3 + 36*a^2*b^7*c*d^8 - 4*a^3*b^6*c^8*d + 12*a^4*b^5*c*d^8 + a^6*b^3*c*d^8 + 126*a^2*b^7*c^3*d^6 - 45*a^2*b^7*c^5*d^4 + 18*a^2*b^7*c^7*d^2 - 118*a^3*b^6*c^2*d^7 - 68*a^3*b^6*c^4*d^5 + 10*a^3*b^6*c^6*d^3 + 111*a^4*b^5*c^3*d^6 + 12*a^4*b^5*c^5*d^4 - 18*a^5*b^4*c^2*d^7 - 36*a^5*b^4*c^4*d^5 + 4*a^6*b^3*c^3*d^6 + 4*a^6*b^3*c^5*d^4 - 6*a*b^8*c^8*d))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (b^3*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + (b^3*((b^3*((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3 - (8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3)*1i)/d^3 - (b^3*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + (b^3*((8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (b^3*((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3 - (8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*1i)/d^3)*1i)/d^3 - (16*tan(e/2 + (f*x)/2)*(8*b^9*c^10 + 24*b^9*c^2*d^8 - 68*b^9*c^4*d^6 + 72*b^9*c^6*d^4 - 36*b^9*c^8*d^2 + 36*a*b^8*c^3*d^7 - 12*a*b^8*c^7*d^3 - 4*a^3*b^6*c*d^9 + 36*a^2*b^7*c^2*d^8 - 72*a^2*b^7*c^4*d^6 + 36*a^2*b^7*c^6*d^4 + 12*a^3*b^6*c^5*d^5 - 8*a^3*b^6*c^7*d^3 - 24*a*b^8*c*d^9))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))))/(d^3*f) - (atan((((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) - (8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*(a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d)*1i)/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)) + ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + (((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*(a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d)*1i)/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))/((16*(24*b^9*c^3*d^6 - 2*b^9*c^9 - 26*b^9*c^5*d^4 + 13*b^9*c^7*d^2 - 60*a*b^8*c^2*d^7 + 6*a*b^8*c^4*d^5 + 6*a*b^8*c^6*d^3 + 36*a^2*b^7*c*d^8 - 4*a^3*b^6*c^8*d + 12*a^4*b^5*c*d^8 + a^6*b^3*c*d^8 + 126*a^2*b^7*c^3*d^6 - 45*a^2*b^7*c^5*d^4 + 18*a^2*b^7*c^7*d^2 - 118*a^3*b^6*c^2*d^7 - 68*a^3*b^6*c^4*d^5 + 10*a^3*b^6*c^6*d^3 + 111*a^4*b^5*c^3*d^6 + 12*a^4*b^5*c^5*d^4 - 18*a^5*b^4*c^2*d^7 - 36*a^5*b^4*c^4*d^5 + 4*a^6*b^3*c^3*d^6 + 4*a^6*b^3*c^5*d^4 - 6*a*b^8*c^8*d))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (16*tan(e/2 + (f*x)/2)*(8*b^9*c^10 + 24*b^9*c^2*d^8 - 68*b^9*c^4*d^6 + 72*b^9*c^6*d^4 - 36*b^9*c^8*d^2 + 36*a*b^8*c^3*d^7 - 12*a*b^8*c^7*d^3 - 4*a^3*b^6*c*d^9 + 36*a^2*b^7*c^2*d^8 - 72*a^2*b^7*c^4*d^6 + 36*a^2*b^7*c^6*d^4 + 12*a^3*b^6*c^5*d^5 - 8*a^3*b^6*c^7*d^3 - 24*a*b^8*c*d^9))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) - (8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*(a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)) - ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*b^6*c^2*d^10 - 16*b^6*c^4*d^8 + 24*b^6*c^6*d^6 - 16*b^6*c^8*d^4 + 4*b^6*c^10*d^2))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(a^6*c*d^12 - 8*b^6*c*d^12 + 4*a^6*c^3*d^10 + 4*a^6*c^5*d^8 + 72*b^6*c^3*d^10 - 124*b^6*c^5*d^8 + 105*b^6*c^7*d^6 - 44*b^6*c^9*d^4 + 8*b^6*c^11*d^2 - 72*a*b^5*c^2*d^11 + 24*a*b^5*c^4*d^9 + 6*a*b^5*c^6*d^7 - 12*a*b^5*c^8*d^5 + 36*a^2*b^4*c*d^12 + 12*a^4*b^2*c*d^12 - 18*a^5*b*c^2*d^11 - 36*a^5*b*c^4*d^9 + 144*a^2*b^4*c^3*d^10 - 81*a^2*b^4*c^5*d^8 + 36*a^2*b^4*c^7*d^6 - 120*a^3*b^3*c^2*d^11 - 68*a^3*b^3*c^4*d^9 + 16*a^3*b^3*c^6*d^7 - 8*a^3*b^3*c^8*d^5 + 111*a^4*b^2*c^3*d^10 + 12*a^4*b^2*c^5*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + ((a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*b^3*c*d^14 - 2*a^3*c^2*d^13 + 6*a^3*c^6*d^9 - 4*a^3*c^8*d^7 - 8*b^3*c^3*d^12 + 6*b^3*c^5*d^10 - 4*b^3*c^7*d^8 + 2*b^3*c^9*d^6 - 12*a*b^2*c^2*d^13 + 18*a*b^2*c^4*d^11 - 6*a*b^2*c^8*d^7 + 18*a^2*b*c^3*d^12 - 36*a^2*b*c^5*d^10 + 18*a^2*b*c^7*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) - (8*tan(e/2 + (f*x)/2)*(4*a^3*c*d^15 - 12*a^3*c^5*d^11 + 8*a^3*c^7*d^9 - 24*b^3*c^2*d^14 + 68*b^3*c^4*d^12 - 72*b^3*c^6*d^10 + 36*b^3*c^8*d^8 - 8*b^3*c^10*d^6 - 36*a*b^2*c^3*d^13 + 12*a*b^2*c^7*d^9 - 36*a^2*b*c^2*d^14 + 72*a^2*b*c^4*d^12 - 36*a^2*b*c^6*d^10 + 24*a*b^2*c*d^15))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6) + (((8*(4*c^2*d^16 - 16*c^4*d^14 + 24*c^6*d^12 - 16*c^8*d^10 + 4*c^10*d^8))/(d^13 - 4*c^2*d^11 + 6*c^4*d^9 - 4*c^6*d^7 + c^8*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^18 - 56*c^3*d^16 + 104*c^5*d^14 - 96*c^7*d^12 + 44*c^9*d^10 - 8*c^11*d^8))/(d^14 - 4*c^2*d^12 + 6*c^4*d^10 - 4*c^6*d^8 + c^8*d^6))*(a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3)))*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d))/(2*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3))))*(a*d - b*c)*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 2*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 8*a*b*c*d^3 + 2*a*b*c^3*d)*1i)/(f*(d^13 - 5*c^2*d^11 + 10*c^4*d^9 - 10*c^6*d^7 + 5*c^8*d^5 - c^10*d^3))","B"
693,1,1423,325,11.797253,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^4,x)","\frac{\frac{18\,a^3\,c^4\,d-5\,a^3\,c^2\,d^3+2\,a^3\,d^5-18\,a^2\,b\,c^5-30\,a^2\,b\,c^3\,d^2+3\,a^2\,b\,c\,d^4+39\,a\,b^2\,c^4\,d+6\,a\,b^2\,c^2\,d^3-4\,b^3\,c^5-11\,b^3\,c^3\,d^2}{3\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-9\,a^3\,c^4\,d^2+6\,a^3\,c^2\,d^4-2\,a^3\,d^6+12\,a^2\,b\,c^5\,d+3\,a^2\,b\,c^3\,d^3-3\,a\,b^2\,c^6-12\,a\,b^2\,c^4\,d^2+3\,b^3\,c^5\,d+2\,b^3\,c^3\,d^3\right)}{c\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,a^3\,c^6\,d+20\,a^3\,c^4\,d^3-3\,a^3\,c^2\,d^5+2\,a^3\,d^7-6\,a^2\,b\,c^7-30\,a^2\,b\,c^5\,d^2-42\,a^2\,b\,c^3\,d^4+3\,a^2\,b\,c\,d^6+12\,a\,b^2\,c^6\,d+51\,a\,b^2\,c^4\,d^3+12\,a\,b^2\,c^2\,d^5-2\,b^3\,c^7-6\,b^3\,c^5\,d^2-17\,b^3\,c^3\,d^4\right)}{c^2\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-27\,a^3\,c^4\,d^2+4\,a^3\,c^2\,d^4-2\,a^3\,d^6+24\,a^2\,b\,c^5\,d+57\,a^2\,b\,c^3\,d^3-6\,a^2\,b\,c\,d^5+3\,a\,b^2\,c^6-66\,a\,b^2\,c^4\,d^2-12\,a\,b^2\,c^2\,d^4+5\,b^3\,c^5\,d+20\,b^3\,c^3\,d^3\right)}{c\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a^3\,c^6\,d+27\,a^3\,c^4\,d^3-12\,a^3\,c^2\,d^5+4\,a^3\,d^7-6\,a^2\,b\,c^7-42\,a^2\,b\,c^5\,d^2-33\,a^2\,b\,c^3\,d^4+6\,a^2\,b\,c\,d^6+15\,a\,b^2\,c^6\,d+60\,a\,b^2\,c^4\,d^3-15\,b^3\,c^5\,d^2-10\,b^3\,c^3\,d^4\right)}{c^2\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}+\frac{2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,c^2+2\,d^2\right)\,\left(18\,a^3\,c^4\,d-5\,a^3\,c^2\,d^3+2\,a^3\,d^5-18\,a^2\,b\,c^5-30\,a^2\,b\,c^3\,d^2+3\,a^2\,b\,c\,d^4+39\,a\,b^2\,c^4\,d+6\,a\,b^2\,c^2\,d^3-4\,b^3\,c^5-11\,b^3\,c^3\,d^2\right)}{3\,c^3\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}}{f\,\left(c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^3+12\,c\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,c^2\,d+8\,d^3\right)+c^3+6\,c^2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,c^2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}+\frac{\mathrm{atan}\left(\frac{\left(\frac{c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c-b\,d\right)\,\left(2\,a^2\,c^2+3\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2+2\,b^2\,d^2\right)}{{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{7/2}}+\frac{\left(a\,c-b\,d\right)\,\left(2\,c^6\,d-6\,c^4\,d^3+6\,c^2\,d^5-2\,d^7\right)\,\left(2\,a^2\,c^2+3\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2+2\,b^2\,d^2\right)}{2\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{7/2}\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}\right)\,\left(c^6-3\,c^4\,d^2+3\,c^2\,d^4-d^6\right)}{2\,a^3\,c^3+3\,a^3\,c\,d^2-12\,a^2\,b\,c^2\,d-3\,a^2\,b\,d^3+3\,a\,b^2\,c^3+12\,a\,b^2\,c\,d^2-3\,b^3\,c^2\,d-2\,b^3\,d^3}\right)\,\left(a\,c-b\,d\right)\,\left(2\,a^2\,c^2+3\,a^2\,d^2-10\,a\,b\,c\,d+3\,b^2\,c^2+2\,b^2\,d^2\right)}{f\,{\left(c+d\right)}^{7/2}\,{\left(c-d\right)}^{7/2}}","Not used",1,"((2*a^3*d^5 - 4*b^3*c^5 - 18*a^2*b*c^5 + 18*a^3*c^4*d - 5*a^3*c^2*d^3 - 11*b^3*c^3*d^2 + 6*a*b^2*c^2*d^3 - 30*a^2*b*c^3*d^2 + 39*a*b^2*c^4*d + 3*a^2*b*c*d^4)/(3*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) - (tan(e/2 + (f*x)/2)^5*(3*b^3*c^5*d - 3*a*b^2*c^6 - 2*a^3*d^6 + 6*a^3*c^2*d^4 - 9*a^3*c^4*d^2 + 2*b^3*c^3*d^3 - 12*a*b^2*c^4*d^2 + 3*a^2*b*c^3*d^3 + 12*a^2*b*c^5*d))/(c*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (2*tan(e/2 + (f*x)/2)^2*(2*a^3*d^7 - 2*b^3*c^7 - 6*a^2*b*c^7 + 6*a^3*c^6*d - 3*a^3*c^2*d^5 + 20*a^3*c^4*d^3 - 17*b^3*c^3*d^4 - 6*b^3*c^5*d^2 + 12*a*b^2*c^2*d^5 + 51*a*b^2*c^4*d^3 - 42*a^2*b*c^3*d^4 - 30*a^2*b*c^5*d^2 + 12*a*b^2*c^6*d + 3*a^2*b*c*d^6))/(c^2*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) - (tan(e/2 + (f*x)/2)*(3*a*b^2*c^6 - 2*a^3*d^6 + 5*b^3*c^5*d + 4*a^3*c^2*d^4 - 27*a^3*c^4*d^2 + 20*b^3*c^3*d^3 - 12*a*b^2*c^2*d^4 - 66*a*b^2*c^4*d^2 + 57*a^2*b*c^3*d^3 - 6*a^2*b*c*d^5 + 24*a^2*b*c^5*d))/(c*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (tan(e/2 + (f*x)/2)^4*(4*a^3*d^7 - 6*a^2*b*c^7 + 6*a^3*c^6*d - 12*a^3*c^2*d^5 + 27*a^3*c^4*d^3 - 10*b^3*c^3*d^4 - 15*b^3*c^5*d^2 + 60*a*b^2*c^4*d^3 - 33*a^2*b*c^3*d^4 - 42*a^2*b*c^5*d^2 + 15*a*b^2*c^6*d + 6*a^2*b*c*d^6))/(c^2*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)) + (2*d*tan(e/2 + (f*x)/2)^3*(3*c^2 + 2*d^2)*(2*a^3*d^5 - 4*b^3*c^5 - 18*a^2*b*c^5 + 18*a^3*c^4*d - 5*a^3*c^2*d^3 - 11*b^3*c^3*d^2 + 6*a*b^2*c^2*d^3 - 30*a^2*b*c^3*d^2 + 39*a*b^2*c^4*d + 3*a^2*b*c*d^4))/(3*c^3*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)))/(f*(c^3*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^2*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^4*(12*c*d^2 + 3*c^3) + tan(e/2 + (f*x)/2)^3*(12*c^2*d + 8*d^3) + c^3 + 6*c^2*d*tan(e/2 + (f*x)/2) + 6*c^2*d*tan(e/2 + (f*x)/2)^5)) + (atan((((c*tan(e/2 + (f*x)/2)*(a*c - b*d)*(2*a^2*c^2 + 3*a^2*d^2 + 3*b^2*c^2 + 2*b^2*d^2 - 10*a*b*c*d))/((c + d)^(7/2)*(c - d)^(7/2)) + ((a*c - b*d)*(2*c^6*d - 2*d^7 + 6*c^2*d^5 - 6*c^4*d^3)*(2*a^2*c^2 + 3*a^2*d^2 + 3*b^2*c^2 + 2*b^2*d^2 - 10*a*b*c*d))/(2*(c + d)^(7/2)*(c - d)^(7/2)*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2)))*(c^6 - d^6 + 3*c^2*d^4 - 3*c^4*d^2))/(2*a^3*c^3 - 2*b^3*d^3 + 3*a*b^2*c^3 - 3*a^2*b*d^3 + 3*a^3*c*d^2 - 3*b^3*c^2*d + 12*a*b^2*c*d^2 - 12*a^2*b*c^2*d))*(a*c - b*d)*(2*a^2*c^2 + 3*a^2*d^2 + 3*b^2*c^2 + 2*b^2*d^2 - 10*a*b*c*d))/(f*(c + d)^(7/2)*(c - d)^(7/2))","B"
694,1,94,54,8.124974,"\text{Not used}","int((B*sin(x) + (B*b)/a)/(a + b*sin(x)),x)","\frac{2\,B\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{b}+\frac{2\,B\,\mathrm{atanh}\left(\frac{-\sin\left(\frac{x}{2}\right)\,a^2+\cos\left(\frac{x}{2}\right)\,a\,b+2\,\sin\left(\frac{x}{2}\right)\,b^2}{\sqrt{b^2-a^2}\,\left(2\,b\,\sin\left(\frac{x}{2}\right)+a\,\cos\left(\frac{x}{2}\right)\right)}\right)\,\sqrt{b^2-a^2}}{a\,b}","Not used",1,"(2*B*atan(sin(x/2)/cos(x/2)))/b + (2*B*atanh((2*b^2*sin(x/2) - a^2*sin(x/2) + a*b*cos(x/2))/((b^2 - a^2)^(1/2)*(2*b*sin(x/2) + a*cos(x/2))))*(b^2 - a^2)^(1/2))/(a*b)","B"
695,1,6,6,7.700991,"\text{Not used}","int((B*sin(x) + (B*a)/b)/(a + b*sin(x)),x)","\frac{B\,x}{b}","Not used",1,"(B*x)/b","B"
696,1,24,12,7.865906,"\text{Not used}","int((a + b*sin(x))/(b + a*sin(x))^2,x)","-\frac{a\,\sin\left(x\right)+b\,\left(\cos\left(x\right)+1\right)}{b\,\left(b+a\,\sin\left(x\right)\right)}","Not used",1,"-(a*sin(x) + b*(cos(x) + 1))/(b*(b + a*sin(x)))","B"
697,1,36,34,7.829835,"\text{Not used}","int(-(sin(x) - 2)/(sin(x) + 2),x)","-x-\frac{8\,\sqrt{3}\,\mathrm{atan}\left(-\frac{\sqrt{3}\,\mathrm{tan}\left(\frac{x}{2}\right)-\sqrt{3}}{3\,\mathrm{tan}\left(\frac{x}{2}\right)+3}\right)}{3}","Not used",1,"- x - (8*3^(1/2)*atan(-(3^(1/2)*tan(x/2) - 3^(1/2))/(3*tan(x/2) + 3)))/3","B"
698,1,8720,235,16.485891,"\text{Not used}","int((c + d*sin(e + f*x))^4/(a + b*sin(e + f*x)),x)","-\frac{\frac{2\,\left(3\,a^2\,d^4-12\,a\,b\,c\,d^3+18\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{3\,b^3}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(a\,d^4-4\,b\,c\,d^3\right)}{b^2}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^2\,d^4-4\,a\,b\,c\,d^3+6\,b^2\,c^2\,d^2+b^2\,d^4\right)}{b^3}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(a^2\,d^4-4\,a\,b\,c\,d^3+6\,b^2\,c^2\,d^2\right)}{b^3}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,d^4-4\,b\,c\,d^3\right)}{b^2}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}+\frac{\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}+\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}-\frac{\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}-\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(2\,a^{10}\,d^{12}-24\,a^9\,b\,c\,d^{11}-4\,a^8\,b^2\,c^4\,d^8+120\,a^8\,b^2\,c^2\,d^{10}+a^8\,b^2\,d^{12}+32\,a^7\,b^3\,c^5\,d^7-336\,a^7\,b^3\,c^3\,d^9-12\,a^7\,b^3\,c\,d^{11}-112\,a^6\,b^4\,c^6\,d^6+584\,a^6\,b^4\,c^4\,d^8+54\,a^6\,b^4\,c^2\,d^{10}+224\,a^5\,b^5\,c^7\,d^5-640\,a^5\,b^5\,c^5\,d^7-116\,a^5\,b^5\,c^3\,d^9-276\,a^4\,b^6\,c^8\,d^4+416\,a^4\,b^6\,c^6\,d^6+129\,a^4\,b^6\,c^4\,d^8+208\,a^3\,b^7\,c^9\,d^3-128\,a^3\,b^7\,c^7\,d^5-72\,a^3\,b^7\,c^5\,d^7-88\,a^2\,b^8\,c^{10}\,d^2-2\,a^2\,b^8\,c^8\,d^4+16\,a^2\,b^8\,c^6\,d^6+16\,a\,b^9\,c^{11}\,d+8\,a\,b^9\,c^9\,d^3\right)}{b^8}+\frac{\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}+\frac{\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}+\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}-\frac{\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}-\frac{\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}-\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)}{b^4}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,d^{12}-96\,a^{10}\,b\,c\,d^{11}+528\,a^9\,b^2\,c^2\,d^{10}+8\,a^9\,b^2\,d^{12}-1760\,a^8\,b^3\,c^3\,d^9-96\,a^8\,b^3\,c\,d^{11}+3944\,a^7\,b^4\,c^4\,d^8+480\,a^7\,b^4\,c^2\,d^{10}+2\,a^7\,b^4\,d^{12}-6208\,a^6\,b^5\,c^5\,d^7-1344\,a^6\,b^5\,c^3\,d^9-24\,a^6\,b^5\,c\,d^{11}+6944\,a^5\,b^6\,c^6\,d^6+2344\,a^5\,b^6\,c^4\,d^8+108\,a^5\,b^6\,c^2\,d^{10}-5440\,a^4\,b^7\,c^7\,d^5-2624\,a^4\,b^7\,c^5\,d^7-232\,a^4\,b^7\,c^3\,d^9+2848\,a^3\,b^8\,c^8\,d^4+1840\,a^3\,b^8\,c^6\,d^6+258\,a^3\,b^8\,c^4\,d^8-896\,a^2\,b^9\,c^9\,d^3-736\,a^2\,b^9\,c^7\,d^5-144\,a^2\,b^9\,c^5\,d^7+128\,a\,b^{10}\,c^{10}\,d^2+128\,a\,b^{10}\,c^8\,d^4+32\,a\,b^{10}\,c^6\,d^6\right)}{b^9}}\right)\,\left(a^3\,d^4\,1{}\mathrm{i}+\frac{b^2\,d\,\left(12\,a\,c^2\,d+a\,d^3\right)\,1{}\mathrm{i}}{2}-\frac{b^3\,d\,\left(8\,c^3+4\,c\,d^2\right)\,1{}\mathrm{i}}{2}-a^2\,b\,c\,d^3\,4{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^4\,f}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(2\,a^{10}\,d^{12}-24\,a^9\,b\,c\,d^{11}-4\,a^8\,b^2\,c^4\,d^8+120\,a^8\,b^2\,c^2\,d^{10}+a^8\,b^2\,d^{12}+32\,a^7\,b^3\,c^5\,d^7-336\,a^7\,b^3\,c^3\,d^9-12\,a^7\,b^3\,c\,d^{11}-112\,a^6\,b^4\,c^6\,d^6+584\,a^6\,b^4\,c^4\,d^8+54\,a^6\,b^4\,c^2\,d^{10}+224\,a^5\,b^5\,c^7\,d^5-640\,a^5\,b^5\,c^5\,d^7-116\,a^5\,b^5\,c^3\,d^9-276\,a^4\,b^6\,c^8\,d^4+416\,a^4\,b^6\,c^6\,d^6+129\,a^4\,b^6\,c^4\,d^8+208\,a^3\,b^7\,c^9\,d^3-128\,a^3\,b^7\,c^7\,d^5-72\,a^3\,b^7\,c^5\,d^7-88\,a^2\,b^8\,c^{10}\,d^2-2\,a^2\,b^8\,c^8\,d^4+16\,a^2\,b^8\,c^6\,d^6+16\,a\,b^9\,c^{11}\,d+8\,a\,b^9\,c^9\,d^3\right)}{b^8}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,d^{12}-96\,a^{10}\,b\,c\,d^{11}+528\,a^9\,b^2\,c^2\,d^{10}+8\,a^9\,b^2\,d^{12}-1760\,a^8\,b^3\,c^3\,d^9-96\,a^8\,b^3\,c\,d^{11}+3944\,a^7\,b^4\,c^4\,d^8+480\,a^7\,b^4\,c^2\,d^{10}+2\,a^7\,b^4\,d^{12}-6208\,a^6\,b^5\,c^5\,d^7-1344\,a^6\,b^5\,c^3\,d^9-24\,a^6\,b^5\,c\,d^{11}+6944\,a^5\,b^6\,c^6\,d^6+2344\,a^5\,b^6\,c^4\,d^8+108\,a^5\,b^6\,c^2\,d^{10}-5440\,a^4\,b^7\,c^7\,d^5-2624\,a^4\,b^7\,c^5\,d^7-232\,a^4\,b^7\,c^3\,d^9+2848\,a^3\,b^8\,c^8\,d^4+1840\,a^3\,b^8\,c^6\,d^6+258\,a^3\,b^8\,c^4\,d^8-896\,a^2\,b^9\,c^9\,d^3-736\,a^2\,b^9\,c^7\,d^5-144\,a^2\,b^9\,c^5\,d^7+128\,a\,b^{10}\,c^{10}\,d^2+128\,a\,b^{10}\,c^8\,d^4+32\,a\,b^{10}\,c^6\,d^6\right)}{b^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(4\,a^8\,b^3\,d^8-32\,a^7\,b^4\,c\,d^7+112\,a^6\,b^5\,c^2\,d^6+4\,a^6\,b^5\,d^8-224\,a^5\,b^6\,c^3\,d^5-32\,a^5\,b^6\,c\,d^7+272\,a^4\,b^7\,c^4\,d^4+88\,a^4\,b^7\,c^2\,d^6+a^4\,b^7\,d^8-192\,a^3\,b^8\,c^5\,d^3-112\,a^3\,b^8\,c^3\,d^5-8\,a^3\,b^8\,c\,d^7+64\,a^2\,b^9\,c^6\,d^2+64\,a^2\,b^9\,c^4\,d^4+16\,a^2\,b^9\,c^2\,d^6\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^9\,b^3\,d^8+64\,a^8\,b^4\,c\,d^7-224\,a^7\,b^5\,c^2\,d^6+4\,a^7\,b^5\,d^8+448\,a^6\,b^6\,c^3\,d^5-32\,a^6\,b^6\,c\,d^7-552\,a^5\,b^7\,c^4\,d^4+136\,a^5\,b^7\,c^2\,d^6+7\,a^5\,b^7\,d^8+416\,a^4\,b^8\,c^5\,d^3-336\,a^4\,b^8\,c^3\,d^5-56\,a^4\,b^8\,c\,d^7-176\,a^3\,b^9\,c^6\,d^2+480\,a^3\,b^9\,c^4\,d^4+160\,a^3\,b^9\,c^2\,d^6+2\,a^3\,b^9\,d^8+32\,a^2\,b^{10}\,c^7\,d-384\,a^2\,b^{10}\,c^5\,d^3-224\,a^2\,b^{10}\,c^3\,d^5-16\,a^2\,b^{10}\,c\,d^7-4\,a\,b^{11}\,c^8+128\,a\,b^{11}\,c^6\,d^2+128\,a\,b^{11}\,c^4\,d^4+32\,a\,b^{11}\,c^2\,d^6\right)}{b^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(\frac{8\,\left(2\,a^4\,b^8\,d^4-8\,a^3\,b^9\,c\,d^3+4\,a^2\,b^{10}\,c^4+24\,a^2\,b^{10}\,c^2\,d^2+2\,a^2\,b^{10}\,d^4-16\,a\,b^{11}\,c^3\,d-8\,a\,b^{11}\,c\,d^3\right)}{b^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^5\,b^8\,d^4-32\,a^4\,b^9\,c\,d^3+48\,a^3\,b^{10}\,c^2\,d^2-32\,a^2\,b^{11}\,c^3\,d+8\,a\,b^{12}\,c^4\right)}{b^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{13}-8\,a^3\,b^{11}\right)}{b^9}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^4\,2{}\mathrm{i}}{f\,\left(b^6-a^2\,b^4\right)}","Not used",1,"- ((2*(3*a^2*d^4 + 2*b^2*d^4 + 18*b^2*c^2*d^2 - 12*a*b*c*d^3))/(3*b^3) + (tan(e/2 + (f*x)/2)^5*(a*d^4 - 4*b*c*d^3))/b^2 + (4*tan(e/2 + (f*x)/2)^2*(a^2*d^4 + b^2*d^4 + 6*b^2*c^2*d^2 - 4*a*b*c*d^3))/b^3 + (2*tan(e/2 + (f*x)/2)^4*(a^2*d^4 + 6*b^2*c^2*d^2 - 4*a*b*c*d^3))/b^3 - (tan(e/2 + (f*x)/2)*(a*d^4 - 4*b*c*d^3))/b^2)/(f*(3*tan(e/2 + (f*x)/2)^2 + 3*tan(e/2 + (f*x)/2)^4 + tan(e/2 + (f*x)/2)^6 + 1)) - (atan(((((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 + (((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 + ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i)*1i)/b^4 + (((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 - (((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 - ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i)*1i)/b^4)/((16*(2*a^10*d^12 + a^8*b^2*d^12 + 8*a*b^9*c^9*d^3 - 12*a^7*b^3*c*d^11 + 16*a^2*b^8*c^6*d^6 - 2*a^2*b^8*c^8*d^4 - 88*a^2*b^8*c^10*d^2 - 72*a^3*b^7*c^5*d^7 - 128*a^3*b^7*c^7*d^5 + 208*a^3*b^7*c^9*d^3 + 129*a^4*b^6*c^4*d^8 + 416*a^4*b^6*c^6*d^6 - 276*a^4*b^6*c^8*d^4 - 116*a^5*b^5*c^3*d^9 - 640*a^5*b^5*c^5*d^7 + 224*a^5*b^5*c^7*d^5 + 54*a^6*b^4*c^2*d^10 + 584*a^6*b^4*c^4*d^8 - 112*a^6*b^4*c^6*d^6 - 336*a^7*b^3*c^3*d^9 + 32*a^7*b^3*c^5*d^7 + 120*a^8*b^2*c^2*d^10 - 4*a^8*b^2*c^4*d^8 + 16*a*b^9*c^11*d - 24*a^9*b*c*d^11))/b^8 + (((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 + (((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 + ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4 - (((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 - (((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 - ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9)*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i))/b^4 + (16*tan(e/2 + (f*x)/2)*(8*a^11*d^12 + 2*a^7*b^4*d^12 + 8*a^9*b^2*d^12 + 32*a*b^10*c^6*d^6 + 128*a*b^10*c^8*d^4 + 128*a*b^10*c^10*d^2 - 24*a^6*b^5*c*d^11 - 96*a^8*b^3*c*d^11 - 144*a^2*b^9*c^5*d^7 - 736*a^2*b^9*c^7*d^5 - 896*a^2*b^9*c^9*d^3 + 258*a^3*b^8*c^4*d^8 + 1840*a^3*b^8*c^6*d^6 + 2848*a^3*b^8*c^8*d^4 - 232*a^4*b^7*c^3*d^9 - 2624*a^4*b^7*c^5*d^7 - 5440*a^4*b^7*c^7*d^5 + 108*a^5*b^6*c^2*d^10 + 2344*a^5*b^6*c^4*d^8 + 6944*a^5*b^6*c^6*d^6 - 1344*a^6*b^5*c^3*d^9 - 6208*a^6*b^5*c^5*d^7 + 480*a^7*b^4*c^2*d^10 + 3944*a^7*b^4*c^4*d^8 - 1760*a^8*b^3*c^3*d^9 + 528*a^9*b^2*c^2*d^10 - 96*a^10*b*c*d^11))/b^9))*(a^3*d^4*1i + (b^2*d*(a*d^3 + 12*a*c^2*d)*1i)/2 - (b^3*d*(4*c*d^2 + 8*c^3)*1i)/2 - a^2*b*c*d^3*4i)*2i)/(b^4*f) - (atan((((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(2*a^10*d^12 + a^8*b^2*d^12 + 8*a*b^9*c^9*d^3 - 12*a^7*b^3*c*d^11 + 16*a^2*b^8*c^6*d^6 - 2*a^2*b^8*c^8*d^4 - 88*a^2*b^8*c^10*d^2 - 72*a^3*b^7*c^5*d^7 - 128*a^3*b^7*c^7*d^5 + 208*a^3*b^7*c^9*d^3 + 129*a^4*b^6*c^4*d^8 + 416*a^4*b^6*c^6*d^6 - 276*a^4*b^6*c^8*d^4 - 116*a^5*b^5*c^3*d^9 - 640*a^5*b^5*c^5*d^7 + 224*a^5*b^5*c^7*d^5 + 54*a^6*b^4*c^2*d^10 + 584*a^6*b^4*c^4*d^8 - 112*a^6*b^4*c^6*d^6 - 336*a^7*b^3*c^3*d^9 + 32*a^7*b^3*c^5*d^7 + 120*a^8*b^2*c^2*d^10 - 4*a^8*b^2*c^4*d^8 + 16*a*b^9*c^11*d - 24*a^9*b*c*d^11))/b^8 + (16*tan(e/2 + (f*x)/2)*(8*a^11*d^12 + 2*a^7*b^4*d^12 + 8*a^9*b^2*d^12 + 32*a*b^10*c^6*d^6 + 128*a*b^10*c^8*d^4 + 128*a*b^10*c^10*d^2 - 24*a^6*b^5*c*d^11 - 96*a^8*b^3*c*d^11 - 144*a^2*b^9*c^5*d^7 - 736*a^2*b^9*c^7*d^5 - 896*a^2*b^9*c^9*d^3 + 258*a^3*b^8*c^4*d^8 + 1840*a^3*b^8*c^6*d^6 + 2848*a^3*b^8*c^8*d^4 - 232*a^4*b^7*c^3*d^9 - 2624*a^4*b^7*c^5*d^7 - 5440*a^4*b^7*c^7*d^5 + 108*a^5*b^6*c^2*d^10 + 2344*a^5*b^6*c^4*d^8 + 6944*a^5*b^6*c^6*d^6 - 1344*a^6*b^5*c^3*d^9 - 6208*a^6*b^5*c^5*d^7 + 480*a^7*b^4*c^2*d^10 + 3944*a^7*b^4*c^4*d^8 - 1760*a^8*b^3*c^3*d^9 + 528*a^9*b^2*c^2*d^10 - 96*a^10*b*c*d^11))/b^9 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(a^4*b^7*d^8 + 4*a^6*b^5*d^8 + 4*a^8*b^3*d^8 - 8*a^3*b^8*c*d^7 - 32*a^5*b^6*c*d^7 - 32*a^7*b^4*c*d^7 + 16*a^2*b^9*c^2*d^6 + 64*a^2*b^9*c^4*d^4 + 64*a^2*b^9*c^6*d^2 - 112*a^3*b^8*c^3*d^5 - 192*a^3*b^8*c^5*d^3 + 88*a^4*b^7*c^2*d^6 + 272*a^4*b^7*c^4*d^4 - 224*a^5*b^6*c^3*d^5 + 112*a^6*b^5*c^2*d^6))/b^8 + (8*tan(e/2 + (f*x)/2)*(2*a^3*b^9*d^8 - 4*a*b^11*c^8 + 7*a^5*b^7*d^8 + 4*a^7*b^5*d^8 - 8*a^9*b^3*d^8 + 32*a*b^11*c^2*d^6 + 128*a*b^11*c^4*d^4 + 128*a*b^11*c^6*d^2 - 16*a^2*b^10*c*d^7 + 32*a^2*b^10*c^7*d - 56*a^4*b^8*c*d^7 - 32*a^6*b^6*c*d^7 + 64*a^8*b^4*c*d^7 - 224*a^2*b^10*c^3*d^5 - 384*a^2*b^10*c^5*d^3 + 160*a^3*b^9*c^2*d^6 + 480*a^3*b^9*c^4*d^4 - 176*a^3*b^9*c^6*d^2 - 336*a^4*b^8*c^3*d^5 + 416*a^4*b^8*c^5*d^3 + 136*a^5*b^7*c^2*d^6 - 552*a^5*b^7*c^4*d^4 + 448*a^6*b^6*c^3*d^5 - 224*a^7*b^5*c^2*d^6))/b^9 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*((8*(4*a^2*b^10*c^4 + 2*a^2*b^10*d^4 + 2*a^4*b^8*d^4 - 8*a^3*b^9*c*d^3 + 24*a^2*b^10*c^2*d^2 - 8*a*b^11*c*d^3 - 16*a*b^11*c^3*d))/b^8 + (8*tan(e/2 + (f*x)/2)*(8*a*b^12*c^4 + 8*a^5*b^8*d^4 - 32*a^2*b^11*c^3*d - 32*a^4*b^9*c*d^3 + 48*a^3*b^10*c^2*d^2))/b^9 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^13 - 8*a^3*b^11))/b^9))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*(-(a + b)*(a - b))^(1/2)*(a*d - b*c)^4*2i)/(f*(b^6 - a^2*b^4))","B"
699,1,5902,156,14.770982,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + b*sin(e + f*x)),x)","\frac{\frac{2\,\left(a\,d^3-3\,b\,c\,d^2\right)}{b^2}+\frac{d^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{b}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a\,d^3-3\,b\,c\,d^2\right)}{b^2}-\frac{d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{b}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}-\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}+\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)\,\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)}{b^3}\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}+\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)\,\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)}{b^3}\right)}{b^3}\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(2\,a^7\,d^9+4\,a^6\,b\,c^3\,d^6-12\,a^6\,b\,c\,d^8-24\,a^5\,b^2\,c^4\,d^5+30\,a^5\,b^2\,c^2\,d^7+a^5\,b^2\,d^9+60\,a^4\,b^3\,c^5\,d^4-36\,a^4\,b^3\,c^3\,d^6-3\,a^4\,b^3\,c\,d^8-76\,a^3\,b^4\,c^6\,d^3+18\,a^3\,b^4\,c^4\,d^5+3\,a^3\,b^4\,c^2\,d^7+48\,a^2\,b^5\,c^7\,d^2-a^2\,b^5\,c^3\,d^6-12\,a\,b^6\,c^8\,d-2\,a\,b^6\,c^6\,d^3\right)}{b^5}-\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}-\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}+\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)\,\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)}{b^3}\right)}{b^3}\right)}{b^3}+\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,\left(\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}+\frac{\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)\,\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)}{b^3}\right)}{b^3}\right)}{b^3}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^8\,d^9-72\,a^7\,b\,c\,d^8+288\,a^6\,b^2\,c^2\,d^7+8\,a^6\,b^2\,d^9-656\,a^5\,b^3\,c^3\,d^6-48\,a^5\,b^3\,c\,d^8+912\,a^4\,b^4\,c^4\,d^5+120\,a^4\,b^4\,c^2\,d^7+2\,a^4\,b^4\,d^9-768\,a^3\,b^5\,c^5\,d^4-152\,a^3\,b^5\,c^3\,d^6-6\,a^3\,b^5\,c\,d^8+360\,a^2\,b^6\,c^6\,d^3+96\,a^2\,b^6\,c^4\,d^5+6\,a^2\,b^6\,c^2\,d^7-72\,a\,b^7\,c^7\,d^2-24\,a\,b^7\,c^5\,d^4-2\,a\,b^7\,c^3\,d^6\right)}{b^6}}\right)\,\left(a^2\,d^3\,1{}\mathrm{i}+\frac{b^2\,d\,\left(6\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^2\,3{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^3\,f}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}-\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}}{\frac{16\,\left(2\,a^7\,d^9+4\,a^6\,b\,c^3\,d^6-12\,a^6\,b\,c\,d^8-24\,a^5\,b^2\,c^4\,d^5+30\,a^5\,b^2\,c^2\,d^7+a^5\,b^2\,d^9+60\,a^4\,b^3\,c^5\,d^4-36\,a^4\,b^3\,c^3\,d^6-3\,a^4\,b^3\,c\,d^8-76\,a^3\,b^4\,c^6\,d^3+18\,a^3\,b^4\,c^4\,d^5+3\,a^3\,b^4\,c^2\,d^7+48\,a^2\,b^5\,c^7\,d^2-a^2\,b^5\,c^3\,d^6-12\,a\,b^6\,c^8\,d-2\,a\,b^6\,c^6\,d^3\right)}{b^5}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^8\,d^9-72\,a^7\,b\,c\,d^8+288\,a^6\,b^2\,c^2\,d^7+8\,a^6\,b^2\,d^9-656\,a^5\,b^3\,c^3\,d^6-48\,a^5\,b^3\,c\,d^8+912\,a^4\,b^4\,c^4\,d^5+120\,a^4\,b^4\,c^2\,d^7+2\,a^4\,b^4\,d^9-768\,a^3\,b^5\,c^5\,d^4-152\,a^3\,b^5\,c^3\,d^6-6\,a^3\,b^5\,c\,d^8+360\,a^2\,b^6\,c^6\,d^3+96\,a^2\,b^6\,c^4\,d^5+6\,a^2\,b^6\,c^2\,d^7-72\,a\,b^7\,c^7\,d^2-24\,a\,b^7\,c^5\,d^4-2\,a\,b^7\,c^3\,d^6\right)}{b^6}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}-\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(4\,a^6\,b^2\,d^6-24\,a^5\,b^3\,c\,d^5+60\,a^4\,b^4\,c^2\,d^4+4\,a^4\,b^4\,d^6-72\,a^3\,b^5\,c^3\,d^3-12\,a^3\,b^5\,c\,d^5+36\,a^2\,b^6\,c^4\,d^2+12\,a^2\,b^6\,c^2\,d^4+a^2\,b^6\,d^6\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^2\,d^6+48\,a^6\,b^3\,c\,d^5-120\,a^5\,b^4\,c^2\,d^4+4\,a^5\,b^4\,d^6+152\,a^4\,b^5\,c^3\,d^3-36\,a^4\,b^5\,c\,d^5-96\,a^3\,b^6\,c^4\,d^2+108\,a^3\,b^6\,c^2\,d^4+7\,a^3\,b^6\,d^6+24\,a^2\,b^7\,c^5\,d-144\,a^2\,b^7\,c^3\,d^3-24\,a^2\,b^7\,c\,d^5-4\,a\,b^8\,c^6+72\,a\,b^8\,c^4\,d^2+24\,a\,b^8\,c^2\,d^4+2\,a\,b^8\,d^6\right)}{b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(\frac{8\,\left(2\,a^3\,b^6\,d^3-4\,a^2\,b^7\,c^3-12\,a^2\,b^7\,c\,d^2+12\,a\,b^8\,c^2\,d+2\,a\,b^8\,d^3\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^4\,b^6\,d^3+24\,a^3\,b^7\,c\,d^2-24\,a^2\,b^8\,c^2\,d+8\,a\,b^9\,c^3\right)}{b^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a\,b^{10}-8\,a^3\,b^8\right)}{b^6}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^3\,2{}\mathrm{i}}{f\,\left(b^5-a^2\,b^3\right)}","Not used",1,"((2*(a*d^3 - 3*b*c*d^2))/b^2 + (d^3*tan(e/2 + (f*x)/2)^3)/b + (2*tan(e/2 + (f*x)/2)^2*(a*d^3 - 3*b*c*d^2))/b^2 - (d^3*tan(e/2 + (f*x)/2))/b)/(f*(2*tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^4 + 1)) + (atan((((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 - (8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 + ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6)*(a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i))/b^3))/b^3)*1i)/b^3 + ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 - (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 + ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6)*(a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i))/b^3))/b^3)*1i)/b^3)/((16*(2*a^7*d^9 + a^5*b^2*d^9 - 2*a*b^6*c^6*d^3 - 3*a^4*b^3*c*d^8 + 4*a^6*b*c^3*d^6 - a^2*b^5*c^3*d^6 + 48*a^2*b^5*c^7*d^2 + 3*a^3*b^4*c^2*d^7 + 18*a^3*b^4*c^4*d^5 - 76*a^3*b^4*c^6*d^3 - 36*a^4*b^3*c^3*d^6 + 60*a^4*b^3*c^5*d^4 + 30*a^5*b^2*c^2*d^7 - 24*a^5*b^2*c^4*d^5 - 12*a*b^6*c^8*d - 12*a^6*b*c*d^8))/b^5 - ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 - (8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 + ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6)*(a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i))/b^3))/b^3))/b^3 + ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*((8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 - (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 + ((32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6)*(a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i))/b^3))/b^3))/b^3 + (16*tan(e/2 + (f*x)/2)*(8*a^8*d^9 + 2*a^4*b^4*d^9 + 8*a^6*b^2*d^9 - 2*a*b^7*c^3*d^6 - 24*a*b^7*c^5*d^4 - 72*a*b^7*c^7*d^2 - 6*a^3*b^5*c*d^8 - 48*a^5*b^3*c*d^8 + 6*a^2*b^6*c^2*d^7 + 96*a^2*b^6*c^4*d^5 + 360*a^2*b^6*c^6*d^3 - 152*a^3*b^5*c^3*d^6 - 768*a^3*b^5*c^5*d^4 + 120*a^4*b^4*c^2*d^7 + 912*a^4*b^4*c^4*d^5 - 656*a^5*b^3*c^3*d^6 + 288*a^6*b^2*c^2*d^7 - 72*a^7*b*c*d^8))/b^6))*(a^2*d^3*1i + (b^2*d*(6*c^2 + d^2)*1i)/2 - a*b*c*d^2*3i)*2i)/(b^3*f) + (atan((((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 - (8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3))*1i)/(b^5 - a^2*b^3) + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 - (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3))*1i)/(b^5 - a^2*b^3))/((16*(2*a^7*d^9 + a^5*b^2*d^9 - 2*a*b^6*c^6*d^3 - 3*a^4*b^3*c*d^8 + 4*a^6*b*c^3*d^6 - a^2*b^5*c^3*d^6 + 48*a^2*b^5*c^7*d^2 + 3*a^3*b^4*c^2*d^7 + 18*a^3*b^4*c^4*d^5 - 76*a^3*b^4*c^6*d^3 - 36*a^4*b^3*c^3*d^6 + 60*a^4*b^3*c^5*d^4 + 30*a^5*b^2*c^2*d^7 - 24*a^5*b^2*c^4*d^5 - 12*a*b^6*c^8*d - 12*a^6*b*c*d^8))/b^5 + (16*tan(e/2 + (f*x)/2)*(8*a^8*d^9 + 2*a^4*b^4*d^9 + 8*a^6*b^2*d^9 - 2*a*b^7*c^3*d^6 - 24*a*b^7*c^5*d^4 - 72*a*b^7*c^7*d^2 - 6*a^3*b^5*c*d^8 - 48*a^5*b^3*c*d^8 + 6*a^2*b^6*c^2*d^7 + 96*a^2*b^6*c^4*d^5 + 360*a^2*b^6*c^6*d^3 - 152*a^3*b^5*c^3*d^6 - 768*a^3*b^5*c^5*d^4 + 120*a^4*b^4*c^2*d^7 + 912*a^4*b^4*c^4*d^5 - 656*a^5*b^3*c^3*d^6 + 288*a^6*b^2*c^2*d^7 - 72*a^7*b*c*d^8))/b^6 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 - (8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3) + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*(a^2*b^6*d^6 + 4*a^4*b^4*d^6 + 4*a^6*b^2*d^6 - 12*a^3*b^5*c*d^5 - 24*a^5*b^3*c*d^5 + 12*a^2*b^6*c^2*d^4 + 36*a^2*b^6*c^4*d^2 - 72*a^3*b^5*c^3*d^3 + 60*a^4*b^4*c^2*d^4))/b^5 + (8*tan(e/2 + (f*x)/2)*(2*a*b^8*d^6 - 4*a*b^8*c^6 + 7*a^3*b^6*d^6 + 4*a^5*b^4*d^6 - 8*a^7*b^2*d^6 + 24*a*b^8*c^2*d^4 + 72*a*b^8*c^4*d^2 - 24*a^2*b^7*c*d^5 + 24*a^2*b^7*c^5*d - 36*a^4*b^5*c*d^5 + 48*a^6*b^3*c*d^5 - 144*a^2*b^7*c^3*d^3 + 108*a^3*b^6*c^2*d^4 - 96*a^3*b^6*c^4*d^2 + 152*a^4*b^5*c^3*d^3 - 120*a^5*b^4*c^2*d^4))/b^6 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*((8*(2*a*b^8*d^3 - 4*a^2*b^7*c^3 + 2*a^3*b^6*d^3 - 12*a^2*b^7*c*d^2 + 12*a*b^8*c^2*d))/b^5 - (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^3 - 8*a^4*b^6*d^3 - 24*a^2*b^8*c^2*d + 24*a^3*b^7*c*d^2))/b^6 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*(32*a^2*b^3 + (8*tan(e/2 + (f*x)/2)*(12*a*b^10 - 8*a^3*b^8))/b^6))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(a*d - b*c)^3*2i)/(f*(b^5 - a^2*b^3))","B"
700,1,2628,93,12.622656,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + b*sin(e + f*x)),x)","-\frac{2\,d^2}{b\,f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{2\,d\,\mathrm{atan}\left(\frac{64\,a^4\,d^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{128\,a^4\,c^2\,d^4+64\,a^4\,d^6-512\,a^3\,b\,c^3\,d^3-384\,a^3\,b\,c\,d^5+576\,a^2\,b^2\,c^4\,d^2+768\,a^2\,b^2\,c^2\,d^4-128\,a\,b^3\,c^5\,d-512\,a\,b^3\,c^3\,d^3}+\frac{384\,a^3\,c\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{384\,a^3\,c\,d^5-\frac{64\,a^4\,d^6}{b}+512\,a^3\,c^3\,d^3+512\,a\,b^2\,c^3\,d^3-768\,a^2\,b\,c^2\,d^4-576\,a^2\,b\,c^4\,d^2-\frac{128\,a^4\,c^2\,d^4}{b}+128\,a\,b^2\,c^5\,d}+\frac{768\,a^2\,c^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{64\,a^4\,d^6}{b^2}+768\,a^2\,c^2\,d^4+576\,a^2\,c^4\,d^2-\frac{384\,a^3\,c\,d^5}{b}-128\,a\,b\,c^5\,d-\frac{512\,a^3\,c^3\,d^3}{b}+\frac{128\,a^4\,c^2\,d^4}{b^2}-512\,a\,b\,c^3\,d^3}+\frac{576\,a^2\,c^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{64\,a^4\,d^6}{b^2}+768\,a^2\,c^2\,d^4+576\,a^2\,c^4\,d^2-\frac{384\,a^3\,c\,d^5}{b}-128\,a\,b\,c^5\,d-\frac{512\,a^3\,c^3\,d^3}{b}+\frac{128\,a^4\,c^2\,d^4}{b^2}-512\,a\,b\,c^3\,d^3}+\frac{512\,a^3\,c^3\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{384\,a^3\,c\,d^5-\frac{64\,a^4\,d^6}{b}+512\,a^3\,c^3\,d^3+512\,a\,b^2\,c^3\,d^3-768\,a^2\,b\,c^2\,d^4-576\,a^2\,b\,c^4\,d^2-\frac{128\,a^4\,c^2\,d^4}{b}+128\,a\,b^2\,c^5\,d}+\frac{128\,a^4\,c^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{128\,a^4\,c^2\,d^4+64\,a^4\,d^6-512\,a^3\,b\,c^3\,d^3-384\,a^3\,b\,c\,d^5+576\,a^2\,b^2\,c^4\,d^2+768\,a^2\,b^2\,c^2\,d^4-128\,a\,b^3\,c^5\,d-512\,a\,b^3\,c^3\,d^3}-\frac{128\,a\,b\,c^5\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{64\,a^4\,d^6}{b^2}+768\,a^2\,c^2\,d^4+576\,a^2\,c^4\,d^2-\frac{384\,a^3\,c\,d^5}{b}-128\,a\,b\,c^5\,d-\frac{512\,a^3\,c^3\,d^3}{b}+\frac{128\,a^4\,c^2\,d^4}{b^2}-512\,a\,b\,c^3\,d^3}-\frac{512\,a\,b\,c^3\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\frac{64\,a^4\,d^6}{b^2}+768\,a^2\,c^2\,d^4+576\,a^2\,c^4\,d^2-\frac{384\,a^3\,c\,d^5}{b}-128\,a\,b\,c^5\,d-\frac{512\,a^3\,c^3\,d^3}{b}+\frac{128\,a^4\,c^2\,d^4}{b^2}-512\,a\,b\,c^3\,d^3}\right)\,\left(a\,d-2\,b\,c\right)}{b^2\,f}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^4\,b\,d^4-4\,a^3\,b^2\,c\,d^3+4\,a^2\,b^3\,c^2\,d^2\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^5\,b\,d^4-8\,a^4\,b^2\,c\,d^3+10\,a^3\,b^3\,c^2\,d^2-2\,a^3\,b^3\,d^4-4\,a^2\,b^4\,c^3\,d+8\,a^2\,b^4\,c\,d^3+a\,b^5\,c^4-8\,a\,b^5\,c^2\,d^2\right)}{b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,b^4\,c^2+a^2\,b^4\,d^2-2\,a\,b^5\,c\,d\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^3\,b^4\,d^2-4\,a^2\,b^5\,c\,d+2\,a\,b^6\,c^2\right)}{b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^4-a^2\,b^2}\right)}{b^4-a^2\,b^2}\right)\,1{}\mathrm{i}}{b^4-a^2\,b^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^5\,b\,d^4-8\,a^4\,b^2\,c\,d^3+10\,a^3\,b^3\,c^2\,d^2-2\,a^3\,b^3\,d^4-4\,a^2\,b^4\,c^3\,d+8\,a^2\,b^4\,c\,d^3+a\,b^5\,c^4-8\,a\,b^5\,c^2\,d^2\right)}{b^3}-\frac{32\,\left(a^4\,b\,d^4-4\,a^3\,b^2\,c\,d^3+4\,a^2\,b^3\,c^2\,d^2\right)}{b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,b^4\,c^2+a^2\,b^4\,d^2-2\,a\,b^5\,c\,d\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^3\,b^4\,d^2-4\,a^2\,b^5\,c\,d+2\,a\,b^6\,c^2\right)}{b^3}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^4-a^2\,b^2}\right)}{b^4-a^2\,b^2}\right)\,1{}\mathrm{i}}{b^4-a^2\,b^2}}{\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^5\,d^6-12\,a^4\,b\,c\,d^5+26\,a^3\,b^2\,c^2\,d^4-24\,a^2\,b^3\,c^3\,d^3+8\,a\,b^4\,c^4\,d^2\right)}{b^3}-\frac{64\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+5\,a^2\,b^2\,c^4\,d^2-2\,a\,b^3\,c^5\,d\right)}{b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^4\,b\,d^4-4\,a^3\,b^2\,c\,d^3+4\,a^2\,b^3\,c^2\,d^2\right)}{b^2}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^5\,b\,d^4-8\,a^4\,b^2\,c\,d^3+10\,a^3\,b^3\,c^2\,d^2-2\,a^3\,b^3\,d^4-4\,a^2\,b^4\,c^3\,d+8\,a^2\,b^4\,c\,d^3+a\,b^5\,c^4-8\,a\,b^5\,c^2\,d^2\right)}{b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,b^4\,c^2+a^2\,b^4\,d^2-2\,a\,b^5\,c\,d\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^3\,b^4\,d^2-4\,a^2\,b^5\,c\,d+2\,a\,b^6\,c^2\right)}{b^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^4-a^2\,b^2}\right)}{b^4-a^2\,b^2}\right)}{b^4-a^2\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^5\,b\,d^4-8\,a^4\,b^2\,c\,d^3+10\,a^3\,b^3\,c^2\,d^2-2\,a^3\,b^3\,d^4-4\,a^2\,b^4\,c^3\,d+8\,a^2\,b^4\,c\,d^3+a\,b^5\,c^4-8\,a\,b^5\,c^2\,d^2\right)}{b^3}-\frac{32\,\left(a^4\,b\,d^4-4\,a^3\,b^2\,c\,d^3+4\,a^2\,b^3\,c^2\,d^2\right)}{b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{32\,\left(a^2\,b^4\,c^2+a^2\,b^4\,d^2-2\,a\,b^5\,c\,d\right)}{b^2}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^3\,b^4\,d^2-4\,a^2\,b^5\,c\,d+2\,a\,b^6\,c^2\right)}{b^3}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,\left(32\,a^2\,b^3+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a\,b^7-2\,a^3\,b^5\right)}{b^3}\right)}{b^4-a^2\,b^2}\right)}{b^4-a^2\,b^2}\right)}{b^4-a^2\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,d-b\,c\right)}^2\,2{}\mathrm{i}}{f\,\left(b^4-a^2\,b^2\right)}","Not used",1,"- (2*d^2)/(b*f*(tan(e/2 + (f*x)/2)^2 + 1)) - (atan((((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*(a^4*b*d^4 - 4*a^3*b^2*c*d^3 + 4*a^2*b^3*c^2*d^2))/b^2 - (32*tan(e/2 + (f*x)/2)*(a*b^5*c^4 + 2*a^5*b*d^4 - 2*a^3*b^3*d^4 - 8*a*b^5*c^2*d^2 + 8*a^2*b^4*c*d^3 - 4*a^2*b^4*c^3*d - 8*a^4*b^2*c*d^3 + 10*a^3*b^3*c^2*d^2))/b^3 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*(a^2*b^4*c^2 + a^2*b^4*d^2 - 2*a*b^5*c*d))/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^2 + 2*a^3*b^4*d^2 - 4*a^2*b^5*c*d))/b^3 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*(32*a^2*b^3 + (32*tan(e/2 + (f*x)/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^4 - a^2*b^2)))/(b^4 - a^2*b^2))*1i)/(b^4 - a^2*b^2) - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*tan(e/2 + (f*x)/2)*(a*b^5*c^4 + 2*a^5*b*d^4 - 2*a^3*b^3*d^4 - 8*a*b^5*c^2*d^2 + 8*a^2*b^4*c*d^3 - 4*a^2*b^4*c^3*d - 8*a^4*b^2*c*d^3 + 10*a^3*b^3*c^2*d^2))/b^3 - (32*(a^4*b*d^4 - 4*a^3*b^2*c*d^3 + 4*a^2*b^3*c^2*d^2))/b^2 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*(a^2*b^4*c^2 + a^2*b^4*d^2 - 2*a*b^5*c*d))/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^2 + 2*a^3*b^4*d^2 - 4*a^2*b^5*c*d))/b^3 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*(32*a^2*b^3 + (32*tan(e/2 + (f*x)/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^4 - a^2*b^2)))/(b^4 - a^2*b^2))*1i)/(b^4 - a^2*b^2))/((64*tan(e/2 + (f*x)/2)*(2*a^5*d^6 + 8*a*b^4*c^4*d^2 - 24*a^2*b^3*c^3*d^3 + 26*a^3*b^2*c^2*d^4 - 12*a^4*b*c*d^5))/b^3 - (64*(a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 5*a^2*b^2*c^4*d^2 - 2*a*b^3*c^5*d))/b^2 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*(a^4*b*d^4 - 4*a^3*b^2*c*d^3 + 4*a^2*b^3*c^2*d^2))/b^2 - (32*tan(e/2 + (f*x)/2)*(a*b^5*c^4 + 2*a^5*b*d^4 - 2*a^3*b^3*d^4 - 8*a*b^5*c^2*d^2 + 8*a^2*b^4*c*d^3 - 4*a^2*b^4*c^3*d - 8*a^4*b^2*c*d^3 + 10*a^3*b^3*c^2*d^2))/b^3 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*(a^2*b^4*c^2 + a^2*b^4*d^2 - 2*a*b^5*c*d))/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^2 + 2*a^3*b^4*d^2 - 4*a^2*b^5*c*d))/b^3 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*(32*a^2*b^3 + (32*tan(e/2 + (f*x)/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^4 - a^2*b^2)))/(b^4 - a^2*b^2)))/(b^4 - a^2*b^2) + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*tan(e/2 + (f*x)/2)*(a*b^5*c^4 + 2*a^5*b*d^4 - 2*a^3*b^3*d^4 - 8*a*b^5*c^2*d^2 + 8*a^2*b^4*c*d^3 - 4*a^2*b^4*c^3*d - 8*a^4*b^2*c*d^3 + 10*a^3*b^3*c^2*d^2))/b^3 - (32*(a^4*b*d^4 - 4*a^3*b^2*c*d^3 + 4*a^2*b^3*c^2*d^2))/b^2 + ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*((32*(a^2*b^4*c^2 + a^2*b^4*d^2 - 2*a*b^5*c*d))/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^2 + 2*a^3*b^4*d^2 - 4*a^2*b^5*c*d))/b^3 - ((-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*(32*a^2*b^3 + (32*tan(e/2 + (f*x)/2)*(3*a*b^7 - 2*a^3*b^5))/b^3))/(b^4 - a^2*b^2)))/(b^4 - a^2*b^2)))/(b^4 - a^2*b^2)))*(-(a + b)*(a - b))^(1/2)*(a*d - b*c)^2*2i)/(f*(b^4 - a^2*b^2)) - (2*d*atan((64*a^4*d^6*tan(e/2 + (f*x)/2))/(64*a^4*d^6 + 128*a^4*c^2*d^4 - 512*a*b^3*c^3*d^3 - 512*a^3*b*c^3*d^3 + 768*a^2*b^2*c^2*d^4 + 576*a^2*b^2*c^4*d^2 - 128*a*b^3*c^5*d - 384*a^3*b*c*d^5) + (384*a^3*c*d^5*tan(e/2 + (f*x)/2))/(384*a^3*c*d^5 - (64*a^4*d^6)/b + 512*a^3*c^3*d^3 + 512*a*b^2*c^3*d^3 - 768*a^2*b*c^2*d^4 - 576*a^2*b*c^4*d^2 - (128*a^4*c^2*d^4)/b + 128*a*b^2*c^5*d) + (768*a^2*c^2*d^4*tan(e/2 + (f*x)/2))/((64*a^4*d^6)/b^2 + 768*a^2*c^2*d^4 + 576*a^2*c^4*d^2 - (384*a^3*c*d^5)/b - 128*a*b*c^5*d - (512*a^3*c^3*d^3)/b + (128*a^4*c^2*d^4)/b^2 - 512*a*b*c^3*d^3) + (576*a^2*c^4*d^2*tan(e/2 + (f*x)/2))/((64*a^4*d^6)/b^2 + 768*a^2*c^2*d^4 + 576*a^2*c^4*d^2 - (384*a^3*c*d^5)/b - 128*a*b*c^5*d - (512*a^3*c^3*d^3)/b + (128*a^4*c^2*d^4)/b^2 - 512*a*b*c^3*d^3) + (512*a^3*c^3*d^3*tan(e/2 + (f*x)/2))/(384*a^3*c*d^5 - (64*a^4*d^6)/b + 512*a^3*c^3*d^3 + 512*a*b^2*c^3*d^3 - 768*a^2*b*c^2*d^4 - 576*a^2*b*c^4*d^2 - (128*a^4*c^2*d^4)/b + 128*a*b^2*c^5*d) + (128*a^4*c^2*d^4*tan(e/2 + (f*x)/2))/(64*a^4*d^6 + 128*a^4*c^2*d^4 - 512*a*b^3*c^3*d^3 - 512*a^3*b*c^3*d^3 + 768*a^2*b^2*c^2*d^4 + 576*a^2*b^2*c^4*d^2 - 128*a*b^3*c^5*d - 384*a^3*b*c*d^5) - (128*a*b*c^5*d*tan(e/2 + (f*x)/2))/((64*a^4*d^6)/b^2 + 768*a^2*c^2*d^4 + 576*a^2*c^4*d^2 - (384*a^3*c*d^5)/b - 128*a*b*c^5*d - (512*a^3*c^3*d^3)/b + (128*a^4*c^2*d^4)/b^2 - 512*a*b*c^3*d^3) - (512*a*b*c^3*d^3*tan(e/2 + (f*x)/2))/((64*a^4*d^6)/b^2 + 768*a^2*c^2*d^4 + 576*a^2*c^4*d^2 - (384*a^3*c*d^5)/b - 128*a*b*c^5*d - (512*a^3*c^3*d^3)/b + (128*a^4*c^2*d^4)/b^2 - 512*a*b*c^3*d^3))*(a*d - 2*b*c))/(b^2*f)","B"
701,1,343,65,10.009488,"\text{Not used}","int((c + d*sin(e + f*x))/(a + b*sin(e + f*x)),x)","\frac{2\,d\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{b\,f}-\frac{a\,\left(d\,\ln\left(\frac{b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}-d\,\ln\left(\frac{b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}\right)-b\,c\,\ln\left(\frac{b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}+b\,c\,\ln\left(\frac{b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{b\,f\,\left(a^2-b^2\right)}","Not used",1,"(2*d*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(b*f) - (a*(d*log((b*cos(e/2 + (f*x)/2) + a*sin(e/2 + (f*x)/2) + cos(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(-(a + b)*(a - b))^(1/2) - d*log((b*cos(e/2 + (f*x)/2) + a*sin(e/2 + (f*x)/2) - cos(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(b^2 - a^2)^(1/2)) - b*c*log((b*cos(e/2 + (f*x)/2) + a*sin(e/2 + (f*x)/2) + cos(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(-(a + b)*(a - b))^(1/2) + b*c*log((b*cos(e/2 + (f*x)/2) + a*sin(e/2 + (f*x)/2) - cos(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(b^2 - a^2)^(1/2))/(b*f*(a^2 - b^2))","B"
702,1,42,47,7.793192,"\text{Not used}","int(1/(a + b*sin(e + f*x)),x)","\frac{2\,\mathrm{atan}\left(\frac{b+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{f\,\sqrt{a^2-b^2}}","Not used",1,"(2*atan((b + a*tan(e/2 + (f*x)/2))/(a^2 - b^2)^(1/2)))/(f*(a^2 - b^2)^(1/2))","B"
703,1,3281,117,9.988746,"\text{Not used}","int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))),x)","-\frac{b\,c^2\,\mathrm{atan}\left(\frac{-a^3\,b^3\,d^2\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^6\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,3{}\mathrm{i}-b^6\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}+b^6\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-b^4\,c\,d\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}+b^6\,c\,d\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a\,b^3\,c^2\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}-a\,b^3\,d^2\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}+a\,b^5\,d^2\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^5\,b\,d^2\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^2\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,b^4\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^4\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^2\,b^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,3{}\mathrm{i}-a^2\,b^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,9{}\mathrm{i}+a^4\,b^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,6{}\mathrm{i}+a^2\,b^2\,c\,d\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}-a^2\,b^4\,c\,d\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a^4\,b^2\,c\,d\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{a^7\,d^2+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^6\,b\,d^2-a^5\,b^2\,c^2-2\,a^5\,b^2\,d^2-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^4\,b^3\,c^2-4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^4\,b^3\,d^2+2\,a^3\,b^4\,c^2+a^3\,b^4\,d^2+4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b^5\,c^2+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b^5\,d^2-a\,b^6\,c^2-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^7\,c^2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(-a^3\,c^2\,d+a^3\,d^3+a^2\,b\,c^3-a^2\,b\,c\,d^2+a\,b^2\,c^2\,d-a\,b^2\,d^3-b^3\,c^3+b^3\,c\,d^2\right)}+\frac{b\,d^2\,\mathrm{atan}\left(\frac{-a^3\,b^3\,d^2\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^6\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+b^4\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,3{}\mathrm{i}-b^6\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}+b^6\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-b^4\,c\,d\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}+b^6\,c\,d\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a\,b^3\,c^2\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}-a\,b^3\,d^2\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}+a\,b^5\,d^2\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^5\,b\,d^2\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^2\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,b^4\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^4\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^2\,b^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,3{}\mathrm{i}-a^2\,b^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,9{}\mathrm{i}+a^4\,b^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,6{}\mathrm{i}+a^2\,b^2\,c\,d\,{\left(b^2-a^2\right)}^{3/2}\,1{}\mathrm{i}-a^2\,b^4\,c\,d\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a^4\,b^2\,c\,d\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{a^7\,d^2+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^6\,b\,d^2-a^5\,b^2\,c^2-2\,a^5\,b^2\,d^2-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^4\,b^3\,c^2-4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^4\,b^3\,d^2+2\,a^3\,b^4\,c^2+a^3\,b^4\,d^2+4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b^5\,c^2+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,b^5\,d^2-a\,b^6\,c^2-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^7\,c^2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(-a^3\,c^2\,d+a^3\,d^3+a^2\,b\,c^3-a^2\,b\,c\,d^2+a\,b^2\,c^2\,d-a\,b^2\,d^3-b^3\,c^3+b^3\,c\,d^2\right)}+\frac{a^2\,d\,\mathrm{atan}\left(\frac{-b^2\,c^3\,d^3\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}-a^2\,d^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+b^2\,d^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}-a\,b\,d^4\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+a\,b\,d^6\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+a^2\,c\,d^3\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}-b^2\,c\,d^3\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c\,d^5\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a^2\,c^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}-b^2\,c^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,9{}\mathrm{i}+b^2\,c^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+a\,b\,c^2\,d^2\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}-a\,b\,c^2\,d^4\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^4\,d^2\,\sqrt{d^2-c^2}\,1{}\mathrm{i}}{-a^2\,c^5\,d^2-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,c^4\,d^3+2\,a^2\,c^3\,d^4+4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,c^2\,d^5-a^2\,c\,d^6-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,d^7+b^2\,c^7+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^2\,c^6\,d-2\,b^2\,c^5\,d^2-4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^2\,c^4\,d^3+b^2\,c^3\,d^4+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^2\,c^2\,d^5}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{f\,\left(-a^3\,c^2\,d+a^3\,d^3+a^2\,b\,c^3-a^2\,b\,c\,d^2+a\,b^2\,c^2\,d-a\,b^2\,d^3-b^3\,c^3+b^3\,c\,d^2\right)}-\frac{b^2\,d\,\mathrm{atan}\left(\frac{-b^2\,c^3\,d^3\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}-a^2\,d^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,c^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-b^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+b^2\,d^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}-a\,b\,d^4\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+a\,b\,d^6\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+a^2\,c\,d^3\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}-b^2\,c\,d^3\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+b^2\,c\,d^5\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^5\,d\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-a^2\,c^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,c^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-a^2\,c^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+b^2\,c^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}-b^2\,c^2\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,9{}\mathrm{i}+b^2\,c^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+a\,b\,c^2\,d^2\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}-a\,b\,c^2\,d^4\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+a\,b\,c^4\,d^2\,\sqrt{d^2-c^2}\,1{}\mathrm{i}}{-a^2\,c^5\,d^2-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,c^4\,d^3+2\,a^2\,c^3\,d^4+4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,c^2\,d^5-a^2\,c\,d^6-2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,a^2\,d^7+b^2\,c^7+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^2\,c^6\,d-2\,b^2\,c^5\,d^2-4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^2\,c^4\,d^3+b^2\,c^3\,d^4+2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,b^2\,c^2\,d^5}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{f\,\left(-a^3\,c^2\,d+a^3\,d^3+a^2\,b\,c^3-a^2\,b\,c\,d^2+a\,b^2\,c^2\,d-a\,b^2\,d^3-b^3\,c^3+b^3\,c\,d^2\right)}","Not used",1,"(b*d^2*atan((b^4*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*3i - a^6*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^3*b^3*d^2*(b^2 - a^2)^(1/2)*2i - b^6*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - b^4*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*4i + b^6*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*4i - b^4*c*d*(b^2 - a^2)^(3/2)*1i + b^6*c*d*(b^2 - a^2)^(1/2)*1i + a*b^3*c^2*(b^2 - a^2)^(3/2)*1i - a*b^3*d^2*(b^2 - a^2)^(3/2)*1i + a*b^5*d^2*(b^2 - a^2)^(1/2)*1i + a^5*b*d^2*(b^2 - a^2)^(1/2)*1i - a^2*b^2*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i + a^2*b^4*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i - a^4*b^2*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^2*b^2*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*3i - a^2*b^4*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*9i + a^4*b^2*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*6i + a^2*b^2*c*d*(b^2 - a^2)^(3/2)*1i - a^2*b^4*c*d*(b^2 - a^2)^(1/2)*2i + a^4*b^2*c*d*(b^2 - a^2)^(1/2)*1i)/(a^7*d^2 - a*b^6*c^2 + 2*a^3*b^4*c^2 - a^5*b^2*c^2 + a^3*b^4*d^2 - 2*a^5*b^2*d^2 - 2*b^7*c^2*tan(e/2 + (f*x)/2) + 2*a^6*b*d^2*tan(e/2 + (f*x)/2) + 4*a^2*b^5*c^2*tan(e/2 + (f*x)/2) - 2*a^4*b^3*c^2*tan(e/2 + (f*x)/2) + 2*a^2*b^5*d^2*tan(e/2 + (f*x)/2) - 4*a^4*b^3*d^2*tan(e/2 + (f*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^3*d^3 - b^3*c^3 + a^2*b*c^3 - a*b^2*d^3 - a^3*c^2*d + b^3*c*d^2 + a*b^2*c^2*d - a^2*b*c*d^2)) - (b*c^2*atan((b^4*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*3i - a^6*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^3*b^3*d^2*(b^2 - a^2)^(1/2)*2i - b^6*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - b^4*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*4i + b^6*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*4i - b^4*c*d*(b^2 - a^2)^(3/2)*1i + b^6*c*d*(b^2 - a^2)^(1/2)*1i + a*b^3*c^2*(b^2 - a^2)^(3/2)*1i - a*b^3*d^2*(b^2 - a^2)^(3/2)*1i + a*b^5*d^2*(b^2 - a^2)^(1/2)*1i + a^5*b*d^2*(b^2 - a^2)^(1/2)*1i - a^2*b^2*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i + a^2*b^4*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i - a^4*b^2*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^2*b^2*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*3i - a^2*b^4*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*9i + a^4*b^2*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*6i + a^2*b^2*c*d*(b^2 - a^2)^(3/2)*1i - a^2*b^4*c*d*(b^2 - a^2)^(1/2)*2i + a^4*b^2*c*d*(b^2 - a^2)^(1/2)*1i)/(a^7*d^2 - a*b^6*c^2 + 2*a^3*b^4*c^2 - a^5*b^2*c^2 + a^3*b^4*d^2 - 2*a^5*b^2*d^2 - 2*b^7*c^2*tan(e/2 + (f*x)/2) + 2*a^6*b*d^2*tan(e/2 + (f*x)/2) + 4*a^2*b^5*c^2*tan(e/2 + (f*x)/2) - 2*a^4*b^3*c^2*tan(e/2 + (f*x)/2) + 2*a^2*b^5*d^2*tan(e/2 + (f*x)/2) - 4*a^4*b^3*d^2*tan(e/2 + (f*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^3*d^3 - b^3*c^3 + a^2*b*c^3 - a*b^2*d^3 - a^3*c^2*d + b^3*c*d^2 + a*b^2*c^2*d - a^2*b*c*d^2)) + (a^2*d*atan((a^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i - b^2*c^3*d^3*(d^2 - c^2)^(1/2)*2i - a^2*d^6*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^6*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - b^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*4i + b^2*d^6*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i - a*b*d^4*(d^2 - c^2)^(3/2)*1i + a*b*d^6*(d^2 - c^2)^(1/2)*1i + a^2*c*d^3*(d^2 - c^2)^(3/2)*1i - b^2*c*d^3*(d^2 - c^2)^(3/2)*1i + b^2*c*d^5*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d*(d^2 - c^2)^(1/2)*1i - a^2*c^2*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i + a^2*c^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - a^2*c^4*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^2*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i - b^2*c^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*9i + b^2*c^4*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + a*b*c^2*d^2*(d^2 - c^2)^(3/2)*1i - a*b*c^2*d^4*(d^2 - c^2)^(1/2)*2i + a*b*c^4*d^2*(d^2 - c^2)^(1/2)*1i)/(b^2*c^7 - a^2*c*d^6 + 2*a^2*c^3*d^4 - a^2*c^5*d^2 + b^2*c^3*d^4 - 2*b^2*c^5*d^2 - 2*a^2*d^7*tan(e/2 + (f*x)/2) + 2*b^2*c^6*d*tan(e/2 + (f*x)/2) + 4*a^2*c^2*d^5*tan(e/2 + (f*x)/2) - 2*a^2*c^4*d^3*tan(e/2 + (f*x)/2) + 2*b^2*c^2*d^5*tan(e/2 + (f*x)/2) - 4*b^2*c^4*d^3*tan(e/2 + (f*x)/2)))*(d^2 - c^2)^(1/2)*2i)/(f*(a^3*d^3 - b^3*c^3 + a^2*b*c^3 - a*b^2*d^3 - a^3*c^2*d + b^3*c*d^2 + a*b^2*c^2*d - a^2*b*c*d^2)) - (b^2*d*atan((a^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i - b^2*c^3*d^3*(d^2 - c^2)^(1/2)*2i - a^2*d^6*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - b^2*c^6*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - b^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*4i + b^2*d^6*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i - a*b*d^4*(d^2 - c^2)^(3/2)*1i + a*b*d^6*(d^2 - c^2)^(1/2)*1i + a^2*c*d^3*(d^2 - c^2)^(3/2)*1i - b^2*c*d^3*(d^2 - c^2)^(3/2)*1i + b^2*c*d^5*(d^2 - c^2)^(1/2)*1i + b^2*c^5*d*(d^2 - c^2)^(1/2)*1i - a^2*c^2*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i + a^2*c^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - a^2*c^4*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + b^2*c^2*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i - b^2*c^2*d^4*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*9i + b^2*c^4*d^2*tan(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + a*b*c^2*d^2*(d^2 - c^2)^(3/2)*1i - a*b*c^2*d^4*(d^2 - c^2)^(1/2)*2i + a*b*c^4*d^2*(d^2 - c^2)^(1/2)*1i)/(b^2*c^7 - a^2*c*d^6 + 2*a^2*c^3*d^4 - a^2*c^5*d^2 + b^2*c^3*d^4 - 2*b^2*c^5*d^2 - 2*a^2*d^7*tan(e/2 + (f*x)/2) + 2*b^2*c^6*d*tan(e/2 + (f*x)/2) + 4*a^2*c^2*d^5*tan(e/2 + (f*x)/2) - 2*a^2*c^4*d^3*tan(e/2 + (f*x)/2) + 2*b^2*c^2*d^5*tan(e/2 + (f*x)/2) - 4*b^2*c^4*d^3*tan(e/2 + (f*x)/2)))*(d^2 - c^2)^(1/2)*2i)/(f*(a^3*d^3 - b^3*c^3 + a^2*b*c^3 - a*b^2*d^3 - a^3*c^2*d + b^3*c*d^2 + a*b^2*c^2*d - a^2*b*c*d^2))","B"
704,1,24122,185,22.739037,"\text{Not used}","int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^2),x)","\frac{\frac{2\,d^2}{\left(c^2-d^2\right)\,\left(a\,d-b\,c\right)}+\frac{2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{c\,\left(c^2-d^2\right)\,\left(a\,d-b\,c\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)\,1{}\mathrm{i}}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}-\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)\,1{}\mathrm{i}}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}}{\frac{64\,\left(a^3\,b^2\,c^3\,d^3-3\,a^2\,b^3\,c^4\,d^2+2\,a^2\,b^3\,c^2\,d^4+2\,a\,b^4\,c^5\,d-3\,a\,b^4\,c^3\,d^3+a\,b^4\,c\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,b^3\,c^3\,d^3-4\,a\,b^4\,c^4\,d^2+2\,a\,b^4\,c^2\,d^4\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}-\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{b^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}\right)}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2}}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2-a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,c^2\right)}+\frac{d\,\mathrm{atan}\left(\frac{\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)\,1{}\mathrm{i}}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}-\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)\,1{}\mathrm{i}}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}}{\frac{64\,\left(a^3\,b^2\,c^3\,d^3-3\,a^2\,b^3\,c^4\,d^2+2\,a^2\,b^3\,c^2\,d^4+2\,a\,b^4\,c^5\,d-3\,a\,b^4\,c^3\,d^3+a\,b^4\,c\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,b^3\,c^3\,d^3-4\,a\,b^4\,c^4\,d^2+2\,a\,b^4\,c^2\,d^4\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}-\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^5\,b\,c^3\,d^5-5\,a^4\,b^2\,c^4\,d^4+2\,a^4\,b^2\,c^2\,d^6+8\,a^3\,b^3\,c^5\,d^3-6\,a^3\,b^3\,c^3\,d^5+a^3\,b^3\,c\,d^7-3\,a^2\,b^4\,c^6\,d^2+2\,a^2\,b^4\,c^4\,d^4-a\,b^5\,c^7\,d+2\,a\,b^5\,c^5\,d^3-a\,b^5\,c^3\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^6\,c^3\,d^5-5\,a^5\,b\,c^4\,d^4+2\,a^5\,b\,c^2\,d^6+8\,a^4\,b^2\,c^5\,d^3-8\,a^4\,b^2\,c^3\,d^5+a^4\,b^2\,c\,d^7-4\,a^3\,b^3\,c^6\,d^2+14\,a^3\,b^3\,c^4\,d^4-5\,a^3\,b^3\,c^2\,d^6+a^2\,b^4\,c^7\,d-20\,a^2\,b^4\,c^5\,d^3+17\,a^2\,b^4\,c^3\,d^5-4\,a^2\,b^4\,c\,d^7-a\,b^5\,c^8+12\,a\,b^5\,c^6\,d^2-13\,a\,b^5\,c^4\,d^4+4\,a\,b^5\,c^2\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^7\,c^5\,d^5+a^7\,c^3\,d^7+5\,a^6\,b\,c^6\,d^4-6\,a^6\,b\,c^4\,d^6+a^6\,b\,c^2\,d^8-10\,a^5\,b^2\,c^7\,d^3+16\,a^5\,b^2\,c^5\,d^5-7\,a^5\,b^2\,c^3\,d^7+a^5\,b^2\,c\,d^9+10\,a^4\,b^3\,c^8\,d^2-24\,a^4\,b^3\,c^6\,d^4+18\,a^4\,b^3\,c^4\,d^6-4\,a^4\,b^3\,c^2\,d^8-5\,a^3\,b^4\,c^9\,d+21\,a^3\,b^4\,c^7\,d^3-22\,a^3\,b^4\,c^5\,d^5+6\,a^3\,b^4\,c^3\,d^7+a^2\,b^5\,c^{10}-10\,a^2\,b^5\,c^8\,d^2+13\,a^2\,b^5\,c^6\,d^4-4\,a^2\,b^5\,c^4\,d^6+2\,a\,b^6\,c^9\,d-3\,a\,b^6\,c^7\,d^3+a\,b^6\,c^5\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,c^4\,d^6+2\,a^7\,c^2\,d^8+10\,a^6\,b\,c^5\,d^5-12\,a^6\,b\,c^3\,d^7+2\,a^6\,b\,c\,d^9-18\,a^5\,b^2\,c^6\,d^4+26\,a^5\,b^2\,c^4\,d^6-8\,a^5\,b^2\,c^2\,d^8+12\,a^4\,b^3\,c^7\,d^3-24\,a^4\,b^3\,c^5\,d^5+12\,a^4\,b^3\,c^3\,d^7+2\,a^3\,b^4\,c^8\,d^2+6\,a^3\,b^4\,c^6\,d^4-8\,a^3\,b^4\,c^4\,d^6-6\,a^2\,b^5\,c^9\,d+4\,a^2\,b^5\,c^7\,d^3+2\,a^2\,b^5\,c^5\,d^5+2\,a\,b^6\,c^{10}-2\,a\,b^6\,c^8\,d^2\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}-\frac{d\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^8\,c^6\,d^6+2\,a^8\,c^4\,d^8-a^8\,c^2\,d^{10}+4\,a^7\,b\,c^7\,d^5-7\,a^7\,b\,c^5\,d^7+2\,a^7\,b\,c^3\,d^9+a^7\,b\,c\,d^{11}-5\,a^6\,b^2\,c^8\,d^4+6\,a^6\,b^2\,c^6\,d^6+3\,a^6\,b^2\,c^4\,d^8-4\,a^6\,b^2\,c^2\,d^{10}+5\,a^5\,b^3\,c^7\,d^5-10\,a^5\,b^3\,c^5\,d^7+5\,a^5\,b^3\,c^3\,d^9+5\,a^4\,b^4\,c^{10}\,d^2-10\,a^4\,b^4\,c^8\,d^4+5\,a^4\,b^4\,c^6\,d^6-4\,a^3\,b^5\,c^{11}\,d+3\,a^3\,b^5\,c^9\,d^3+6\,a^3\,b^5\,c^7\,d^5-5\,a^3\,b^5\,c^5\,d^7+a^2\,b^6\,c^{12}+2\,a^2\,b^6\,c^{10}\,d^2-7\,a^2\,b^6\,c^8\,d^4+4\,a^2\,b^6\,c^6\,d^6-a\,b^7\,c^{11}\,d+2\,a\,b^7\,c^9\,d^3-a\,b^7\,c^7\,d^5\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^8\,c^7\,d^5-7\,a^8\,c^5\,d^7+8\,a^8\,c^3\,d^9-3\,a^8\,c\,d^{11}-10\,a^7\,b\,c^8\,d^4+35\,a^7\,b\,c^6\,d^6-40\,a^7\,b\,c^4\,d^8+15\,a^7\,b\,c^2\,d^{10}+20\,a^6\,b^2\,c^9\,d^3-73\,a^6\,b^2\,c^7\,d^5+90\,a^6\,b^2\,c^5\,d^7-41\,a^6\,b^2\,c^3\,d^9+4\,a^6\,b^2\,c\,d^{11}-20\,a^5\,b^3\,c^{10}\,d^2+85\,a^5\,b^3\,c^8\,d^4-130\,a^5\,b^3\,c^6\,d^6+85\,a^5\,b^3\,c^4\,d^8-20\,a^5\,b^3\,c^2\,d^{10}+10\,a^4\,b^4\,c^{11}\,d-65\,a^4\,b^4\,c^9\,d^3+140\,a^4\,b^4\,c^7\,d^5-125\,a^4\,b^4\,c^5\,d^7+40\,a^4\,b^4\,c^3\,d^9-2\,a^3\,b^5\,c^{12}+37\,a^3\,b^5\,c^{10}\,d^2-108\,a^3\,b^5\,c^8\,d^4+113\,a^3\,b^5\,c^6\,d^6-40\,a^3\,b^5\,c^4\,d^8-15\,a^2\,b^6\,c^{11}\,d+50\,a^2\,b^6\,c^9\,d^3-55\,a^2\,b^6\,c^7\,d^5+20\,a^2\,b^6\,c^5\,d^7+3\,a\,b^7\,c^{12}-10\,a\,b^7\,c^{10}\,d^2+11\,a\,b^7\,c^8\,d^4-4\,a\,b^7\,c^6\,d^6\right)}{a^3\,c^4\,d^3-2\,a^3\,c^2\,d^5+a^3\,d^7-3\,a^2\,b\,c^5\,d^2+6\,a^2\,b\,c^3\,d^4-3\,a^2\,b\,c\,d^6+3\,a\,b^2\,c^6\,d-6\,a\,b^2\,c^4\,d^3+3\,a\,b^2\,c^2\,d^5-b^3\,c^7+2\,b^3\,c^5\,d^2-b^3\,c^3\,d^4}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}\right)\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)}{-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,b\,c^2+a\,c\,d+b\,d^2\right)\,2{}\mathrm{i}}{f\,\left(-a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-3\,a^2\,c^2\,d^6+a^2\,d^8+2\,a\,b\,c^7\,d-6\,a\,b\,c^5\,d^3+6\,a\,b\,c^3\,d^5-2\,a\,b\,c\,d^7-b^2\,c^8+3\,b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+b^2\,c^2\,d^6\right)}","Not used",1,"((2*d^2)/((c^2 - d^2)*(a*d - b*c)) + (2*d^3*tan(e/2 + (f*x)/2))/(c*(c^2 - d^2)*(a*d - b*c)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2)) + (b^2*atan(((b^2*(b^2 - a^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d))*1i)/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d) - (b^2*(b^2 - a^2)^(1/2)*((32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d))*1i)/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d))/((64*(2*a^2*b^3*c^2*d^4 - 3*a*b^4*c^3*d^3 - 3*a^2*b^3*c^4*d^2 + a^3*b^2*c^3*d^3 + a*b^4*c*d^5 + 2*a*b^4*c^5*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (64*tan(e/2 + (f*x)/2)*(2*a*b^4*c^2*d^4 - 4*a*b^4*c^4*d^2 + 2*a^2*b^3*c^3*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (b^2*(b^2 - a^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d) - (b^2*(b^2 - a^2)^(1/2)*((32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (b^2*(b^2 - a^2)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^4*d^2 - b^4*c^2 + a^2*b^2*c^2 - a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)) + (d*atan(((d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d)*1i)/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3) - (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d)*1i)/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))/((64*(2*a^2*b^3*c^2*d^4 - 3*a*b^4*c^3*d^3 - 3*a^2*b^3*c^4*d^2 + a^3*b^2*c^3*d^3 + a*b^4*c*d^5 + 2*a*b^4*c^5*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (64*tan(e/2 + (f*x)/2)*(2*a*b^4*c^2*d^4 - 4*a*b^4*c^4*d^2 + 2*a^2*b^3*c^3*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3) - (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(2*a*b^5*c^5*d^3 - a*b^5*c^3*d^5 + a^3*b^3*c*d^7 + a^5*b*c^3*d^5 + 2*a^2*b^4*c^4*d^4 - 3*a^2*b^4*c^6*d^2 - 6*a^3*b^3*c^3*d^5 + 8*a^3*b^3*c^5*d^3 + 2*a^4*b^2*c^2*d^6 - 5*a^4*b^2*c^4*d^4 - a*b^5*c^7*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (32*tan(e/2 + (f*x)/2)*(a^6*c^3*d^5 - a*b^5*c^8 + 4*a*b^5*c^2*d^6 - 13*a*b^5*c^4*d^4 + 12*a*b^5*c^6*d^2 - 4*a^2*b^4*c*d^7 + a^2*b^4*c^7*d + a^4*b^2*c*d^7 + 2*a^5*b*c^2*d^6 - 5*a^5*b*c^4*d^4 + 17*a^2*b^4*c^3*d^5 - 20*a^2*b^4*c^5*d^3 - 5*a^3*b^3*c^2*d^6 + 14*a^3*b^3*c^4*d^4 - 4*a^3*b^3*c^6*d^2 - 8*a^4*b^2*c^3*d^5 + 8*a^4*b^2*c^5*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^5*c^10 + a^7*c^3*d^7 - a^7*c^5*d^5 + a*b^6*c^5*d^5 - 3*a*b^6*c^7*d^3 - 5*a^3*b^4*c^9*d + a^5*b^2*c*d^9 + a^6*b*c^2*d^8 - 6*a^6*b*c^4*d^6 + 5*a^6*b*c^6*d^4 - 4*a^2*b^5*c^4*d^6 + 13*a^2*b^5*c^6*d^4 - 10*a^2*b^5*c^8*d^2 + 6*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^5*d^5 + 21*a^3*b^4*c^7*d^3 - 4*a^4*b^3*c^2*d^8 + 18*a^4*b^3*c^4*d^6 - 24*a^4*b^3*c^6*d^4 + 10*a^4*b^3*c^8*d^2 - 7*a^5*b^2*c^3*d^7 + 16*a^5*b^2*c^5*d^5 - 10*a^5*b^2*c^7*d^3 + 2*a*b^6*c^9*d))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(2*a*b^6*c^10 + 2*a^7*c^2*d^8 - 2*a^7*c^4*d^6 - 2*a*b^6*c^8*d^2 - 6*a^2*b^5*c^9*d - 12*a^6*b*c^3*d^7 + 10*a^6*b*c^5*d^5 + 2*a^2*b^5*c^5*d^5 + 4*a^2*b^5*c^7*d^3 - 8*a^3*b^4*c^4*d^6 + 6*a^3*b^4*c^6*d^4 + 2*a^3*b^4*c^8*d^2 + 12*a^4*b^3*c^3*d^7 - 24*a^4*b^3*c^5*d^5 + 12*a^4*b^3*c^7*d^3 - 8*a^5*b^2*c^2*d^8 + 26*a^5*b^2*c^4*d^6 - 18*a^5*b^2*c^6*d^4 + 2*a^6*b*c*d^9))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) - (d*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^2*b^6*c^12 - a^8*c^2*d^10 + 2*a^8*c^4*d^8 - a^8*c^6*d^6 - a*b^7*c^7*d^5 + 2*a*b^7*c^9*d^3 - 4*a^3*b^5*c^11*d + 2*a^7*b*c^3*d^9 - 7*a^7*b*c^5*d^7 + 4*a^7*b*c^7*d^5 + 4*a^2*b^6*c^6*d^6 - 7*a^2*b^6*c^8*d^4 + 2*a^2*b^6*c^10*d^2 - 5*a^3*b^5*c^5*d^7 + 6*a^3*b^5*c^7*d^5 + 3*a^3*b^5*c^9*d^3 + 5*a^4*b^4*c^6*d^6 - 10*a^4*b^4*c^8*d^4 + 5*a^4*b^4*c^10*d^2 + 5*a^5*b^3*c^3*d^9 - 10*a^5*b^3*c^5*d^7 + 5*a^5*b^3*c^7*d^5 - 4*a^6*b^2*c^2*d^10 + 3*a^6*b^2*c^4*d^8 + 6*a^6*b^2*c^6*d^6 - 5*a^6*b^2*c^8*d^4 - a*b^7*c^11*d + a^7*b*c*d^11))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6) + (32*tan(e/2 + (f*x)/2)*(3*a*b^7*c^12 - 3*a^8*c*d^11 - 2*a^3*b^5*c^12 + 8*a^8*c^3*d^9 - 7*a^8*c^5*d^7 + 2*a^8*c^7*d^5 - 4*a*b^7*c^6*d^6 + 11*a*b^7*c^8*d^4 - 10*a*b^7*c^10*d^2 - 15*a^2*b^6*c^11*d + 10*a^4*b^4*c^11*d + 4*a^6*b^2*c*d^11 + 15*a^7*b*c^2*d^10 - 40*a^7*b*c^4*d^8 + 35*a^7*b*c^6*d^6 - 10*a^7*b*c^8*d^4 + 20*a^2*b^6*c^5*d^7 - 55*a^2*b^6*c^7*d^5 + 50*a^2*b^6*c^9*d^3 - 40*a^3*b^5*c^4*d^8 + 113*a^3*b^5*c^6*d^6 - 108*a^3*b^5*c^8*d^4 + 37*a^3*b^5*c^10*d^2 + 40*a^4*b^4*c^3*d^9 - 125*a^4*b^4*c^5*d^7 + 140*a^4*b^4*c^7*d^5 - 65*a^4*b^4*c^9*d^3 - 20*a^5*b^3*c^2*d^10 + 85*a^5*b^3*c^4*d^8 - 130*a^5*b^3*c^6*d^6 + 85*a^5*b^3*c^8*d^4 - 20*a^5*b^3*c^10*d^2 - 41*a^6*b^2*c^3*d^9 + 90*a^6*b^2*c^5*d^7 - 73*a^6*b^2*c^7*d^5 + 20*a^6*b^2*c^9*d^3))/(a^3*d^7 - b^3*c^7 - 2*a^3*c^2*d^5 + a^3*c^4*d^3 - b^3*c^3*d^4 + 2*b^3*c^5*d^2 + 3*a*b^2*c^2*d^5 - 6*a*b^2*c^4*d^3 + 6*a^2*b*c^3*d^4 - 3*a^2*b*c^5*d^2 + 3*a*b^2*c^6*d - 3*a^2*b*c*d^6))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))*(b*d^2 - 2*b*c^2 + a*c*d))/(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3)))*(-(c + d)^3*(c - d)^3)^(1/2)*(b*d^2 - 2*b*c^2 + a*c*d)*2i)/(f*(a^2*d^8 - b^2*c^8 - 3*a^2*c^2*d^6 + 3*a^2*c^4*d^4 - a^2*c^6*d^2 + b^2*c^2*d^6 - 3*b^2*c^4*d^4 + 3*b^2*c^6*d^2 - 2*a*b*c*d^7 + 2*a*b*c^7*d + 6*a*b*c^3*d^5 - 6*a*b*c^5*d^3))","B"
705,1,62873,284,30.300142,"\text{Not used}","int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^3),x)","-\frac{\frac{6\,b\,c^3\,d^2-4\,a\,c^2\,d^3-3\,b\,c\,d^4+a\,d^5}{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(17\,b\,c^3\,d^2-11\,a\,c^2\,d^3-8\,b\,c\,d^4+2\,a\,d^5\right)}{c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(6\,b\,c^3\,d^2-4\,a\,c^2\,d^3-3\,b\,c\,d^4+a\,d^5\right)}{c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(c^4-2\,c^2\,d^2+d^4\right)}+\frac{d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(7\,b\,c^3\,d^2-5\,a\,c^2\,d^3-4\,b\,c\,d^4+2\,a\,d^5\right)}{c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(c^4-2\,c^2\,d^2+d^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^8\,b\,c^5\,d^8+4\,a^8\,b\,c^3\,d^{10}+a^8\,b\,c\,d^{12}-32\,a^7\,b^2\,c^6\,d^7-20\,a^7\,b^2\,c^4\,d^9-2\,a^7\,b^2\,c^2\,d^{11}+112\,a^6\,b^3\,c^7\,d^6+20\,a^6\,b^3\,c^5\,d^8-a^6\,b^3\,c^3\,d^{10}+4\,a^6\,b^3\,c\,d^{12}-216\,a^5\,b^4\,c^8\,d^5+64\,a^5\,b^4\,c^6\,d^7-20\,a^5\,b^4\,c^4\,d^9-8\,a^5\,b^4\,c^2\,d^{11}+240\,a^4\,b^5\,c^9\,d^4-188\,a^4\,b^5\,c^7\,d^6+95\,a^4\,b^5\,c^5\,d^8-16\,a^4\,b^5\,c^3\,d^{10}+4\,a^4\,b^5\,c\,d^{12}-140\,a^3\,b^6\,c^{10}\,d^3+164\,a^3\,b^6\,c^8\,d^5-98\,a^3\,b^6\,c^6\,d^7+24\,a^3\,b^6\,c^4\,d^9-4\,a^3\,b^6\,c^2\,d^{11}+28\,a^2\,b^7\,c^{11}\,d^2-28\,a^2\,b^7\,c^9\,d^4+a^2\,b^7\,c^7\,d^6+12\,a^2\,b^7\,c^5\,d^8-4\,a^2\,b^7\,c^3\,d^{10}+4\,a\,b^8\,c^{12}\,d-16\,a\,b^8\,c^{10}\,d^3+24\,a\,b^8\,c^8\,d^5-16\,a\,b^8\,c^6\,d^7+4\,a\,b^8\,c^4\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^5\,d^8+4\,a^9\,c^3\,d^{10}+a^9\,c\,d^{12}-32\,a^8\,b\,c^6\,d^7-20\,a^8\,b\,c^4\,d^9-2\,a^8\,b\,c^2\,d^{11}+112\,a^7\,b^2\,c^7\,d^6+12\,a^7\,b^2\,c^5\,d^8-9\,a^7\,b^2\,c^3\,d^{10}+2\,a^7\,b^2\,c\,d^{12}-216\,a^6\,b^3\,c^8\,d^5+128\,a^6\,b^3\,c^6\,d^7+20\,a^6\,b^3\,c^4\,d^9-4\,a^6\,b^3\,c^2\,d^{11}+240\,a^5\,b^4\,c^9\,d^4-412\,a^5\,b^4\,c^7\,d^6+55\,a^5\,b^4\,c^5\,d^8-14\,a^5\,b^4\,c^3\,d^{10}-4\,a^5\,b^4\,c\,d^{12}-144\,a^4\,b^5\,c^{10}\,d^3+612\,a^4\,b^5\,c^8\,d^5-250\,a^4\,b^5\,c^6\,d^7+80\,a^4\,b^5\,c^4\,d^9+8\,a^4\,b^5\,c^2\,d^{11}+40\,a^3\,b^6\,c^{11}\,d^2-564\,a^3\,b^6\,c^9\,d^4+481\,a^3\,b^6\,c^7\,d^6-274\,a^3\,b^6\,c^5\,d^8+72\,a^3\,b^6\,c^3\,d^{10}-16\,a^3\,b^6\,c\,d^{12}-8\,a^2\,b^7\,c^{12}\,d+336\,a^2\,b^7\,c^{10}\,d^3-472\,a^2\,b^7\,c^8\,d^5+372\,a^2\,b^7\,c^6\,d^7-152\,a^2\,b^7\,c^4\,d^9+32\,a^2\,b^7\,c^2\,d^{11}+4\,a\,b^8\,c^{13}-96\,a\,b^8\,c^{11}\,d^2+176\,a\,b^8\,c^9\,d^4-162\,a\,b^8\,c^7\,d^6+76\,a\,b^8\,c^5\,d^8-16\,a\,b^8\,c^3\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^{10}\,c^8\,d^8-6\,a^{10}\,c^6\,d^{10}+2\,a^{10}\,c^2\,d^{14}-32\,a^9\,b\,c^9\,d^7+54\,a^9\,b\,c^7\,d^9-12\,a^9\,b\,c^5\,d^{11}-10\,a^9\,b\,c^3\,d^{13}+112\,a^8\,b^2\,c^{10}\,d^6-218\,a^8\,b^2\,c^8\,d^8+102\,a^8\,b^2\,c^6\,d^{10}+2\,a^8\,b^2\,c^4\,d^{12}+2\,a^8\,b^2\,c^2\,d^{14}-224\,a^7\,b^3\,c^{11}\,d^5+522\,a^7\,b^3\,c^9\,d^7-394\,a^7\,b^3\,c^7\,d^9+122\,a^7\,b^3\,c^5\,d^{11}-30\,a^7\,b^3\,c^3\,d^{13}+4\,a^7\,b^3\,c\,d^{15}+280\,a^6\,b^4\,c^{12}\,d^4-822\,a^6\,b^4\,c^{10}\,d^6+894\,a^6\,b^4\,c^8\,d^8-466\,a^6\,b^4\,c^6\,d^{10}+138\,a^6\,b^4\,c^4\,d^{12}-24\,a^6\,b^4\,c^2\,d^{14}-224\,a^5\,b^5\,c^{13}\,d^3+886\,a^5\,b^5\,c^{11}\,d^5-1290\,a^5\,b^5\,c^9\,d^7+878\,a^5\,b^5\,c^7\,d^9-310\,a^5\,b^5\,c^5\,d^{11}+60\,a^5\,b^5\,c^3\,d^{13}+112\,a^4\,b^6\,c^{14}\,d^2-654\,a^4\,b^6\,c^{12}\,d^4+1202\,a^4\,b^6\,c^{10}\,d^6-970\,a^4\,b^6\,c^8\,d^8+390\,a^4\,b^6\,c^6\,d^{10}-80\,a^4\,b^6\,c^4\,d^{12}-32\,a^3\,b^7\,c^{15}\,d+318\,a^3\,b^7\,c^{13}\,d^3-702\,a^3\,b^7\,c^{11}\,d^5+638\,a^3\,b^7\,c^9\,d^7-282\,a^3\,b^7\,c^7\,d^9+60\,a^3\,b^7\,c^5\,d^{11}+4\,a^2\,b^8\,c^{16}-92\,a^2\,b^8\,c^{14}\,d^2+234\,a^2\,b^8\,c^{12}\,d^4-232\,a^2\,b^8\,c^{10}\,d^6+110\,a^2\,b^8\,c^8\,d^8-24\,a^2\,b^8\,c^6\,d^{10}+12\,a\,b^9\,c^{15}\,d-34\,a\,b^9\,c^{13}\,d^3+36\,a\,b^9\,c^{11}\,d^5-18\,a\,b^9\,c^9\,d^7+4\,a\,b^9\,c^7\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,c^7\,d^9-12\,a^{10}\,c^5\,d^{11}+4\,a^{10}\,c\,d^{15}-64\,a^9\,b\,c^8\,d^8+108\,a^9\,b\,c^6\,d^{10}-24\,a^9\,b\,c^4\,d^{12}-20\,a^9\,b\,c^2\,d^{14}+224\,a^8\,b^2\,c^9\,d^7-436\,a^8\,b^2\,c^7\,d^9+204\,a^8\,b^2\,c^5\,d^{11}+4\,a^8\,b^2\,c^3\,d^{13}+4\,a^8\,b^2\,c\,d^{15}-440\,a^7\,b^3\,c^{10}\,d^6+1004\,a^7\,b^3\,c^8\,d^8-708\,a^7\,b^3\,c^6\,d^{10}+164\,a^7\,b^3\,c^4\,d^{12}-20\,a^7\,b^3\,c^2\,d^{14}+512\,a^6\,b^4\,c^{11}\,d^5-1404\,a^6\,b^4\,c^9\,d^7+1308\,a^6\,b^4\,c^7\,d^9-452\,a^6\,b^4\,c^5\,d^{11}+36\,a^6\,b^4\,c^3\,d^{13}-328\,a^5\,b^5\,c^{12}\,d^4+1172\,a^5\,b^5\,c^{10}\,d^6-1380\,a^5\,b^5\,c^8\,d^8+556\,a^5\,b^5\,c^6\,d^{10}-20\,a^5\,b^5\,c^4\,d^{12}+64\,a^4\,b^6\,c^{13}\,d^3-508\,a^4\,b^6\,c^{11}\,d^5+804\,a^4\,b^6\,c^9\,d^7-340\,a^4\,b^6\,c^7\,d^9-20\,a^4\,b^6\,c^5\,d^{11}+56\,a^3\,b^7\,c^{14}\,d^2+36\,a^3\,b^7\,c^{12}\,d^4-204\,a^3\,b^7\,c^{10}\,d^6+76\,a^3\,b^7\,c^8\,d^8+36\,a^3\,b^7\,c^6\,d^{10}-40\,a^2\,b^8\,c^{15}\,d+56\,a^2\,b^8\,c^{13}\,d^3-12\,a^2\,b^8\,c^{11}\,d^5+16\,a^2\,b^8\,c^9\,d^7-20\,a^2\,b^8\,c^7\,d^9+8\,a\,b^9\,c^{16}-16\,a\,b^9\,c^{14}\,d^2+12\,a\,b^9\,c^{12}\,d^4-8\,a\,b^9\,c^{10}\,d^6+4\,a\,b^9\,c^8\,d^8\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^{11}\,c^{10}\,d^9-16\,a^{11}\,c^8\,d^{11}+24\,a^{11}\,c^6\,d^{13}-16\,a^{11}\,c^4\,d^{15}+4\,a^{11}\,c^2\,d^{17}-28\,a^{10}\,b\,c^{11}\,d^8+108\,a^{10}\,b\,c^9\,d^{10}-152\,a^{10}\,b\,c^7\,d^{12}+88\,a^{10}\,b\,c^5\,d^{14}-12\,a^{10}\,b\,c^3\,d^{16}-4\,a^{10}\,b\,c\,d^{18}+80\,a^9\,b^2\,c^{12}\,d^7-292\,a^9\,b^2\,c^{10}\,d^9+368\,a^9\,b^2\,c^8\,d^{11}-152\,a^9\,b^2\,c^6\,d^{13}-32\,a^9\,b^2\,c^4\,d^{15}+28\,a^9\,b^2\,c^2\,d^{17}-112\,a^8\,b^3\,c^{13}\,d^6+368\,a^8\,b^3\,c^{11}\,d^8-352\,a^8\,b^3\,c^9\,d^{10}-32\,a^8\,b^3\,c^7\,d^{12}+208\,a^8\,b^3\,c^5\,d^{14}-80\,a^8\,b^3\,c^3\,d^{16}+56\,a^7\,b^4\,c^{14}\,d^5-112\,a^7\,b^4\,c^{12}\,d^7-112\,a^7\,b^4\,c^{10}\,d^9+448\,a^7\,b^4\,c^8\,d^{11}-392\,a^7\,b^4\,c^6\,d^{13}+112\,a^7\,b^4\,c^4\,d^{15}+56\,a^6\,b^5\,c^{15}\,d^4-280\,a^6\,b^5\,c^{13}\,d^6+560\,a^6\,b^5\,c^{11}\,d^8-560\,a^6\,b^5\,c^9\,d^{10}+280\,a^6\,b^5\,c^7\,d^{12}-56\,a^6\,b^5\,c^5\,d^{14}-112\,a^5\,b^6\,c^{16}\,d^3+392\,a^5\,b^6\,c^{14}\,d^5-448\,a^5\,b^6\,c^{12}\,d^7+112\,a^5\,b^6\,c^{10}\,d^9+112\,a^5\,b^6\,c^8\,d^{11}-56\,a^5\,b^6\,c^6\,d^{13}+80\,a^4\,b^7\,c^{17}\,d^2-208\,a^4\,b^7\,c^{15}\,d^4+32\,a^4\,b^7\,c^{13}\,d^6+352\,a^4\,b^7\,c^{11}\,d^8-368\,a^4\,b^7\,c^9\,d^{10}+112\,a^4\,b^7\,c^7\,d^{12}-28\,a^3\,b^8\,c^{18}\,d+32\,a^3\,b^8\,c^{16}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\,b^5\,c^2\,d^{11}+40\,a^3\,b^6\,c^{11}\,d^2-564\,a^3\,b^6\,c^9\,d^4+481\,a^3\,b^6\,c^7\,d^6-274\,a^3\,b^6\,c^5\,d^8+72\,a^3\,b^6\,c^3\,d^{10}-16\,a^3\,b^6\,c\,d^{12}-8\,a^2\,b^7\,c^{12}\,d+336\,a^2\,b^7\,c^{10}\,d^3-472\,a^2\,b^7\,c^8\,d^5+372\,a^2\,b^7\,c^6\,d^7-152\,a^2\,b^7\,c^4\,d^9+32\,a^2\,b^7\,c^2\,d^{11}+4\,a\,b^8\,c^{13}-96\,a\,b^8\,c^{11}\,d^2+176\,a\,b^8\,c^9\,d^4-162\,a\,b^8\,c^7\,d^6+76\,a\,b^8\,c^5\,d^8-16\,a\,b^8\,c^3\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\left(4\,a^8\,b\,c^5\,d^8+4\,a^8\,b\,c^3\,d^{10}+a^8\,b\,c\,d^{12}-32\,a^7\,b^2\,c^6\,d^7-20\,a^7\,b^2\,c^4\,d^9-2\,a^7\,b^2\,c^2\,d^{11}+112\,a^6\,b^3\,c^7\,d^6+20\,a^6\,b^3\,c^5\,d^8-a^6\,b^3\,c^3\,d^{10}+4\,a^6\,b^3\,c\,d^{12}-216\,a^5\,b^4\,c^8\,d^5+64\,a^5\,b^4\,c^6\,d^7-20\,a^5\,b^4\,c^4\,d^9-8\,a^5\,b^4\,c^2\,d^{11}+240\,a^4\,b^5\,c^9\,d^4-188\,a^4\,b^5\,c^7\,d^6+95\,a^4\,b^5\,c^5\,d^8-16\,a^4\,b^5\,c^3\,d^{10}+4\,a^4\,b^5\,c\,d^{12}-140\,a^3\,b^6\,c^{10}\,d^3+164\,a^3\,b^6\,c^8\,d^5-98\,a^3\,b^6\,c^6\,d^7+24\,a^3\,b^6\,c^4\,d^9-4\,a^3\,b^6\,c^2\,d^{11}+28\,a^2\,b^7\,c^{11}\,d^2-28\,a^2\,b^7\,c^9\,d^4+a^2\,b^7\,c^7\,d^6+12\,a^2\,b^7\,c^5\,d^8-4\,a^2\,b^7\,c^3\,d^{10}+4\,a\,b^8\,c^{12}\,d-16\,a\,b^8\,c^{10}\,d^3+24\,a\,b^8\,c^8\,d^5-16\,a\,b^8\,c^6\,d^7+4\,a\,b^8\,c^4\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^{10}\,c^8\,d^8-6\,a^{10}\,c^6\,d^{10}+2\,a^{10}\,c^2\,d^{14}-32\,a^9\,b\,c^9\,d^7+54\,a^9\,b\,c^7\,d^9-12\,a^9\,b\,c^5\,d^{11}-10\,a^9\,b\,c^3\,d^{13}+112\,a^8\,b^2\,c^{10}\,d^6-218\,a^8\,b^2\,c^8\,d^8+102\,a^8\,b^2\,c^6\,d^{10}+2\,a^8\,b^2\,c^4\,d^{12}+2\,a^8\,b^2\,c^2\,d^{14}-224\,a^7\,b^3\,c^{11}\,d^5+522\,a^7\,b^3\,c^9\,d^7-394\,a^7\,b^3\,c^7\,d^9+122\,a^7\,b^3\,c^5\,d^{11}-30\,a^7\,b^3\,c^3\,d^{13}+4\,a^7\,b^3\,c\,d^{15}+280\,a^6\,b^4\,c^{12}\,d^4-822\,a^6\,b^4\,c^{10}\,d^6+894\,a^6\,b^4\,c^8\,d^8-466\,a^6\,b^4\,c^6\,d^{10}+138\,a^6\,b^4\,c^4\,d^{12}-24\,a^6\,b^4\,c^2\,d^{14}-224\,a^5\,b^5\,c^{13}\,d^3+886\,a^5\,b^5\,c^{11}\,d^5-1290\,a^5\,b^5\,c^9\,d^7+878\,a^5\,b^5\,c^7\,d^9-310\,a^5\,b^5\,c^5\,d^{11}+60\,a^5\,b^5\,c^3\,d^{13}+112\,a^4\,b^6\,c^{14}\,d^2-654\,a^4\,b^6\,c^{12}\,d^4+1202\,a^4\,b^6\,c^{10}\,d^6-970\,a^4\,b^6\,c^8\,d^8+390\,a^4\,b^6\,c^6\,d^{10}-80\,a^4\,b^6\,c^4\,d^{12}-32\,a^3\,b^7\,c^{15}\,d+318\,a^3\,b^7\,c^{13}\,d^3-702\,a^3\,b^7\,c^{11}\,d^5+638\,a^3\,b^7\,c^9\,d^7-282\,a^3\,b^7\,c^7\,d^9+60\,a^3\,b^7\,c^5\,d^{11}+4\,a^2\,b^8\,c^{16}-92\,a^2\,b^8\,c^{14}\,d^2+234\,a^2\,b^8\,c^{12}\,d^4-232\,a^2\,b^8\,c^{10}\,d^6+110\,a^2\,b^8\,c^8\,d^8-24\,a^2\,b^8\,c^6\,d^{10}+12\,a\,b^9\,c^{15}\,d-34\,a\,b^9\,c^{13}\,d^3+36\,a\,b^9\,c^{11}\,d^5-18\,a\,b^9\,c^9\,d^7+4\,a\,b^9\,c^7\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,c^7\,d^9-12\,a^{10}\,c^5\,d^{11}+4\,a^{10}\,c\,d^{15}-64\,a^9\,b\,c^8\,d^8+108\,a^9\,b\,c^6\,d^{10}-24\,a^9\,b\,c^4\,d^{12}-20\,a^9\,b\,c^2\,d^{14}+224\,a^8\,b^2\,c^9\,d^7-436\,a^8\,b^2\,c^7\,d^9+204\,a^8\,b^2\,c^5\,d^{11}+4\,a^8\,b^2\,c^3\,d^{13}+4\,a^8\,b^2\,c\,d^{15}-440\,a^7\,b^3\,c^{10}\,d^6+1004\,a^7\,b^3\,c^8\,d^8-708\,a^7\,b^3\,c^6\,d^{10}+164\,a^7\,b^3\,c^4\,d^{12}-20\,a^7\,b^3\,c^2\,d^{14}+512\,a^6\,b^4\,c^{11}\,d^5-1404\,a^6\,b^4\,c^9\,d^7+1308\,a^6\,b^4\,c^7\,d^9-452\,a^6\,b^4\,c^5\,d^{11}+36\,a^6\,b^4\,c^3\,d^{13}-328\,a^5\,b^5\,c^{12}\,d^4+1172\,a^5\,b^5\,c^{10}\,d^6-1380\,a^5\,b^5\,c^8\,d^8+556\,a^5\,b^5\,c^6\,d^{10}-20\,a^5\,b^5\,c^4\,d^{12}+64\,a^4\,b^6\,c^{13}\,d^3-508\,a^4\,b^6\,c^{11}\,d^5+804\,a^4\,b^6\,c^9\,d^7-340\,a^4\,b^6\,c^7\,d^9-20\,a^4\,b^6\,c^5\,d^{11}+56\,a^3\,b^7\,c^{14}\,d^2+36\,a^3\,b^7\,c^{12}\,d^4-204\,a^3\,b^7\,c^{10}\,d^6+76\,a^3\,b^7\,c^8\,d^8+36\,a^3\,b^7\,c^6\,d^{10}-40\,a^2\,b^8\,c^{15}\,d+56\,a^2\,b^8\,c^{13}\,d^3-12\,a^2\,b^8\,c^{11}\,d^5+16\,a^2\,b^8\,c^9\,d^7-20\,a^2\,b^8\,c^7\,d^9+8\,a\,b^9\,c^{16}-16\,a\,b^9\,c^{14}\,d^2+12\,a\,b^9\,c^{12}\,d^4-8\,a\,b^9\,c^{10}\,d^6+4\,a\,b^9\,c^8\,d^8\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^{11}\,c^{10}\,d^9-16\,a^{11}\,c^8\,d^{11}+24\,a^{11}\,c^6\,d^{13}-16\,a^{11}\,c^4\,d^{15}+4\,a^{11}\,c^2\,d^{17}-28\,a^{10}\,b\,c^{11}\,d^8+108\,a^{10}\,b\,c^9\,d^{10}-152\,a^{10}\,b\,c^7\,d^{12}+88\,a^{10}\,b\,c^5\,d^{14}-12\,a^{10}\,b\,c^3\,d^{16}-4\,a^{10}\,b\,c\,d^{18}+80\,a^9\,b^2\,c^{12}\,d^7-292\,a^9\,b^2\,c^{10}\,d^9+368\,a^9\,b^2\,c^8\,d^{11}-152\,a^9\,b^2\,c^6\,d^{13}-32\,a^9\,b^2\,c^4\,d^{15}+28\,a^9\,b^2\,c^2\,d^{17}-112\,a^8\,b^3\,c^{13}\,d^6+368\,a^8\,b^3\,c^{11}\,d^8-352\,a^8\,b^3\,c^9\,d^{10}-32\,a^8\,b^3\,c^7\,d^{12}+208\,a^8\,b^3\,c^5\,d^{14}-80\,a^8\,b^3\,c^3\,d^{16}+56\,a^7\,b^4\,c^{14}\,d^5-112\,a^7\,b^4\,c^{12}\,d^7-112\,a^7\,b^4\,c^{10}\,d^9+448\,a^7\,b^4\,c^8\,d^{11}-392\,a^7\,b^4\,c^6\,d^{13}+112\,a^7\,b^4\,c^4\,d^{15}+56\,a^6\,b^5\,c^{15}\,d^4-280\,a^6\,b^5\,c^{13}\,d^6+560\,a^6\,b^5\,c^{11}\,d^8-560\,a^6\,b^5\,c^9\,d^{10}+280\,a^6\,b^5\,c^7\,d^{12}-56\,a^6\,b^5\,c^5\,d^{14}-112\,a^5\,b^6\,c^{16}\,d^3+392\,a^5\,b^6\,c^{14}\,d^5-448\,a^5\,b^6\,c^{12}\,d^7+112\,a^5\,b^6\,c^{10}\,d^9+112\,a^5\,b^6\,c^8\,d^{11}-56\,a^5\,b^6\,c^6\,d^{13}+80\,a^4\,b^7\,c^{17}\,d^2-208\,a^4\,b^7\,c^{15}\,d^4+32\,a^4\,b^7\,c^{13}\,d^6+352\,a^4\,b^7\,c^{11}\,d^8-368\,a^4\,b^7\,c^9\,d^{10}+112\,a^4\,b^7\,c^7\,d^{12}-28\,a^3\,b^8\,c^{18}\,d+32\,a^3\,b^8\,c^{16}\,d^3+152\,a^3\,b^8\,c^{14}\,d^5-368\,a^3\,b^8\,c^{12}\,d^7+292\,a^3\,b^8\,c^{10}\,d^9-80\,a^3\,b^8\,c^8\,d^{11}+4\,a^2\,b^9\,c^{19}+12\,a^2\,b^9\,c^{17}\,d^2-88\,a^2\,b^9\,c^{15}\,d^4+152\,a^2\,b^9\,c^{13}\,d^6-108\,a^2\,b^9\,c^{11}\,d^8+28\,a^2\,b^9\,c^9\,d^{10}-4\,a\,b^{10}\,c^{18}\,d+16\,a\,b^{10}\,c^{16}\,d^3-24\,a\,b^{10}\,c^{14}\,d^5+16\,a\,b^{10}\,c^{12}\,d^7-4\,a\,b^{10}\,c^{10}\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,c^{11}\,d^8-44\,a^{11}\,c^9\,d^{10}+96\,a^{11}\,c^7\,d^{12}-104\,a^{11}\,c^5\,d^{14}+56\,a^{11}\,c^3\,d^{16}-12\,a^{11}\,c\,d^{18}-64\,a^{10}\,b\,c^{12}\,d^7+352\,a^{10}\,b\,c^{10}\,d^9-768\,a^{10}\,b\,c^8\,d^{11}+832\,a^{10}\,b\,c^6\,d^{13}-448\,a^{10}\,b\,c^4\,d^{15}+96\,a^{10}\,b\,c^2\,d^{17}+224\,a^9\,b^2\,c^{13}\,d^6-1244\,a^9\,b^2\,c^{11}\,d^8+2752\,a^9\,b^2\,c^9\,d^{10}-3048\,a^9\,b^2\,c^7\,d^{12}+1712\,a^9\,b^2\,c^5\,d^{14}-412\,a^9\,b^2\,c^3\,d^{16}+16\,a^9\,b^2\,c\,d^{18}-448\,a^8\,b^3\,c^{14}\,d^5+2560\,a^8\,b^3\,c^{12}\,d^7-5888\,a^8\,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,a^7\,b^2\,c^6\,d^7-20\,a^7\,b^2\,c^4\,d^9-2\,a^7\,b^2\,c^2\,d^{11}+112\,a^6\,b^3\,c^7\,d^6+20\,a^6\,b^3\,c^5\,d^8-a^6\,b^3\,c^3\,d^{10}+4\,a^6\,b^3\,c\,d^{12}-216\,a^5\,b^4\,c^8\,d^5+64\,a^5\,b^4\,c^6\,d^7-20\,a^5\,b^4\,c^4\,d^9-8\,a^5\,b^4\,c^2\,d^{11}+240\,a^4\,b^5\,c^9\,d^4-188\,a^4\,b^5\,c^7\,d^6+95\,a^4\,b^5\,c^5\,d^8-16\,a^4\,b^5\,c^3\,d^{10}+4\,a^4\,b^5\,c\,d^{12}-140\,a^3\,b^6\,c^{10}\,d^3+164\,a^3\,b^6\,c^8\,d^5-98\,a^3\,b^6\,c^6\,d^7+24\,a^3\,b^6\,c^4\,d^9-4\,a^3\,b^6\,c^2\,d^{11}+28\,a^2\,b^7\,c^{11}\,d^2-28\,a^2\,b^7\,c^9\,d^4+a^2\,b^7\,c^7\,d^6+12\,a^2\,b^7\,c^5\,d^8-4\,a^2\,b^7\,c^3\,d^{10}+4\,a\,b^8\,c^{12}\,d-16\,a\,b^8\,c^{10}\,d^3+24\,a\,b^8\,c^8\,d^5-16\,a\,b^8\,c^6\,d^7+4\,a\,b^8\,c^4\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^5\,d^8+4\,a^9\,c^3\,d^{10}+a^9\,c\,d^{12}-32\,a^8\,b\,c^6\,d^7-20\,a^8\,b\,c^4\,d^9-2\,a^8\,b\,c^2\,d^{11}+112\,a^7\,b^2\,c^7\,d^6+12\,a^7\,b^2\,c^5\,d^8-9\,a^7\,b^2\,c^3\,d^{10}+2\,a^7\,b^2\,c\,d^{12}-216\,a^6\,b^3\,c^8\,d^5+128\,a^6\,b^3\,c^6\,d^7+20\,a^6\,b^3\,c^4\,d^9-4\,a^6\,b^3\,c^2\,d^{11}+240\,a^5\,b^4\,c^9\,d^4-412\,a^5\,b^4\,c^7\,d^6+55\,a^5\,b^4\,c^5\,d^8-14\,a^5\,b^4\,c^3\,d^{10}-4\,a^5\,b^4\,c\,d^{12}-144\,a^4\,b^5\,c^{10}\,d^3+612\,a^4\,b^5\,c^8\,d^5-250\,a^4\,b^5\,c^6\,d^7+80\,a^4\,b^5\,c^4\,d^9+8\,a^4\,b^5\,c^2\,d^{11}+40\,a^3\,b^6\,c^{11}\,d^2-564\,a^3\,b^6\,c^9\,d^4+481\,a^3\,b^6\,c^7\,d^6-274\,a^3\,b^6\,c^5\,d^8+72\,a^3\,b^6\,c^3\,d^{10}-16\,a^3\,b^6\,c\,d^{12}-8\,a^2\,b^7\,c^{12}\,d+336\,a^2\,b^7\,c^{10}\,d^3-472\,a^2\,b^7\,c^8\,d^5+372\,a^2\,b^7\,c^6\,d^7-152\,a^2\,b^7\,c^4\,d^9+32\,a^2\,b^7\,c^2\,d^{11}+4\,a\,b^8\,c^{13}-96\,a\,b^8\,c^{11}\,d^2+176\,a\,b^8\,c^9\,d^4-162\,a\,b^8\,c^7\,d^6+76\,a\,b^8\,c^5\,d^8-16\,a\,b^8\,c^3\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^{10}\,c^8\,d^8-6\,a^{10}\,c^6\,d^{10}+2\,a^{10}\,c^2\,d^{14}-32\,a^9\,b\,c^9\,d^7+54\,a^9\,b\,c^7\,d^9-12\,a^9\,b\,c^5\,d^{11}-10\,a^9\,b\,c^3\,d^{13}+112\,a^8\,b^2\,c^{10}\,d^6-218\,a^8\,b^2\,c^8\,d^8+102\,a^8\,b^2\,c^6\,d^{10}+2\,a^8\,b^2\,c^4\,d^{12}+2\,a^8\,b^2\,c^2\,d^{14}-224\,a^7\,b^3\,c^{11}\,d^5+522\,a^7\,b^3\,c^9\,d^7-394\,a^7\,b^3\,c^7\,d^9+122\,a^7\,b^3\,c^5\,d^{11}-30\,a^7\,b^3\,c^3\,d^{13}+4\,a^7\,b^3\,c\,d^{15}+280\,a^6\,b^4\,c^{12}\,d^4-822\,a^6\,b^4\,c^{10}\,d^6+894\,a^6\,b^4\,c^8\,d^8-466\,a^6\,b^4\,c^6\,d^{10}+138\,a^6\,b^4\,c^4\,d^{12}-24\,a^6\,b^4\,c^2\,d^{14}-224\,a^5\,b^5\,c^{13}\,d^3+886\,a^5\,b^5\,c^{11}\,d^5-1290\,a^5\,b^5\,c^9\,d^7+878\,a^5\,b^5\,c^7\,d^9-310\,a^5\,b^5\,c^5\,d^{11}+60\,a^5\,b^5\,c^3\,d^{13}+112\,a^4\,b^6\,c^{14}\,d^2-654\,a^4\,b^6\,c^{12}\,d^4+1202\,a^4\,b^6\,c^{10}\,d^6-970\,a^4\,b^6\,c^8\,d^8+390\,a^4\,b^6\,c^6\,d^{10}-80\,a^4\,b^6\,c^4\,d^{12}-32\,a^3\,b^7\,c^{15}\,d+318\,a^3\,b^7\,c^{13}\,d^3-702\,a^3\,b^7\,c^{11}\,d^5+638\,a^3\,b^7\,c^9\,d^7-282\,a^3\,b^7\,c^7\,d^9+60\,a^3\,b^7\,c^5\,d^{11}+4\,a^2\,b^8\,c^{16}-92\,a^2\,b^8\,c^{14}\,d^2+234\,a^2\,b^8\,c^{12}\,d^4-232\,a^2\,b^8\,c^{10}\,d^6+110\,a^2\,b^8\,c^8\,d^8-24\,a^2\,b^8\,c^6\,d^{10}+12\,a\,b^9\,c^{15}\,d-34\,a\,b^9\,c^{13}\,d^3+36\,a\,b^9\,c^{11}\,d^5-18\,a\,b^9\,c^9\,d^7+4\,a\,b^9\,c^7\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3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5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{b^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(4\,a^{11}\,c^{10}\,d^9-16\,a^{11}\,c^8\,d^{11}+24\,a^{11}\,c^6\,d^{13}-16\,a^{11}\,c^4\,d^{15}+4\,a^{11}\,c^2\,d^{17}-28\,a^{10}\,b\,c^{11}\,d^8+108\,a^{10}\,b\,c^9\,d^{10}-152\,a^{10}\,b\,c^7\,d^{12}+88\,a^{10}\,b\,c^5\,d^{14}-12\,a^{10}\,b\,c^3\,d^{16}-4\,a^{10}\,b\,c\,d^{18}+80\,a^9\,b^2\,c^{12}\,d^7-292\,a^9\,b^2\,c^{10}\,d^9+368\,a^9\,b^2\,c^8\,d^{11}-152\,a^9\,b^2\,c^6\,d^{13}-32\,a^9\,b^2\,c^4\,d^{15}+28\,a^9\,b^2\,c^2\,d^{17}-112\,a^8\,b^3\,c^{13}\,d^6+368\,a^8\,b^3\,c^{11}\,d^8-352\,a^8\,b^3\,c^9\,d^{10}-32\,a^8\,b^3\,c^7\,d^{12}+208\,a^8\,b^3\,c^5\,d^{14}-80\,a^8\,b^3\,c^3\,d^{16}+56\,a^7\,b^4\,c^{14}\,d^5-112\,a^7\,b^4\,c^{12}\,d^7-112\,a^7\,b^4\,c^{10}\,d^9+448\,a^7\,b^4\,c^8\,d^{11}-392\,a^7\,b^4\,c^6\,d^{13}+112\,a^7\,b^4\,c^4\,d^{15}+56\,a^6\,b^5\,c^{15}\,d^4-280\,a^6\,b^5\,c^{13}\,d^6+560\,a^6\,b^5\,c^{11}\,d^8-560\,a^6\,b^5\,c^9\,d^{10}+280\,a^6\,b^5\,c^7\,d^{12}-56\,a^6\,b^5\,c^5\,d^{14}-112\,a^5\,b^6\,c^{16}\,d^3+392\,a^5\,b^6\,c^{14}\,d^5-448\,a^5\,b^6\,c^{12}\,d^7+112\,a^5\,b^6\,c^{10}\,d^9+112\,a^5\,b^6\,c^8\,d^{11}-56\,a^5\,b^6\,c^6\,d^{13}+80\,a^4\,b^7\,c^{17}\,d^2-208\,a^4\,b^7\,c^{15}\,d^4+32\,a^4\,b^7\,c^{13}\,d^6+352\,a^4\,b^7\,c^{11}\,d^8-368\,a^4\,b^7\,c^9\,d^{10}+112\,a^4\,b^7\,c^7\,d^{12}-28\,a^3\,b^8\,c^{18}\,d+32\,a^3\,b^8\,c^{16}\,d^3+152\,a^3\,b^8\,c^{14}\,d^5-368\,a^3\,b^8\,c^{12}\,d^7+292\,a^3\,b^8\,c^{10}\,d^9-80\,a^3\,b^8\,c^8\,d^{11}+4\,a^2\,b^9\,c^{19}+12\,a^2\,b^9\,c^{17}\,d^2-88\,a^2\,b^9\,c^{15}\,d^4+152\,a^2\,b^9\,c^{13}\,d^6-108\,a^2\,b^9\,c^{11}\,d^8+28\,a^2\,b^9\,c^9\,d^{10}-4\,a\,b^{10}\,c^{18}\,d+16\,a\,b^{10}\,c^{16}\,d^3-24\,a\,b^{10}\,c^{14}\,d^5+16\,a\,b^{10}\,c^{12}\,d^7-4\,a\,b^{10}\,c^{10}\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,c^{11}\,d^8-44\,a^{11}\,c^9\,d^{10}+96\,a^{11}\,c^7\,d^{12}-104\,a^{11}\,c^5\,d^{14}+56\,a^{11}\,c^3\,d^{16}-12\,a^{11}\,c\,d^{18}-64\,a^{10}\,b\,c^{12}\,d^7+352\,a^{10}\,b\,c^{10}\,d^9-768\,a^{10}\,b\,c^8\,d^{11}+832\,a^{10}\,b\,c^6\,d^{13}-448\,a^{10}\,b\,c^4\,d^{15}+96\,a^{10}\,b\,c^2\,d^{17}+224\,a^9\,b^2\,c^{13}\,d^6-1244\,a^9\,b^2\,c^{11}\,d^8+2752\,a^9\,b^2\,c^9\,d^{10}-3048\,a^9\,b^2\,c^7\,d^{12}+1712\,a^9\,b^2\,c^5\,d^{14}-412\,a^9\,b^2\,c^3\,d^{16}+16\,a^9\,b^2\,c\,d^{18}-448\,a^8\,b^3\,c^{14}\,d^5+2560\,a^8\,b^3\,c^{12}\,d^7-5888\,a^8\,b^3\,c^{10}\,d^9+6912\,a^8\,b^3\,c^8\,d^{11}-4288\,a^8\,b^3\,c^6\,d^{13}+1280\,a^8\,b^3\,c^4\,d^{15}-128\,a^8\,b^3\,c^2\,d^{17}+560\,a^7\,b^4\,c^{15}\,d^4-3416\,a^7\,b^4\,c^{13}\,d^6+8512\,a^7\,b^4\,c^{11}\,d^8-11088\,a^7\,b^4\,c^9\,d^{10}+7952\,a^7\,b^4\,c^7\,d^{12}-2968\,a^7\,b^4\,c^5\,d^{14}+448\,a^7\,b^4\,c^3\,d^{16}-448\,a^6\,b^5\,c^{16}\,d^3+3136\,a^6\,b^5\,c^{14}\,d^5-8960\,a^6\,b^5\,c^{12}\,d^7+13440\,a^6\,b^5\,c^{10}\,d^9-11200\,a^6\,b^5\,c^8\,d^{11}+4928\,a^6\,b^5\,c^6\,d^{13}-896\,a^6\,b^5\,c^4\,d^{15}+224\,a^5\,b^6\,c^{17}\,d^2-2072\,a^5\,b^6\,c^{15}\,d^4+7168\,a^5\,b^6\,c^{13}\,d^6-12432\,a^5\,b^6\,c^{11}\,d^8+11648\,a^5\,b^6\,c^9\,d^{10}-5656\,a^5\,b^6\,c^7\,d^{12}+1120\,a^5\,b^6\,c^5\,d^{14}-64\,a^4\,b^7\,c^{18}\,d+1024\,a^4\,b^7\,c^{16}\,d^3-4352\,a^4\,b^7\,c^{14}\,d^5+8448\,a^4\,b^7\,c^{12}\,d^7-8512\,a^4\,b^7\,c^{10}\,d^9+4352\,a^4\,b^7\,c^8\,d^{11}-896\,a^4\,b^7\,c^6\,d^{13}+8\,a^3\,b^8\,c^{19}-380\,a^3\,b^8\,c^{17}\,d^2+1888\,a^3\,b^8\,c^{15}\,d^4-3912\,a^3\,b^8\,c^{13}\,d^6+4088\,a^3\,b^8\,c^{11}\,d^8-2140\,a^3\,b^8\,c^9\,d^{10}+448\,a^3\,b^8\,c^7\,d^{12}+96\,a^2\,b^9\,c^{18}\,d-512\,a^2\,b^9\,c^{16}\,d^3+1088\,a^2\,b^9\,c^{14}\,d^5-1152\,a^2\,b^9\,c^{12}\,d^7+608\,a^2\,b^9\,c^{10}\,d^9-128\,a^2\,b^9\,c^8\,d^{11}-12\,a\,b^{10}\,c^{19}+64\,a\,b^{10}\,c^{17}\,d^2-136\,a\,b^{10}\,c^{15}\,d^4+144\,a\,b^{10}\,c^{13}\,d^6-76\,a\,b^{10}\,c^{11}\,d^8+16\,a\,b^{10}\,c^9\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}\right)}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^3\,b^2\,d^3-a^2\,b^3\,c^3+3\,a^2\,b^3\,c\,d^2-3\,a\,b^4\,c^2\,d+b^5\,c^3}\right)}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^3\,b^2\,d^3-a^2\,b^3\,c^3+3\,a^2\,b^3\,c\,d^2-3\,a\,b^4\,c^2\,d+b^5\,c^3}\right)}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^3\,b^2\,d^3-a^2\,b^3\,c^3+3\,a^2\,b^3\,c\,d^2-3\,a\,b^4\,c^2\,d+b^5\,c^3}}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^3\,b^2\,d^3-a^2\,b^3\,c^3+3\,a^2\,b^3\,c\,d^2-3\,a\,b^4\,c^2\,d+b^5\,c^3\right)}-\frac{d\,\mathrm{atan}\left(\frac{\frac{d\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^5\,d^8+4\,a^9\,c^3\,d^{10}+a^9\,c\,d^{12}-32\,a^8\,b\,c^6\,d^7-20\,a^8\,b\,c^4\,d^9-2\,a^8\,b\,c^2\,d^{11}+112\,a^7\,b^2\,c^7\,d^6+12\,a^7\,b^2\,c^5\,d^8-9\,a^7\,b^2\,c^3\,d^{10}+2\,a^7\,b^2\,c\,d^{12}-216\,a^6\,b^3\,c^8\,d^5+128\,a^6\,b^3\,c^6\,d^7+20\,a^6\,b^3\,c^4\,d^9-4\,a^6\,b^3\,c^2\,d^{11}+240\,a^5\,b^4\,c^9\,d^4-412\,a^5\,b^4\,c^7\,d^6+55\,a^5\,b^4\,c^5\,d^8-14\,a^5\,b^4\,c^3\,d^{10}-4\,a^5\,b^4\,c\,d^{12}-144\,a^4\,b^5\,c^{10}\,d^3+612\,a^4\,b^5\,c^8\,d^5-250\,a^4\,b^5\,c^6\,d^7+80\,a^4\,b^5\,c^4\,d^9+8\,a^4\,b^5\,c^2\,d^{11}+40\,a^3\,b^6\,c^{11}\,d^2-564\,a^3\,b^6\,c^9\,d^4+481\,a^3\,b^6\,c^7\,d^6-274\,a^3\,b^6\,c^5\,d^8+72\,a^3\,b^6\,c^3\,d^{10}-16\,a^3\,b^6\,c\,d^{12}-8\,a^2\,b^7\,c^{12}\,d+336\,a^2\,b^7\,c^{10}\,d^3-472\,a^2\,b^7\,c^8\,d^5+372\,a^2\,b^7\,c^6\,d^7-152\,a^2\,b^7\,c^4\,d^9+32\,a^2\,b^7\,c^2\,d^{11}+4\,a\,b^8\,c^{13}-96\,a\,b^8\,c^{11}\,d^2+176\,a\,b^8\,c^9\,d^4-162\,a\,b^8\,c^7\,d^6+76\,a\,b^8\,c^5\,d^8-16\,a\,b^8\,c^3\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\left(4\,a^8\,b\,c^5\,d^8+4\,a^8\,b\,c^3\,d^{10}+a^8\,b\,c\,d^{12}-32\,a^7\,b^2\,c^6\,d^7-20\,a^7\,b^2\,c^4\,d^9-2\,a^7\,b^2\,c^2\,d^{11}+112\,a^6\,b^3\,c^7\,d^6+20\,a^6\,b^3\,c^5\,d^8-a^6\,b^3\,c^3\,d^{10}+4\,a^6\,b^3\,c\,d^{12}-216\,a^5\,b^4\,c^8\,d^5+64\,a^5\,b^4\,c^6\,d^7-20\,a^5\,b^4\,c^4\,d^9-8\,a^5\,b^4\,c^2\,d^{11}+240\,a^4\,b^5\,c^9\,d^4-188\,a^4\,b^5\,c^7\,d^6+95\,a^4\,b^5\,c^5\,d^8-16\,a^4\,b^5\,c^3\,d^{10}+4\,a^4\,b^5\,c\,d^{12}-140\,a^3\,b^6\,c^{10}\,d^3+164\,a^3\,b^6\,c^8\,d^5-98\,a^3\,b^6\,c^6\,d^7+24\,a^3\,b^6\,c^4\,d^9-4\,a^3\,b^6\,c^2\,d^{11}+28\,a^2\,b^7\,c^{11}\,d^2-28\,a^2\,b^7\,c^9\,d^4+a^2\,b^7\,c^7\,d^6+12\,a^2\,b^7\,c^5\,d^8-4\,a^2\,b^7\,c^3\,d^{10}+4\,a\,b^8\,c^{12}\,d-16\,a\,b^8\,c^{10}\,d^3+24\,a\,b^8\,c^8\,d^5-16\,a\,b^8\,c^6\,d^7+4\,a\,b^8\,c^4\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{d\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,c^8\,d^8-6\,a^{10}\,c^6\,d^{10}+2\,a^{10}\,c^2\,d^{14}-32\,a^9\,b\,c^9\,d^7+54\,a^9\,b\,c^7\,d^9-12\,a^9\,b\,c^5\,d^{11}-10\,a^9\,b\,c^3\,d^{13}+112\,a^8\,b^2\,c^{10}\,d^6-218\,a^8\,b^2\,c^8\,d^8+102\,a^8\,b^2\,c^6\,d^{10}+2\,a^8\,b^2\,c^4\,d^{12}+2\,a^8\,b^2\,c^2\,d^{14}-224\,a^7\,b^3\,c^{11}\,d^5+522\,a^7\,b^3\,c^9\,d^7-394\,a^7\,b^3\,c^7\,d^9+122\,a^7\,b^3\,c^5\,d^{11}-30\,a^7\,b^3\,c^3\,d^{13}+4\,a^7\,b^3\,c\,d^{15}+280\,a^6\,b^4\,c^{12}\,d^4-822\,a^6\,b^4\,c^{10}\,d^6+894\,a^6\,b^4\,c^8\,d^8-466\,a^6\,b^4\,c^6\,d^{10}+138\,a^6\,b^4\,c^4\,d^{12}-24\,a^6\,b^4\,c^2\,d^{14}-224\,a^5\,b^5\,c^{13}\,d^3+886\,a^5\,b^5\,c^{11}\,d^5-1290\,a^5\,b^5\,c^9\,d^7+878\,a^5\,b^5\,c^7\,d^9-310\,a^5\,b^5\,c^5\,d^{11}+60\,a^5\,b^5\,c^3\,d^{13}+112\,a^4\,b^6\,c^{14}\,d^2-654\,a^4\,b^6\,c^{12}\,d^4+1202\,a^4\,b^6\,c^{10}\,d^6-970\,a^4\,b^6\,c^8\,d^8+390\,a^4\,b^6\,c^6\,d^{10}-80\,a^4\,b^6\,c^4\,d^{12}-32\,a^3\,b^7\,c^{15}\,d+318\,a^3\,b^7\,c^{13}\,d^3-702\,a^3\,b^7\,c^{11}\,d^5+638\,a^3\,b^7\,c^9\,d^7-282\,a^3\,b^7\,c^7\,d^9+60\,a^3\,b^7\,c^5\,d^{11}+4\,a^2\,b^8\,c^{16}-92\,a^2\,b^8\,c^{14}\,d^2+234\,a^2\,b^8\,c^{12}\,d^4-232\,a^2\,b^8\,c^{10}\,d^6+110\,a^2\,b^8\,c^8\,d^8-24\,a^2\,b^8\,c^6\,d^{10}+12\,a\,b^9\,c^{15}\,d-34\,a\,b^9\,c^{13}\,d^3+36\,a\,b^9\,c^{11}\,d^5-18\,a\,b^9\,c^9\,d^7+4\,a\,b^9\,c^7\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,c^7\,d^9-12\,a^{10}\,c^5\,d^{11}+4\,a^{10}\,c\,d^{15}-64\,a^9\,b\,c^8\,d^8+108\,a^9\,b\,c^6\,d^{10}-24\,a^9\,b\,c^4\,d^{12}-20\,a^9\,b\,c^2\,d^{14}+224\,a^8\,b^2\,c^9\,d^7-436\,a^8\,b^2\,c^7\,d^9+204\,a^8\,b^2\,c^5\,d^{11}+4\,a^8\,b^2\,c^3\,d^{13}+4\,a^8\,b^2\,c\,d^{15}-440\,a^7\,b^3\,c^{10}\,d^6+1004\,a^7\,b^3\,c^8\,d^8-708\,a^7\,b^3\,c^6\,d^{10}+164\,a^7\,b^3\,c^4\,d^{12}-20\,a^7\,b^3\,c^2\,d^{14}+512\,a^6\,b^4\,c^{11}\,d^5-1404\,a^6\,b^4\,c^9\,d^7+1308\,a^6\,b^4\,c^7\,d^9-452\,a^6\,b^4\,c^5\,d^{11}+36\,a^6\,b^4\,c^3\,d^{13}-328\,a^5\,b^5\,c^{12}\,d^4+1172\,a^5\,b^5\,c^{10}\,d^6-1380\,a^5\,b^5\,c^8\,d^8+556\,a^5\,b^5\,c^6\,d^{10}-20\,a^5\,b^5\,c^4\,d^{12}+64\,a^4\,b^6\,c^{13}\,d^3-508\,a^4\,b^6\,c^{11}\,d^5+804\,a^4\,b^6\,c^9\,d^7-340\,a^4\,b^6\,c^7\,d^9-20\,a^4\,b^6\,c^5\,d^{11}+56\,a^3\,b^7\,c^{14}\,d^2+36\,a^3\,b^7\,c^{12}\,d^4-204\,a^3\,b^7\,c^{10}\,d^6+76\,a^3\,b^7\,c^8\,d^8+36\,a^3\,b^7\,c^6\,d^{10}-40\,a^2\,b^8\,c^{15}\,d+56\,a^2\,b^8\,c^{13}\,d^3-12\,a^2\,b^8\,c^{11}\,d^5+16\,a^2\,b^8\,c^9\,d^7-20\,a^2\,b^8\,c^7\,d^9+8\,a\,b^9\,c^{16}-16\,a\,b^9\,c^{14}\,d^2+12\,a\,b^9\,c^{12}\,d^4-8\,a\,b^9\,c^{10}\,d^6+4\,a\,b^9\,c^8\,d^8\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{d\,\left(\frac{8\,\left(4\,a^{11}\,c^{10}\,d^9-16\,a^{11}\,c^8\,d^{11}+24\,a^{11}\,c^6\,d^{13}-16\,a^{11}\,c^4\,d^{15}+4\,a^{11}\,c^2\,d^{17}-28\,a^{10}\,b\,c^{11}\,d^8+108\,a^{10}\,b\,c^9\,d^{10}-152\,a^{10}\,b\,c^7\,d^{12}+88\,a^{10}\,b\,c^5\,d^{14}-12\,a^{10}\,b\,c^3\,d^{16}-4\,a^{10}\,b\,c\,d^{18}+80\,a^9\,b^2\,c^{12}\,d^7-292\,a^9\,b^2\,c^{10}\,d^9+368\,a^9\,b^2\,c^8\,d^{11}-152\,a^9\,b^2\,c^6\,d^{13}-32\,a^9\,b^2\,c^4\,d^{15}+28\,a^9\,b^2\,c^2\,d^{17}-112\,a^8\,b^3\,c^{13}\,d^6+368\,a^8\,b^3\,c^{11}\,d^8-352\,a^8\,b^3\,c^9\,d^{10}-32\,a^8\,b^3\,c^7\,d^{12}+208\,a^8\,b^3\,c^5\,d^{14}-80\,a^8\,b^3\,c^3\,d^{16}+56\,a^7\,b^4\,c^{14}\,d^5-112\,a^7\,b^4\,c^{12}\,d^7-112\,a^7\,b^4\,c^{10}\,d^9+448\,a^7\,b^4\,c^8\,d^{11}-392\,a^7\,b^4\,c^6\,d^{13}+112\,a^7\,b^4\,c^4\,d^{15}+56\,a^6\,b^5\,c^{15}\,d^4-280\,a^6\,b^5\,c^{13}\,d^6+560\,a^6\,b^5\,c^{11}\,d^8-560\,a^6\,b^5\,c^9\,d^{10}+280\,a^6\,b^5\,c^7\,d^{12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,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)\,1{}\mathrm{i}}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}-\frac{d\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^8\,b\,c^5\,d^8+4\,a^8\,b\,c^3\,d^{10}+a^8\,b\,c\,d^{12}-32\,a^7\,b^2\,c^6\,d^7-20\,a^7\,b^2\,c^4\,d^9-2\,a^7\,b^2\,c^2\,d^{11}+112\,a^6\,b^3\,c^7\,d^6+20\,a^6\,b^3\,c^5\,d^8-a^6\,b^3\,c^3\,d^{10}+4\,a^6\,b^3\,c\,d^{12}-216\,a^5\,b^4\,c^8\,d^5+64\,a^5\,b^4\,c^6\,d^7-20\,a^5\,b^4\,c^4\,d^9-8\,a^5\,b^4\,c^2\,d^{11}+240\,a^4\,b^5\,c^9\,d^4-188\,a^4\,b^5\,c^7\,d^6+95\,a^4\,b^5\,c^5\,d^8-16\,a^4\,b^5\,c^3\,d^{10}+4\,a^4\,b^5\,c\,d^{12}-140\,a^3\,b^6\,c^{10}\,d^3+164\,a^3\,b^6\,c^8\,d^5-98\,a^3\,b^6\,c^6\,d^7+24\,a^3\,b^6\,c^4\,d^9-4\,a^3\,b^6\,c^2\,d^{11}+28\,a^2\,b^7\,c^{11}\,d^2-28\,a^2\,b^7\,c^9\,d^4+a^2\,b^7\,c^7\,d^6+12\,a^2\,b^7\,c^5\,d^8-4\,a^2\,b^7\,c^3\,d^{10}+4\,a\,b^8\,c^{12}\,d-16\,a\,b^8\,c^{10}\,d^3+24\,a\,b^8\,c^8\,d^5-16\,a\,b^8\,c^6\,d^7+4\,a\,b^8\,c^4\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^5\,d^8+4\,a^9\,c^3\,d^{10}+a^9\,c\,d^{12}-32\,a^8\,b\,c^6\,d^7-20\,a^8\,b\,c^4\,d^9-2\,a^8\,b\,c^2\,d^{11}+112\,a^7\,b^2\,c^7\,d^6+12\,a^7\,b^2\,c^5\,d^8-9\,a^7\,b^2\,c^3\,d^{10}+2\,a^7\,b^2\,c\,d^{12}-216\,a^6\,b^3\,c^8\,d^5+128\,a^6\,b^3\,c^6\,d^7+20\,a^6\,b^3\,c^4\,d^9-4\,a^6\,b^3\,c^2\,d^{11}+240\,a^5\,b^4\,c^9\,d^4-412\,a^5\,b^4\,c^7\,d^6+55\,a^5\,b^4\,c^5\,d^8-14\,a^5\,b^4\,c^3\,d^{10}-4\,a^5\,b^4\,c\,d^{12}-144\,a^4\,b^5\,c^{10}\,d^3+612\,a^4\,b^5\,c^8\,d^5-250\,a^4\,b^5\,c^6\,d^7+80\,a^4\,b^5\,c^4\,d^9+8\,a^4\,b^5\,c^2\,d^{11}+40\,a^3\,b^6\,c^{11}\,d^2-564\,a^3\,b^6\,c^9\,d^4+481\,a^3\,b^6\,c^7\,d^6-274\,a^3\,b^6\,c^5\,d^8+72\,a^3\,b^6\,c^3\,d^{10}-16\,a^3\,b^6\,c\,d^{12}-8\,a^2\,b^7\,c^{12}\,d+336\,a^2\,b^7\,c^{10}\,d^3-472\,a^2\,b^7\,c^8\,d^5+372\,a^2\,b^7\,c^6\,d^7-152\,a^2\,b^7\,c^4\,d^9+32\,a^2\,b^7\,c^2\,d^{11}+4\,a\,b^8\,c^{13}-96\,a\,b^8\,c^{11}\,d^2+176\,a\,b^8\,c^9\,d^4-162\,a\,b^8\,c^7\,d^6+76\,a\,b^8\,c^5\,d^8-16\,a\,b^8\,c^3\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{d\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,c^8\,d^8-6\,a^{10}\,c^6\,d^{10}+2\,a^{10}\,c^2\,d^{14}-32\,a^9\,b\,c^9\,d^7+54\,a^9\,b\,c^7\,d^9-12\,a^9\,b\,c^5\,d^{11}-10\,a^9\,b\,c^3\,d^{13}+112\,a^8\,b^2\,c^{10}\,d^6-218\,a^8\,b^2\,c^8\,d^8+102\,a^8\,b^2\,c^6\,d^{10}+2\,a^8\,b^2\,c^4\,d^{12}+2\,a^8\,b^2\,c^2\,d^{14}-224\,a^7\,b^3\,c^{11}\,d^5+522\,a^7\,b^3\,c^9\,d^7-394\,a^7\,b^3\,c^7\,d^9+122\,a^7\,b^3\,c^5\,d^{11}-30\,a^7\,b^3\,c^3\,d^{13}+4\,a^7\,b^3\,c\,d^{15}+280\,a^6\,b^4\,c^{12}\,d^4-822\,a^6\,b^4\,c^{10}\,d^6+894\,a^6\,b^4\,c^8\,d^8-466\,a^6\,b^4\,c^6\,d^{10}+138\,a^6\,b^4\,c^4\,d^{12}-24\,a^6\,b^4\,c^2\,d^{14}-224\,a^5\,b^5\,c^{13}\,d^3+886\,a^5\,b^5\,c^{11}\,d^5-1290\,a^5\,b^5\,c^9\,d^7+878\,a^5\,b^5\,c^7\,d^9-310\,a^5\,b^5\,c^5\,d^{11}+60\,a^5\,b^5\,c^3\,d^{13}+112\,a^4\,b^6\,c^{14}\,d^2-654\,a^4\,b^6\,c^{12}\,d^4+1202\,a^4\,b^6\,c^{10}\,d^6-970\,a^4\,b^6\,c^8\,d^8+390\,a^4\,b^6\,c^6\,d^{10}-80\,a^4\,b^6\,c^4\,d^{12}-32\,a^3\,b^7\,c^{15}\,d+318\,a^3\,b^7\,c^{13}\,d^3-702\,a^3\,b^7\,c^{11}\,d^5+638\,a^3\,b^7\,c^9\,d^7-282\,a^3\,b^7\,c^7\,d^9+60\,a^3\,b^7\,c^5\,d^{11}+4\,a^2\,b^8\,c^{16}-92\,a^2\,b^8\,c^{14}\,d^2+234\,a^2\,b^8\,c^{12}\,d^4-232\,a^2\,b^8\,c^{10}\,d^6+110\,a^2\,b^8\,c^8\,d^8-24\,a^2\,b^8\,c^6\,d^{10}+12\,a\,b^9\,c^{15}\,d-34\,a\,b^9\,c^{13}\,d^3+36\,a\,b^9\,c^{11}\,d^5-18\,a\,b^9\,c^9\,d^7+4\,a\,b^9\,c^7\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,c^7\,d^9-12\,a^{10}\,c^5\,d^{11}+4\,a^{10}\,c\,d^{15}-64\,a^9\,b\,c^8\,d^8+108\,a^9\,b\,c^6\,d^{10}-24\,a^9\,b\,c^4\,d^{12}-20\,a^9\,b\,c^2\,d^{14}+224\,a^8\,b^2\,c^9\,d^7-436\,a^8\,b^2\,c^7\,d^9+204\,a^8\,b^2\,c^5\,d^{11}+4\,a^8\,b^2\,c^3\,d^{13}+4\,a^8\,b^2\,c\,d^{15}-440\,a^7\,b^3\,c^{10}\,d^6+1004\,a^7\,b^3\,c^8\,d^8-708\,a^7\,b^3\,c^6\,d^{10}+164\,a^7\,b^3\,c^4\,d^{12}-20\,a^7\,b^3\,c^2\,d^{14}+512\,a^6\,b^4\,c^{11}\,d^5-1404\,a^6\,b^4\,c^9\,d^7+1308\,a^6\,b^4\,c^7\,d^9-452\,a^6\,b^4\,c^5\,d^{11}+36\,a^6\,b^4\,c^3\,d^{13}-328\,a^5\,b^5\,c^{12}\,d^4+1172\,a^5\,b^5\,c^{10}\,d^6-1380\,a^5\,b^5\,c^8\,d^8+556\,a^5\,b^5\,c^6\,d^{10}-20\,a^5\,b^5\,c^4\,d^{12}+64\,a^4\,b^6\,c^{13}\,d^3-508\,a^4\,b^6\,c^{11}\,d^5+804\,a^4\,b^6\,c^9\,d^7-340\,a^4\,b^6\,c^7\,d^9-20\,a^4\,b^6\,c^5\,d^{11}+56\,a^3\,b^7\,c^{14}\,d^2+36\,a^3\,b^7\,c^{12}\,d^4-204\,a^3\,b^7\,c^{10}\,d^6+76\,a^3\,b^7\,c^8\,d^8+36\,a^3\,b^7\,c^6\,d^{10}-40\,a^2\,b^8\,c^{15}\,d+56\,a^2\,b^8\,c^{13}\,d^3-12\,a^2\,b^8\,c^{11}\,d^5+16\,a^2\,b^8\,c^9\,d^7-20\,a^2\,b^8\,c^7\,d^9+8\,a\,b^9\,c^{16}-16\,a\,b^9\,c^{14}\,d^2+12\,a\,b^9\,c^{12}\,d^4-8\,a\,b^9\,c^{10}\,d^6+4\,a\,b^9\,c^8\,d^8\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{d\,\left(\frac{8\,\left(4\,a^{11}\,c^{10}\,d^9-16\,a^{11}\,c^8\,d^{11}+24\,a^{11}\,c^6\,d^{13}-16\,a^{11}\,c^4\,d^{15}+4\,a^{11}\,c^2\,d^{17}-28\,a^{10}\,b\,c^{11}\,d^8+108\,a^{10}\,b\,c^9\,d^{10}-152\,a^{10}\,b\,c^7\,d^{12}+88\,a^{10}\,b\,c^5\,d^{14}-12\,a^{10}\,b\,c^3\,d^{16}-4\,a^{10}\,b\,c\,d^{18}+80\,a^9\,b^2\,c^{12}\,d^7-292\,a^9\,b^2\,c^{10}\,d^9+368\,a^9\,b^2\,c^8\,d^{11}-152\,a^9\,b^2\,c^6\,d^{13}-32\,a^9\,b^2\,c^4\,d^{15}+28\,a^9\,b^2\,c^2\,d^{17}-112\,a^8\,b^3\,c^{13}\,d^6+368\,a^8\,b^3\,c^{11}\,d^8-352\,a^8\,b^3\,c^9\,d^{10}-32\,a^8\,b^3\,c^7\,d^{12}+208\,a^8\,b^3\,c^5\,d^{14}-80\,a^8\,b^3\,c^3\,d^{16}+56\,a^7\,b^4\,c^{14}\,d^5-112\,a^7\,b^4\,c^{12}\,d^7-112\,a^7\,b^4\,c^{10}\,d^9+448\,a^7\,b^4\,c^8\,d^{11}-392\,a^7\,b^4\,c^6\,d^{13}+112\,a^7\,b^4\,c^4\,d^{15}+56\,a^6\,b^5\,c^{15}\,d^4-280\,a^6\,b^5\,c^{13}\,d^6+560\,a^6\,b^5\,c^{11}\,d^8-560\,a^6\,b^5\,c^9\,d^{10}+280\,a^6\,b^5\,c^7\,d^{12}-56\,a^6\,b^5\,c^5\,d^{14}-112\,a^5\,b^6\,c^{16}\,d^3+392\,a^5\,b^6\,c^{14}\,d^5-448\,a^5\,b^6\,c^{12}\,d^7+112\,a^5\,b^6\,c^{10}\,d^9+112\,a^5\,b^6\,c^8\,d^{11}-56\,a^5\,b^6\,c^6\,d^{13}+80\,a^4\,b^7\,c^{17}\,d^2-208\,a^4\,b^7\,c^{15}\,d^4+32\,a^4\,b^7\,c^{13}\,d^6+352\,a^4\,b^7\,c^{11}\,d^8-368\,a^4\,b^7\,c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{16}\,d^3+1088\,a^2\,b^9\,c^{14}\,d^5-1152\,a^2\,b^9\,c^{12}\,d^7+608\,a^2\,b^9\,c^{10}\,d^9-128\,a^2\,b^9\,c^8\,d^{11}-12\,a\,b^{10}\,c^{19}+64\,a\,b^{10}\,c^{17}\,d^2-136\,a\,b^{10}\,c^{15}\,d^4+144\,a\,b^{10}\,c^{13}\,d^6-76\,a\,b^{10}\,c^{11}\,d^8+16\,a\,b^{10}\,c^9\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}-\frac{d\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,a^8\,b\,c^5\,d^8+4\,a^8\,b\,c^3\,d^{10}+a^8\,b\,c\,d^{12}-32\,a^7\,b^2\,c^6\,d^7-20\,a^7\,b^2\,c^4\,d^9-2\,a^7\,b^2\,c^2\,d^{11}+112\,a^6\,b^3\,c^7\,d^6+20\,a^6\,b^3\,c^5\,d^8-a^6\,b^3\,c^3\,d^{10}+4\,a^6\,b^3\,c\,d^{12}-216\,a^5\,b^4\,c^8\,d^5+64\,a^5\,b^4\,c^6\,d^7-20\,a^5\,b^4\,c^4\,d^9-8\,a^5\,b^4\,c^2\,d^{11}+240\,a^4\,b^5\,c^9\,d^4-188\,a^4\,b^5\,c^7\,d^6+95\,a^4\,b^5\,c^5\,d^8-16\,a^4\,b^5\,c^3\,d^{10}+4\,a^4\,b^5\,c\,d^{12}-140\,a^3\,b^6\,c^{10}\,d^3+164\,a^3\,b^6\,c^8\,d^5-98\,a^3\,b^6\,c^6\,d^7+24\,a^3\,b^6\,c^4\,d^9-4\,a^3\,b^6\,c^2\,d^{11}+28\,a^2\,b^7\,c^{11}\,d^2-28\,a^2\,b^7\,c^9\,d^4+a^2\,b^7\,c^7\,d^6+12\,a^2\,b^7\,c^5\,d^8-4\,a^2\,b^7\,c^3\,d^{10}+4\,a\,b^8\,c^{12}\,d-16\,a\,b^8\,c^{10}\,d^3+24\,a\,b^8\,c^8\,d^5-16\,a\,b^8\,c^6\,d^7+4\,a\,b^8\,c^4\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^5\,d^8+4\,a^9\,c^3\,d^{10}+a^9\,c\,d^{12}-32\,a^8\,b\,c^6\,d^7-20\,a^8\,b\,c^4\,d^9-2\,a^8\,b\,c^2\,d^{11}+112\,a^7\,b^2\,c^7\,d^6+12\,a^7\,b^2\,c^5\,d^8-9\,a^7\,b^2\,c^3\,d^{10}+2\,a^7\,b^2\,c\,d^{12}-216\,a^6\,b^3\,c^8\,d^5+128\,a^6\,b^3\,c^6\,d^7+20\,a^6\,b^3\,c^4\,d^9-4\,a^6\,b^3\,c^2\,d^{11}+240\,a^5\,b^4\,c^9\,d^4-412\,a^5\,b^4\,c^7\,d^6+55\,a^5\,b^4\,c^5\,d^8-14\,a^5\,b^4\,c^3\,d^{10}-4\,a^5\,b^4\,c\,d^{12}-144\,a^4\,b^5\,c^{10}\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}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}+\frac{d\,\left(\frac{8\,\left(4\,a^{11}\,c^{10}\,d^9-16\,a^{11}\,c^8\,d^{11}+24\,a^{11}\,c^6\,d^{13}-16\,a^{11}\,c^4\,d^{15}+4\,a^{11}\,c^2\,d^{17}-28\,a^{10}\,b\,c^{11}\,d^8+108\,a^{10}\,b\,c^9\,d^{10}-152\,a^{10}\,b\,c^7\,d^{12}+88\,a^{10}\,b\,c^5\,d^{14}-12\,a^{10}\,b\,c^3\,d^{16}-4\,a^{10}\,b\,c\,d^{18}+80\,a^9\,b^2\,c^{12}\,d^7-292\,a^9\,b^2\,c^{10}\,d^9+368\,a^9\,b^2\,c^8\,d^{11}-152\,a^9\,b^2\,c^6\,d^{13}-32\,a^9\,b^2\,c^4\,d^{15}+28\,a^9\,b^2\,c^2\,d^{17}-112\,a^8\,b^3\,c^{13}\,d^6+368\,a^8\,b^3\,c^{11}\,d^8-352\,a^8\,b^3\,c^9\,d^{10}-32\,a^8\,b^3\,c^7\,d^{12}+208\,a^8\,b^3\,c^5\,d^{14}-80\,a^8\,b^3\,c^3\,d^{16}+56\,a^7\,b^4\,c^{14}\,d^5-112\,a^7\,b^4\,c^{12}\,d^7-112\,a^7\,b^4\,c^{10}\,d^9+448\,a^7\,b^4\,c^8\,d^{11}-392\,a^7\,b^4\,c^6\,d^{13}+112\,a^7\,b^4\,c^4\,d^{15}+56\,a^6\,b^5\,c^{15}\,d^4-280\,a^6\,b^5\,c^{13}\,d^6+560\,a^6\,b^5\,c^{11}\,d^8-560\,a^6\,b^5\,c^9\,d^{10}+280\,a^6\,b^5\,c^7\,d^{12}-56\,a^6\,b^5\,c^5\,d^{14}-112\,a^5\,b^6\,c^{16}\,d^3+392\,a^5\,b^6\,c^{14}\,d^5-448\,a^5\,b^6\,c^{12}\,d^7+112\,a^5\,b^6\,c^{10}\,d^9+112\,a^5\,b^6\,c^8\,d^{11}-56\,a^5\,b^6\,c^6\,d^{13}+80\,a^4\,b^7\,c^{17}\,d^2-208\,a^4\,b^7\,c^{15}\,d^4+32\,a^4\,b^7\,c^{13}\,d^6+352\,a^4\,b^7\,c^{11}\,d^8-368\,a^4\,b^7\,c^9\,d^{10}+112\,a^4\,b^7\,c^7\,d^{12}-28\,a^3\,b^8\,c^{18}\,d+32\,a^3\,b^8\,c^{16}\,d^3+152\,a^3\,b^8\,c^{14}\,d^5-368\,a^3\,b^8\,c^{12}\,d^7+292\,a^3\,b^8\,c^{10}\,d^9-80\,a^3\,b^8\,c^8\,d^{11}+4\,a^2\,b^9\,c^{19}+12\,a^2\,b^9\,c^{17}\,d^2-88\,a^2\,b^9\,c^{15}\,d^4+152\,a^2\,b^9\,c^{13}\,d^6-108\,a^2\,b^9\,c^{11}\,d^8+28\,a^2\,b^9\,c^9\,d^{10}-4\,a\,b^{10}\,c^{18}\,d+16\,a\,b^{10}\,c^{16}\,d^3-24\,a\,b^{10}\,c^{14}\,d^5+16\,a\,b^{10}\,c^{12}\,d^7-4\,a\,b^{10}\,c^{10}\,d^9\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,c^{11}\,d^8-44\,a^{11}\,c^9\,d^{10}+96\,a^{11}\,c^7\,d^{12}-104\,a^{11}\,c^5\,d^{14}+56\,a^{11}\,c^3\,d^{16}-12\,a^{11}\,c\,d^{18}-64\,a^{10}\,b\,c^{12}\,d^7+352\,a^{10}\,b\,c^{10}\,d^9-768\,a^{10}\,b\,c^8\,d^{11}+832\,a^{10}\,b\,c^6\,d^{13}-448\,a^{10}\,b\,c^4\,d^{15}+96\,a^{10}\,b\,c^2\,d^{17}+224\,a^9\,b^2\,c^{13}\,d^6-1244\,a^9\,b^2\,c^{11}\,d^8+2752\,a^9\,b^2\,c^9\,d^{10}-3048\,a^9\,b^2\,c^7\,d^{12}+1712\,a^9\,b^2\,c^5\,d^{14}-412\,a^9\,b^2\,c^3\,d^{16}+16\,a^9\,b^2\,c\,d^{18}-448\,a^8\,b^3\,c^{14}\,d^5+2560\,a^8\,b^3\,c^{12}\,d^7-5888\,a^8\,b^3\,c^{10}\,d^9+6912\,a^8\,b^3\,c^8\,d^{11}-4288\,a^8\,b^3\,c^6\,d^{13}+1280\,a^8\,b^3\,c^4\,d^{15}-128\,a^8\,b^3\,c^2\,d^{17}+560\,a^7\,b^4\,c^{15}\,d^4-3416\,a^7\,b^4\,c^{13}\,d^6+8512\,a^7\,b^4\,c^{11}\,d^8-11088\,a^7\,b^4\,c^9\,d^{10}+7952\,a^7\,b^4\,c^7\,d^{12}-2968\,a^7\,b^4\,c^5\,d^{14}+448\,a^7\,b^4\,c^3\,d^{16}-448\,a^6\,b^5\,c^{16}\,d^3+3136\,a^6\,b^5\,c^{14}\,d^5-8960\,a^6\,b^5\,c^{12}\,d^7+13440\,a^6\,b^5\,c^{10}\,d^9-11200\,a^6\,b^5\,c^8\,d^{11}+4928\,a^6\,b^5\,c^6\,d^{13}-896\,a^6\,b^5\,c^4\,d^{15}+224\,a^5\,b^6\,c^{17}\,d^2-2072\,a^5\,b^6\,c^{15}\,d^4+7168\,a^5\,b^6\,c^{13}\,d^6-12432\,a^5\,b^6\,c^{11}\,d^8+11648\,a^5\,b^6\,c^9\,d^{10}-5656\,a^5\,b^6\,c^7\,d^{12}+1120\,a^5\,b^6\,c^5\,d^{14}-64\,a^4\,b^7\,c^{18}\,d+1024\,a^4\,b^7\,c^{16}\,d^3-4352\,a^4\,b^7\,c^{14}\,d^5+8448\,a^4\,b^7\,c^{12}\,d^7-8512\,a^4\,b^7\,c^{10}\,d^9+4352\,a^4\,b^7\,c^8\,d^{11}-896\,a^4\,b^7\,c^6\,d^{13}+8\,a^3\,b^8\,c^{19}-380\,a^3\,b^8\,c^{17}\,d^2+1888\,a^3\,b^8\,c^{15}\,d^4-3912\,a^3\,b^8\,c^{13}\,d^6+4088\,a^3\,b^8\,c^{11}\,d^8-2140\,a^3\,b^8\,c^9\,d^{10}+448\,a^3\,b^8\,c^7\,d^{12}+96\,a^2\,b^9\,c^{18}\,d-512\,a^2\,b^9\,c^{16}\,d^3+1088\,a^2\,b^9\,c^{14}\,d^5-1152\,a^2\,b^9\,c^{12}\,d^7+608\,a^2\,b^9\,c^{10}\,d^9-128\,a^2\,b^9\,c^8\,d^{11}-12\,a\,b^{10}\,c^{19}+64\,a\,b^{10}\,c^{17}\,d^2-136\,a\,b^{10}\,c^{15}\,d^4+144\,a\,b^{10}\,c^{13}\,d^6-76\,a\,b^{10}\,c^{11}\,d^8+16\,a\,b^{10}\,c^9\,d^{10}\right)}{a^6\,c^8\,d^6-4\,a^6\,c^6\,d^8+6\,a^6\,c^4\,d^{10}-4\,a^6\,c^2\,d^{12}+a^6\,d^{14}-6\,a^5\,b\,c^9\,d^5+24\,a^5\,b\,c^7\,d^7-36\,a^5\,b\,c^5\,d^9+24\,a^5\,b\,c^3\,d^{11}-6\,a^5\,b\,c\,d^{13}+15\,a^4\,b^2\,c^{10}\,d^4-60\,a^4\,b^2\,c^8\,d^6+90\,a^4\,b^2\,c^6\,d^8-60\,a^4\,b^2\,c^4\,d^{10}+15\,a^4\,b^2\,c^2\,d^{12}-20\,a^3\,b^3\,c^{11}\,d^3+80\,a^3\,b^3\,c^9\,d^5-120\,a^3\,b^3\,c^7\,d^7+80\,a^3\,b^3\,c^5\,d^9-20\,a^3\,b^3\,c^3\,d^{11}+15\,a^2\,b^4\,c^{12}\,d^2-60\,a^2\,b^4\,c^{10}\,d^4+90\,a^2\,b^4\,c^8\,d^6-60\,a^2\,b^4\,c^6\,d^8+15\,a^2\,b^4\,c^4\,d^{10}-6\,a\,b^5\,c^{13}\,d+24\,a\,b^5\,c^{11}\,d^3-36\,a\,b^5\,c^9\,d^5+24\,a\,b^5\,c^7\,d^7-6\,a\,b^5\,c^5\,d^9+b^6\,c^{14}-4\,b^6\,c^{12}\,d^2+6\,b^6\,c^{10}\,d^4-4\,b^6\,c^8\,d^6+b^6\,c^6\,d^8}\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)}{2\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}}\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-6\,a\,b\,c^3\,d+6\,b^2\,c^4-5\,b^2\,c^2\,d^2+2\,b^2\,d^4\right)\,1{}\mathrm{i}}{f\,\left(-a^3\,c^{10}\,d^3+5\,a^3\,c^8\,d^5-10\,a^3\,c^6\,d^7+10\,a^3\,c^4\,d^9-5\,a^3\,c^2\,d^{11}+a^3\,d^{13}+3\,a^2\,b\,c^{11}\,d^2-15\,a^2\,b\,c^9\,d^4+30\,a^2\,b\,c^7\,d^6-30\,a^2\,b\,c^5\,d^8+15\,a^2\,b\,c^3\,d^{10}-3\,a^2\,b\,c\,d^{12}-3\,a\,b^2\,c^{12}\,d+15\,a\,b^2\,c^{10}\,d^3-30\,a\,b^2\,c^8\,d^5+30\,a\,b^2\,c^6\,d^7-15\,a\,b^2\,c^4\,d^9+3\,a\,b^2\,c^2\,d^{11}+b^3\,c^{13}-5\,b^3\,c^{11}\,d^2+10\,b^3\,c^9\,d^4-10\,b^3\,c^7\,d^6+5\,b^3\,c^5\,d^8-b^3\,c^3\,d^{10}\right)}","Not used",1,"(b^3*atan(((b^3*(b^2 - a^2)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 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6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 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128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2))*1i)/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2) - (b^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 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16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2))*1i)/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2))/((16*(36*a*b^7*c^5*d^5 - 18*a*b^7*c^3*d^7 - 34*a*b^7*c^7*d^3 + 4*a^3*b^5*c*d^9 + a^5*b^3*c*d^9 + 2*a^2*b^6*c^2*d^8 - 25*a^2*b^6*c^4*d^6 + 50*a^2*b^6*c^6*d^4 - 36*a^2*b^6*c^8*d^2 - a^3*b^5*c^3*d^7 - 16*a^3*b^5*c^5*d^5 + 40*a^3*b^5*c^7*d^3 + a^4*b^4*c^2*d^8 - 8*a^4*b^4*c^4*d^6 - 20*a^4*b^4*c^6*d^4 + 4*a^5*b^3*c^3*d^7 + 4*a^5*b^3*c^5*d^5 + 4*a*b^7*c*d^9 + 12*a*b^7*c^9*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (16*tan(e/2 + (f*x)/2)*(4*a*b^7*c^2*d^8 - 26*a*b^7*c^4*d^6 + 52*a*b^7*c^6*d^4 - 48*a*b^7*c^8*d^2 + 4*a^2*b^6*c*d^9 + 2*a^4*b^4*c*d^9 - 2*a^2*b^6*c^3*d^7 - 20*a^2*b^6*c^5*d^5 + 72*a^2*b^6*c^7*d^3 + 2*a^3*b^5*c^2*d^8 - 16*a^3*b^5*c^4*d^6 - 40*a^3*b^5*c^6*d^4 + 8*a^4*b^4*c^3*d^7 + 8*a^4*b^4*c^5*d^5))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (b^3*(b^2 - a^2)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 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36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 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896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2) - (b^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (b^3*(b^2 - a^2)^(1/2)*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))/(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^5*d^3 + b^5*c^3 - a^2*b^3*c^3 - a^3*b^2*d^3 + 3*a^2*b^3*c*d^2 + 3*a^3*b^2*c^2*d - 3*a*b^4*c^2*d - 3*a^4*b*c*d^2)) - ((a*d^5 - 4*a*c^2*d^3 + 6*b*c^3*d^2 - 3*b*c*d^4)/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)) + (d*tan(e/2 + (f*x)/2)*(2*a*d^5 - 11*a*c^2*d^3 + 17*b*c^3*d^2 - 8*b*c*d^4))/(c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(a*d^5 - 4*a*c^2*d^3 + 6*b*c^3*d^2 - 3*b*c*d^4))/(c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)) + (d*tan(e/2 + (f*x)/2)^3*(2*a*d^5 - 5*a*c^2*d^3 + 7*b*c^3*d^2 - 4*b*c*d^4))/(c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(c^4 + d^4 - 2*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) - (d*atan(((d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)) - (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))/((16*(36*a*b^7*c^5*d^5 - 18*a*b^7*c^3*d^7 - 34*a*b^7*c^7*d^3 + 4*a^3*b^5*c*d^9 + a^5*b^3*c*d^9 + 2*a^2*b^6*c^2*d^8 - 25*a^2*b^6*c^4*d^6 + 50*a^2*b^6*c^6*d^4 - 36*a^2*b^6*c^8*d^2 - a^3*b^5*c^3*d^7 - 16*a^3*b^5*c^5*d^5 + 40*a^3*b^5*c^7*d^3 + a^4*b^4*c^2*d^8 - 8*a^4*b^4*c^4*d^6 - 20*a^4*b^4*c^6*d^4 + 4*a^5*b^3*c^3*d^7 + 4*a^5*b^3*c^5*d^5 + 4*a*b^7*c*d^9 + 12*a*b^7*c^9*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (16*tan(e/2 + (f*x)/2)*(4*a*b^7*c^2*d^8 - 26*a*b^7*c^4*d^6 + 52*a*b^7*c^6*d^4 - 48*a*b^7*c^8*d^2 + 4*a^2*b^6*c*d^9 + 2*a^4*b^4*c*d^9 - 2*a^2*b^6*c^3*d^7 - 20*a^2*b^6*c^5*d^5 + 72*a^2*b^6*c^7*d^3 + 2*a^3*b^5*c^2*d^8 - 16*a^3*b^5*c^4*d^6 - 40*a^3*b^5*c^6*d^4 + 8*a^4*b^4*c^3*d^7 + 8*a^4*b^4*c^5*d^5))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)) - (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a*b^8*c^4*d^9 - 16*a*b^8*c^6*d^7 + 24*a*b^8*c^8*d^5 - 16*a*b^8*c^10*d^3 + 4*a^4*b^5*c*d^12 + 4*a^6*b^3*c*d^12 + 4*a^8*b*c^3*d^10 + 4*a^8*b*c^5*d^8 - 4*a^2*b^7*c^3*d^10 + 12*a^2*b^7*c^5*d^8 + a^2*b^7*c^7*d^6 - 28*a^2*b^7*c^9*d^4 + 28*a^2*b^7*c^11*d^2 - 4*a^3*b^6*c^2*d^11 + 24*a^3*b^6*c^4*d^9 - 98*a^3*b^6*c^6*d^7 + 164*a^3*b^6*c^8*d^5 - 140*a^3*b^6*c^10*d^3 - 16*a^4*b^5*c^3*d^10 + 95*a^4*b^5*c^5*d^8 - 188*a^4*b^5*c^7*d^6 + 240*a^4*b^5*c^9*d^4 - 8*a^5*b^4*c^2*d^11 - 20*a^5*b^4*c^4*d^9 + 64*a^5*b^4*c^6*d^7 - 216*a^5*b^4*c^8*d^5 - a^6*b^3*c^3*d^10 + 20*a^6*b^3*c^5*d^8 + 112*a^6*b^3*c^7*d^6 - 2*a^7*b^2*c^2*d^11 - 20*a^7*b^2*c^4*d^9 - 32*a^7*b^2*c^6*d^7 + 4*a*b^8*c^12*d + a^8*b*c*d^12))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(4*a*b^8*c^13 + a^9*c*d^12 + 4*a^9*c^3*d^10 + 4*a^9*c^5*d^8 - 16*a*b^8*c^3*d^10 + 76*a*b^8*c^5*d^8 - 162*a*b^8*c^7*d^6 + 176*a*b^8*c^9*d^4 - 96*a*b^8*c^11*d^2 - 8*a^2*b^7*c^12*d - 16*a^3*b^6*c*d^12 - 4*a^5*b^4*c*d^12 + 2*a^7*b^2*c*d^12 - 2*a^8*b*c^2*d^11 - 20*a^8*b*c^4*d^9 - 32*a^8*b*c^6*d^7 + 32*a^2*b^7*c^2*d^11 - 152*a^2*b^7*c^4*d^9 + 372*a^2*b^7*c^6*d^7 - 472*a^2*b^7*c^8*d^5 + 336*a^2*b^7*c^10*d^3 + 72*a^3*b^6*c^3*d^10 - 274*a^3*b^6*c^5*d^8 + 481*a^3*b^6*c^7*d^6 - 564*a^3*b^6*c^9*d^4 + 40*a^3*b^6*c^11*d^2 + 8*a^4*b^5*c^2*d^11 + 80*a^4*b^5*c^4*d^9 - 250*a^4*b^5*c^6*d^7 + 612*a^4*b^5*c^8*d^5 - 144*a^4*b^5*c^10*d^3 - 14*a^5*b^4*c^3*d^10 + 55*a^5*b^4*c^5*d^8 - 412*a^5*b^4*c^7*d^6 + 240*a^5*b^4*c^9*d^4 - 4*a^6*b^3*c^2*d^11 + 20*a^6*b^3*c^4*d^9 + 128*a^6*b^3*c^6*d^7 - 216*a^6*b^3*c^8*d^5 - 9*a^7*b^2*c^3*d^10 + 12*a^7*b^2*c^5*d^8 + 112*a^7*b^2*c^7*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^2*b^8*c^16 + 2*a^10*c^2*d^14 - 6*a^10*c^6*d^10 + 4*a^10*c^8*d^8 + 4*a*b^9*c^7*d^9 - 18*a*b^9*c^9*d^7 + 36*a*b^9*c^11*d^5 - 34*a*b^9*c^13*d^3 - 32*a^3*b^7*c^15*d + 4*a^7*b^3*c*d^15 - 10*a^9*b*c^3*d^13 - 12*a^9*b*c^5*d^11 + 54*a^9*b*c^7*d^9 - 32*a^9*b*c^9*d^7 - 24*a^2*b^8*c^6*d^10 + 110*a^2*b^8*c^8*d^8 - 232*a^2*b^8*c^10*d^6 + 234*a^2*b^8*c^12*d^4 - 92*a^2*b^8*c^14*d^2 + 60*a^3*b^7*c^5*d^11 - 282*a^3*b^7*c^7*d^9 + 638*a^3*b^7*c^9*d^7 - 702*a^3*b^7*c^11*d^5 + 318*a^3*b^7*c^13*d^3 - 80*a^4*b^6*c^4*d^12 + 390*a^4*b^6*c^6*d^10 - 970*a^4*b^6*c^8*d^8 + 1202*a^4*b^6*c^10*d^6 - 654*a^4*b^6*c^12*d^4 + 112*a^4*b^6*c^14*d^2 + 60*a^5*b^5*c^3*d^13 - 310*a^5*b^5*c^5*d^11 + 878*a^5*b^5*c^7*d^9 - 1290*a^5*b^5*c^9*d^7 + 886*a^5*b^5*c^11*d^5 - 224*a^5*b^5*c^13*d^3 - 24*a^6*b^4*c^2*d^14 + 138*a^6*b^4*c^4*d^12 - 466*a^6*b^4*c^6*d^10 + 894*a^6*b^4*c^8*d^8 - 822*a^6*b^4*c^10*d^6 + 280*a^6*b^4*c^12*d^4 - 30*a^7*b^3*c^3*d^13 + 122*a^7*b^3*c^5*d^11 - 394*a^7*b^3*c^7*d^9 + 522*a^7*b^3*c^9*d^7 - 224*a^7*b^3*c^11*d^5 + 2*a^8*b^2*c^2*d^14 + 2*a^8*b^2*c^4*d^12 + 102*a^8*b^2*c^6*d^10 - 218*a^8*b^2*c^8*d^8 + 112*a^8*b^2*c^10*d^6 + 12*a*b^9*c^15*d))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (8*tan(e/2 + (f*x)/2)*(8*a*b^9*c^16 + 4*a^10*c*d^15 - 12*a^10*c^5*d^11 + 8*a^10*c^7*d^9 + 4*a*b^9*c^8*d^8 - 8*a*b^9*c^10*d^6 + 12*a*b^9*c^12*d^4 - 16*a*b^9*c^14*d^2 - 40*a^2*b^8*c^15*d + 4*a^8*b^2*c*d^15 - 20*a^9*b*c^2*d^14 - 24*a^9*b*c^4*d^12 + 108*a^9*b*c^6*d^10 - 64*a^9*b*c^8*d^8 - 20*a^2*b^8*c^7*d^9 + 16*a^2*b^8*c^9*d^7 - 12*a^2*b^8*c^11*d^5 + 56*a^2*b^8*c^13*d^3 + 36*a^3*b^7*c^6*d^10 + 76*a^3*b^7*c^8*d^8 - 204*a^3*b^7*c^10*d^6 + 36*a^3*b^7*c^12*d^4 + 56*a^3*b^7*c^14*d^2 - 20*a^4*b^6*c^5*d^11 - 340*a^4*b^6*c^7*d^9 + 804*a^4*b^6*c^9*d^7 - 508*a^4*b^6*c^11*d^5 + 64*a^4*b^6*c^13*d^3 - 20*a^5*b^5*c^4*d^12 + 556*a^5*b^5*c^6*d^10 - 1380*a^5*b^5*c^8*d^8 + 1172*a^5*b^5*c^10*d^6 - 328*a^5*b^5*c^12*d^4 + 36*a^6*b^4*c^3*d^13 - 452*a^6*b^4*c^5*d^11 + 1308*a^6*b^4*c^7*d^9 - 1404*a^6*b^4*c^9*d^7 + 512*a^6*b^4*c^11*d^5 - 20*a^7*b^3*c^2*d^14 + 164*a^7*b^3*c^4*d^12 - 708*a^7*b^3*c^6*d^10 + 1004*a^7*b^3*c^8*d^8 - 440*a^7*b^3*c^10*d^6 + 4*a^8*b^2*c^3*d^13 + 204*a^8*b^2*c^5*d^11 - 436*a^8*b^2*c^7*d^9 + 224*a^8*b^2*c^9*d^7))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) + (d*((8*(4*a^2*b^9*c^19 + 4*a^11*c^2*d^17 - 16*a^11*c^4*d^15 + 24*a^11*c^6*d^13 - 16*a^11*c^8*d^11 + 4*a^11*c^10*d^9 - 4*a*b^10*c^10*d^9 + 16*a*b^10*c^12*d^7 - 24*a*b^10*c^14*d^5 + 16*a*b^10*c^16*d^3 - 28*a^3*b^8*c^18*d - 12*a^10*b*c^3*d^16 + 88*a^10*b*c^5*d^14 - 152*a^10*b*c^7*d^12 + 108*a^10*b*c^9*d^10 - 28*a^10*b*c^11*d^8 + 28*a^2*b^9*c^9*d^10 - 108*a^2*b^9*c^11*d^8 + 152*a^2*b^9*c^13*d^6 - 88*a^2*b^9*c^15*d^4 + 12*a^2*b^9*c^17*d^2 - 80*a^3*b^8*c^8*d^11 + 292*a^3*b^8*c^10*d^9 - 368*a^3*b^8*c^12*d^7 + 152*a^3*b^8*c^14*d^5 + 32*a^3*b^8*c^16*d^3 + 112*a^4*b^7*c^7*d^12 - 368*a^4*b^7*c^9*d^10 + 352*a^4*b^7*c^11*d^8 + 32*a^4*b^7*c^13*d^6 - 208*a^4*b^7*c^15*d^4 + 80*a^4*b^7*c^17*d^2 - 56*a^5*b^6*c^6*d^13 + 112*a^5*b^6*c^8*d^11 + 112*a^5*b^6*c^10*d^9 - 448*a^5*b^6*c^12*d^7 + 392*a^5*b^6*c^14*d^5 - 112*a^5*b^6*c^16*d^3 - 56*a^6*b^5*c^5*d^14 + 280*a^6*b^5*c^7*d^12 - 560*a^6*b^5*c^9*d^10 + 560*a^6*b^5*c^11*d^8 - 280*a^6*b^5*c^13*d^6 + 56*a^6*b^5*c^15*d^4 + 112*a^7*b^4*c^4*d^15 - 392*a^7*b^4*c^6*d^13 + 448*a^7*b^4*c^8*d^11 - 112*a^7*b^4*c^10*d^9 - 112*a^7*b^4*c^12*d^7 + 56*a^7*b^4*c^14*d^5 - 80*a^8*b^3*c^3*d^16 + 208*a^8*b^3*c^5*d^14 - 32*a^8*b^3*c^7*d^12 - 352*a^8*b^3*c^9*d^10 + 368*a^8*b^3*c^11*d^8 - 112*a^8*b^3*c^13*d^6 + 28*a^9*b^2*c^2*d^17 - 32*a^9*b^2*c^4*d^15 - 152*a^9*b^2*c^6*d^13 + 368*a^9*b^2*c^8*d^11 - 292*a^9*b^2*c^10*d^9 + 80*a^9*b^2*c^12*d^7 - 4*a*b^10*c^18*d - 4*a^10*b*c*d^18))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13) - (8*tan(e/2 + (f*x)/2)*(8*a^3*b^8*c^19 - 12*a^11*c*d^18 - 12*a*b^10*c^19 + 56*a^11*c^3*d^16 - 104*a^11*c^5*d^14 + 96*a^11*c^7*d^12 - 44*a^11*c^9*d^10 + 8*a^11*c^11*d^8 + 16*a*b^10*c^9*d^10 - 76*a*b^10*c^11*d^8 + 144*a*b^10*c^13*d^6 - 136*a*b^10*c^15*d^4 + 64*a*b^10*c^17*d^2 + 96*a^2*b^9*c^18*d - 64*a^4*b^7*c^18*d + 16*a^9*b^2*c*d^18 + 96*a^10*b*c^2*d^17 - 448*a^10*b*c^4*d^15 + 832*a^10*b*c^6*d^13 - 768*a^10*b*c^8*d^11 + 352*a^10*b*c^10*d^9 - 64*a^10*b*c^12*d^7 - 128*a^2*b^9*c^8*d^11 + 608*a^2*b^9*c^10*d^9 - 1152*a^2*b^9*c^12*d^7 + 1088*a^2*b^9*c^14*d^5 - 512*a^2*b^9*c^16*d^3 + 448*a^3*b^8*c^7*d^12 - 2140*a^3*b^8*c^9*d^10 + 4088*a^3*b^8*c^11*d^8 - 3912*a^3*b^8*c^13*d^6 + 1888*a^3*b^8*c^15*d^4 - 380*a^3*b^8*c^17*d^2 - 896*a^4*b^7*c^6*d^13 + 4352*a^4*b^7*c^8*d^11 - 8512*a^4*b^7*c^10*d^9 + 8448*a^4*b^7*c^12*d^7 - 4352*a^4*b^7*c^14*d^5 + 1024*a^4*b^7*c^16*d^3 + 1120*a^5*b^6*c^5*d^14 - 5656*a^5*b^6*c^7*d^12 + 11648*a^5*b^6*c^9*d^10 - 12432*a^5*b^6*c^11*d^8 + 7168*a^5*b^6*c^13*d^6 - 2072*a^5*b^6*c^15*d^4 + 224*a^5*b^6*c^17*d^2 - 896*a^6*b^5*c^4*d^15 + 4928*a^6*b^5*c^6*d^13 - 11200*a^6*b^5*c^8*d^11 + 13440*a^6*b^5*c^10*d^9 - 8960*a^6*b^5*c^12*d^7 + 3136*a^6*b^5*c^14*d^5 - 448*a^6*b^5*c^16*d^3 + 448*a^7*b^4*c^3*d^16 - 2968*a^7*b^4*c^5*d^14 + 7952*a^7*b^4*c^7*d^12 - 11088*a^7*b^4*c^9*d^10 + 8512*a^7*b^4*c^11*d^8 - 3416*a^7*b^4*c^13*d^6 + 560*a^7*b^4*c^15*d^4 - 128*a^8*b^3*c^2*d^17 + 1280*a^8*b^3*c^4*d^15 - 4288*a^8*b^3*c^6*d^13 + 6912*a^8*b^3*c^8*d^11 - 5888*a^8*b^3*c^10*d^9 + 2560*a^8*b^3*c^12*d^7 - 448*a^8*b^3*c^14*d^5 - 412*a^9*b^2*c^3*d^16 + 1712*a^9*b^2*c^5*d^14 - 3048*a^9*b^2*c^7*d^12 + 2752*a^9*b^2*c^9*d^10 - 1244*a^9*b^2*c^11*d^8 + 224*a^9*b^2*c^13*d^6))/(a^6*d^14 + b^6*c^14 - 4*a^6*c^2*d^12 + 6*a^6*c^4*d^10 - 4*a^6*c^6*d^8 + a^6*c^8*d^6 + b^6*c^6*d^8 - 4*b^6*c^8*d^6 + 6*b^6*c^10*d^4 - 4*b^6*c^12*d^2 - 6*a*b^5*c^5*d^9 + 24*a*b^5*c^7*d^7 - 36*a*b^5*c^9*d^5 + 24*a*b^5*c^11*d^3 + 24*a^5*b*c^3*d^11 - 36*a^5*b*c^5*d^9 + 24*a^5*b*c^7*d^7 - 6*a^5*b*c^9*d^5 + 15*a^2*b^4*c^4*d^10 - 60*a^2*b^4*c^6*d^8 + 90*a^2*b^4*c^8*d^6 - 60*a^2*b^4*c^10*d^4 + 15*a^2*b^4*c^12*d^2 - 20*a^3*b^3*c^3*d^11 + 80*a^3*b^3*c^5*d^9 - 120*a^3*b^3*c^7*d^7 + 80*a^3*b^3*c^9*d^5 - 20*a^3*b^3*c^11*d^3 + 15*a^4*b^2*c^2*d^12 - 60*a^4*b^2*c^4*d^10 + 90*a^4*b^2*c^6*d^8 - 60*a^4*b^2*c^8*d^6 + 15*a^4*b^2*c^10*d^4 - 6*a*b^5*c^13*d - 6*a^5*b*c*d^13))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12)))*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12))))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 6*b^2*c^4 + 2*b^2*d^4 + 2*a^2*c^2*d^2 - 5*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(f*(a^3*d^13 + b^3*c^13 - 5*a^3*c^2*d^11 + 10*a^3*c^4*d^9 - 10*a^3*c^6*d^7 + 5*a^3*c^8*d^5 - a^3*c^10*d^3 - b^3*c^3*d^10 + 5*b^3*c^5*d^8 - 10*b^3*c^7*d^6 + 10*b^3*c^9*d^4 - 5*b^3*c^11*d^2 + 3*a*b^2*c^2*d^11 - 15*a*b^2*c^4*d^9 + 30*a*b^2*c^6*d^7 - 30*a*b^2*c^8*d^5 + 15*a*b^2*c^10*d^3 + 15*a^2*b*c^3*d^10 - 30*a^2*b*c^5*d^8 + 30*a^2*b*c^7*d^6 - 15*a^2*b*c^9*d^4 + 3*a^2*b*c^11*d^2 - 3*a*b^2*c^12*d - 3*a^2*b*c*d^12))","B"
706,1,13700,306,20.451506,"\text{Not used}","int((c + d*sin(e + f*x))^4/(a + b*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(3\,a^4\,d^4-8\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4-4\,a\,b^3\,c^3\,d+4\,a\,b^3\,c\,d^3+b^4\,c^4\right)}{b^3\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a^4\,d^4-8\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-a^2\,b^2\,d^4-4\,a\,b^3\,c^3\,d+4\,a\,b^3\,c\,d^3+b^4\,c^4-b^4\,d^4\right)}{b^3\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,a^4\,d^4-16\,a^3\,b\,c\,d^3+12\,a^2\,b^2\,c^2\,d^2-5\,a^2\,b^2\,d^4-8\,a\,b^3\,c^3\,d+8\,a\,b^3\,c\,d^3+2\,b^4\,c^4+b^4\,d^4\right)}{b^3\,\left(a^2-b^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(3\,a^4\,d^4-8\,a^3\,b\,c\,d^3+12\,a^2\,b^2\,c^2\,d^2-a^2\,b^2\,d^4-8\,a\,b^3\,c^3\,d+2\,b^4\,c^4\right)}{a\,b^2\,\left(a^2-b^2\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(9\,a^4\,d^4-24\,a^3\,b\,c\,d^3+12\,a^2\,b^2\,c^2\,d^2-7\,a^2\,b^2\,d^4-8\,a\,b^3\,c^3\,d+16\,a\,b^3\,c\,d^3+2\,b^4\,c^4\right)}{a\,b^2\,\left(a^2-b^2\right)}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,a^4\,d^4-8\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4-4\,a\,b^3\,c^3\,d+4\,a\,b^3\,c\,d^3+b^4\,c^4\right)}{a\,b^2\,\left(a^2-b^2\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(54\,a^{11}\,d^{12}-432\,a^{10}\,b\,c\,d^{11}+36\,a^9\,b^2\,c^4\,d^8+1584\,a^9\,b^2\,c^2\,d^{10}-81\,a^9\,b^2\,d^{12}-192\,a^8\,b^3\,c^5\,d^7-3472\,a^8\,b^3\,c^3\,d^9+648\,a^8\,b^3\,c\,d^{11}+400\,a^7\,b^4\,c^6\,d^6+4860\,a^7\,b^4\,c^4\,d^8-2394\,a^7\,b^4\,c^2\,d^{10}+9\,a^7\,b^4\,d^{12}-384\,a^6\,b^5\,c^7\,d^5-4128\,a^6\,b^5\,c^5\,d^7+5424\,a^6\,b^5\,c^3\,d^9-60\,a^6\,b^5\,c\,d^{11}+132\,a^5\,b^6\,c^8\,d^4+1552\,a^5\,b^6\,c^6\,d^6-8277\,a^5\,b^6\,c^4\,d^8+126\,a^5\,b^6\,c^2\,d^{10}+4\,a^5\,b^6\,d^{12}+32\,a^4\,b^7\,c^9\,d^3+480\,a^4\,b^7\,c^7\,d^5+8592\,a^4\,b^7\,c^5\,d^7-76\,a^4\,b^7\,c^3\,d^9-12\,a^4\,b^7\,c\,d^{11}-24\,a^3\,b^8\,c^{10}\,d^2-690\,a^3\,b^8\,c^8\,d^4-5784\,a^3\,b^8\,c^6\,d^6-63\,a^3\,b^8\,c^4\,d^8+12\,a^3\,b^8\,c^2\,d^{10}+192\,a^2\,b^9\,c^9\,d^3+2256\,a^2\,b^9\,c^7\,d^5+96\,a^2\,b^9\,c^5\,d^7-4\,a^2\,b^9\,c^3\,d^9-384\,a\,b^{10}\,c^8\,d^4-32\,a\,b^{10}\,c^6\,d^6\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}-\frac{\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}-\frac{\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)}{b^4}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(216\,a^{12}\,d^{12}-1728\,a^{11}\,b\,c\,d^{11}+5904\,a^{10}\,b^2\,c^2\,d^{10}-432\,a^{10}\,b^2\,d^{12}-11008\,a^9\,b^3\,c^3\,d^9+3744\,a^9\,b^3\,c\,d^{11}+11736\,a^8\,b^4\,c^4\,d^8-13776\,a^8\,b^4\,c^2\,d^{10}+126\,a^8\,b^4\,d^{12}-6528\,a^7\,b^5\,c^5\,d^7+27808\,a^7\,b^5\,c^3\,d^9-1488\,a^7\,b^5\,c\,d^{11}+928\,a^6\,b^6\,c^6\,d^6-32976\,a^6\,b^6\,c^4\,d^8+6636\,a^6\,b^6\,c^2\,d^{10}+82\,a^6\,b^6\,d^{12}+768\,a^5\,b^7\,c^7\,d^5+22464\,a^5\,b^7\,c^5\,d^7-15360\,a^5\,b^7\,c^3\,d^9-504\,a^5\,b^7\,c\,d^{11}-288\,a^4\,b^8\,c^8\,d^4-7504\,a^4\,b^8\,c^6\,d^6+20406\,a^4\,b^8\,c^4\,d^8+1212\,a^4\,b^8\,c^2\,d^{10}+8\,a^4\,b^8\,d^{12}+384\,a^3\,b^9\,c^7\,d^5-15744\,a^3\,b^9\,c^5\,d^7-1432\,a^3\,b^9\,c^3\,d^9-24\,a^3\,b^9\,c\,d^{11}+288\,a^2\,b^{10}\,c^8\,d^4+6576\,a^2\,b^{10}\,c^6\,d^6+834\,a^2\,b^{10}\,c^4\,d^8+24\,a^2\,b^{10}\,c^2\,d^{10}-1152\,a\,b^{11}\,c^7\,d^5-192\,a\,b^{11}\,c^5\,d^7-8\,a\,b^{11}\,c^3\,d^9\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}}\right)\,\left(a^2\,d^4\,3{}\mathrm{i}+\frac{b^2\,d^2\,\left(12\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^3\,8{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^4\,f}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(54\,a^{11}\,d^{12}-432\,a^{10}\,b\,c\,d^{11}+36\,a^9\,b^2\,c^4\,d^8+1584\,a^9\,b^2\,c^2\,d^{10}-81\,a^9\,b^2\,d^{12}-192\,a^8\,b^3\,c^5\,d^7-3472\,a^8\,b^3\,c^3\,d^9+648\,a^8\,b^3\,c\,d^{11}+400\,a^7\,b^4\,c^6\,d^6+4860\,a^7\,b^4\,c^4\,d^8-2394\,a^7\,b^4\,c^2\,d^{10}+9\,a^7\,b^4\,d^{12}-384\,a^6\,b^5\,c^7\,d^5-4128\,a^6\,b^5\,c^5\,d^7+5424\,a^6\,b^5\,c^3\,d^9-60\,a^6\,b^5\,c\,d^{11}+132\,a^5\,b^6\,c^8\,d^4+1552\,a^5\,b^6\,c^6\,d^6-8277\,a^5\,b^6\,c^4\,d^8+126\,a^5\,b^6\,c^2\,d^{10}+4\,a^5\,b^6\,d^{12}+32\,a^4\,b^7\,c^9\,d^3+480\,a^4\,b^7\,c^7\,d^5+8592\,a^4\,b^7\,c^5\,d^7-76\,a^4\,b^7\,c^3\,d^9-12\,a^4\,b^7\,c\,d^{11}-24\,a^3\,b^8\,c^{10}\,d^2-690\,a^3\,b^8\,c^8\,d^4-5784\,a^3\,b^8\,c^6\,d^6-63\,a^3\,b^8\,c^4\,d^8+12\,a^3\,b^8\,c^2\,d^{10}+192\,a^2\,b^9\,c^9\,d^3+2256\,a^2\,b^9\,c^7\,d^5+96\,a^2\,b^9\,c^5\,d^7-4\,a^2\,b^9\,c^3\,d^9-384\,a\,b^{10}\,c^8\,d^4-32\,a\,b^{10}\,c^6\,d^6\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(216\,a^{12}\,d^{12}-1728\,a^{11}\,b\,c\,d^{11}+5904\,a^{10}\,b^2\,c^2\,d^{10}-432\,a^{10}\,b^2\,d^{12}-11008\,a^9\,b^3\,c^3\,d^9+3744\,a^9\,b^3\,c\,d^{11}+11736\,a^8\,b^4\,c^4\,d^8-13776\,a^8\,b^4\,c^2\,d^{10}+126\,a^8\,b^4\,d^{12}-6528\,a^7\,b^5\,c^5\,d^7+27808\,a^7\,b^5\,c^3\,d^9-1488\,a^7\,b^5\,c\,d^{11}+928\,a^6\,b^6\,c^6\,d^6-32976\,a^6\,b^6\,c^4\,d^8+6636\,a^6\,b^6\,c^2\,d^{10}+82\,a^6\,b^6\,d^{12}+768\,a^5\,b^7\,c^7\,d^5+22464\,a^5\,b^7\,c^5\,d^7-15360\,a^5\,b^7\,c^3\,d^9-504\,a^5\,b^7\,c\,d^{11}-288\,a^4\,b^8\,c^8\,d^4-7504\,a^4\,b^8\,c^6\,d^6+20406\,a^4\,b^8\,c^4\,d^8+1212\,a^4\,b^8\,c^2\,d^{10}+8\,a^4\,b^8\,d^{12}+384\,a^3\,b^9\,c^7\,d^5-15744\,a^3\,b^9\,c^5\,d^7-1432\,a^3\,b^9\,c^3\,d^9-24\,a^3\,b^9\,c\,d^{11}+288\,a^2\,b^{10}\,c^8\,d^4+6576\,a^2\,b^{10}\,c^6\,d^6+834\,a^2\,b^{10}\,c^4\,d^8+24\,a^2\,b^{10}\,c^2\,d^{10}-1152\,a\,b^{11}\,c^7\,d^5-192\,a\,b^{11}\,c^5\,d^7-8\,a\,b^{11}\,c^3\,d^9\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}+\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}-\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(36\,a^{10}\,b^3\,d^8-192\,a^9\,b^4\,c\,d^7+400\,a^8\,b^5\,c^2\,d^6-60\,a^8\,b^5\,d^8-384\,a^7\,b^6\,c^3\,d^5+352\,a^7\,b^6\,c\,d^7+144\,a^6\,b^7\,c^4\,d^4-776\,a^6\,b^7\,c^2\,d^6+13\,a^6\,b^7\,d^8+768\,a^5\,b^8\,c^3\,d^5-128\,a^5\,b^8\,c\,d^7-288\,a^4\,b^9\,c^4\,d^4+352\,a^4\,b^9\,c^2\,d^6+10\,a^4\,b^9\,d^8-384\,a^3\,b^{10}\,c^3\,d^5-32\,a^3\,b^{10}\,c\,d^7+144\,a^2\,b^{11}\,c^4\,d^4+24\,a^2\,b^{11}\,c^2\,d^6+a^2\,b^{11}\,d^8\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-72\,a^{11}\,b^3\,d^8+384\,a^{10}\,b^4\,c\,d^7-800\,a^9\,b^5\,c^2\,d^6+228\,a^9\,b^5\,d^8+768\,a^8\,b^6\,c^3\,d^5-1280\,a^8\,b^6\,c\,d^7-264\,a^7\,b^7\,c^4\,d^4+2824\,a^7\,b^7\,c^2\,d^6-197\,a^7\,b^7\,d^8-64\,a^6\,b^8\,c^5\,d^3-2976\,a^6\,b^8\,c^3\,d^5+1216\,a^6\,b^8\,c\,d^7+48\,a^5\,b^9\,c^6\,d^2+1376\,a^5\,b^9\,c^4\,d^4-2864\,a^5\,b^9\,c^2\,d^6+16\,a^5\,b^9\,d^8-96\,a^4\,b^{10}\,c^5\,d^3+3200\,a^4\,b^{10}\,c^3\,d^5-224\,a^4\,b^{10}\,c\,d^7-4\,a^3\,b^{11}\,c^8-96\,a^3\,b^{11}\,c^6\,d^2-1680\,a^3\,b^{11}\,c^4\,d^4+680\,a^3\,b^{11}\,c^2\,d^6+19\,a^3\,b^{11}\,d^8+32\,a^2\,b^{12}\,c^7\,d+384\,a^2\,b^{12}\,c^5\,d^3-768\,a^2\,b^{12}\,c^3\,d^5-64\,a^2\,b^{12}\,c\,d^7-64\,a\,b^{13}\,c^6\,d^2+288\,a\,b^{13}\,c^4\,d^4+48\,a\,b^{13}\,c^2\,d^6+2\,a\,b^{13}\,d^8\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(6\,a^7\,b^8\,d^4-16\,a^6\,b^9\,c\,d^3-4\,a^5\,b^{10}\,c^4-14\,a^5\,b^{10}\,d^4+16\,a^4\,b^{11}\,c^3\,d+48\,a^4\,b^{11}\,c\,d^3+4\,a^3\,b^{12}\,c^4-24\,a^3\,b^{12}\,c^2\,d^2+6\,a^3\,b^{12}\,d^4-16\,a^2\,b^{13}\,c^3\,d-32\,a^2\,b^{13}\,c\,d^3+24\,a\,b^{14}\,c^2\,d^2+2\,a\,b^{14}\,d^4\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^8\,b^8\,d^4-64\,a^7\,b^9\,c\,d^3+48\,a^6\,b^{10}\,c^2\,d^2-56\,a^6\,b^{10}\,d^4+160\,a^5\,b^{11}\,c\,d^3-8\,a^4\,b^{12}\,c^4-144\,a^4\,b^{12}\,c^2\,d^2+32\,a^4\,b^{12}\,d^4+32\,a^3\,b^{13}\,c^3\,d-96\,a^3\,b^{13}\,c\,d^3+8\,a^2\,b^{14}\,c^4+96\,a^2\,b^{14}\,c^2\,d^2-32\,a\,b^{15}\,c^3\,d\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}-\frac{\left(\frac{8\,\left(4\,a^6\,b^{11}-8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8-2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^7\,b^{11}+28\,a^5\,b^{13}-32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9-2\,a^2\,b^{11}+b^{13}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,d\,a^2+c\,a\,b-4\,d\,b^2\right)\,2{}\mathrm{i}}{f\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"((2*(3*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*d^4 + 6*a^2*b^2*c^2*d^2 + 4*a*b^3*c*d^3 - 4*a*b^3*c^3*d - 8*a^3*b*c*d^3))/(b^3*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)^4*(3*a^4*d^4 + b^4*c^4 - b^4*d^4 - a^2*b^2*d^4 + 6*a^2*b^2*c^2*d^2 + 4*a*b^3*c*d^3 - 4*a*b^3*c^3*d - 8*a^3*b*c*d^3))/(b^3*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)^2*(6*a^4*d^4 + 2*b^4*c^4 + b^4*d^4 - 5*a^2*b^2*d^4 + 12*a^2*b^2*c^2*d^2 + 8*a*b^3*c*d^3 - 8*a*b^3*c^3*d - 16*a^3*b*c*d^3))/(b^3*(a^2 - b^2)) + (tan(e/2 + (f*x)/2)^5*(3*a^4*d^4 + 2*b^4*c^4 - a^2*b^2*d^4 + 12*a^2*b^2*c^2*d^2 - 8*a*b^3*c^3*d - 8*a^3*b*c*d^3))/(a*b^2*(a^2 - b^2)) + (tan(e/2 + (f*x)/2)*(9*a^4*d^4 + 2*b^4*c^4 - 7*a^2*b^2*d^4 + 12*a^2*b^2*c^2*d^2 + 16*a*b^3*c*d^3 - 8*a*b^3*c^3*d - 24*a^3*b*c*d^3))/(a*b^2*(a^2 - b^2)) + (4*tan(e/2 + (f*x)/2)^3*(3*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*d^4 + 6*a^2*b^2*c^2*d^2 + 4*a*b^3*c*d^3 - 4*a*b^3*c^3*d - 8*a^3*b*c*d^3))/(a*b^2*(a^2 - b^2)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + 3*a*tan(e/2 + (f*x)/2)^2 + 3*a*tan(e/2 + (f*x)/2)^4 + a*tan(e/2 + (f*x)/2)^6 + 4*b*tan(e/2 + (f*x)/2)^3 + 2*b*tan(e/2 + (f*x)/2)^5)) + (atan(((((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4)*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i)*1i)/b^4 + (((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4)*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i)*1i)/b^4)/((16*(54*a^11*d^12 + 4*a^5*b^6*d^12 + 9*a^7*b^4*d^12 - 81*a^9*b^2*d^12 - 32*a*b^10*c^6*d^6 - 384*a*b^10*c^8*d^4 - 12*a^4*b^7*c*d^11 - 60*a^6*b^5*c*d^11 + 648*a^8*b^3*c*d^11 - 4*a^2*b^9*c^3*d^9 + 96*a^2*b^9*c^5*d^7 + 2256*a^2*b^9*c^7*d^5 + 192*a^2*b^9*c^9*d^3 + 12*a^3*b^8*c^2*d^10 - 63*a^3*b^8*c^4*d^8 - 5784*a^3*b^8*c^6*d^6 - 690*a^3*b^8*c^8*d^4 - 24*a^3*b^8*c^10*d^2 - 76*a^4*b^7*c^3*d^9 + 8592*a^4*b^7*c^5*d^7 + 480*a^4*b^7*c^7*d^5 + 32*a^4*b^7*c^9*d^3 + 126*a^5*b^6*c^2*d^10 - 8277*a^5*b^6*c^4*d^8 + 1552*a^5*b^6*c^6*d^6 + 132*a^5*b^6*c^8*d^4 + 5424*a^6*b^5*c^3*d^9 - 4128*a^6*b^5*c^5*d^7 - 384*a^6*b^5*c^7*d^5 - 2394*a^7*b^4*c^2*d^10 + 4860*a^7*b^4*c^4*d^8 + 400*a^7*b^4*c^6*d^6 - 3472*a^8*b^3*c^3*d^9 - 192*a^8*b^3*c^5*d^7 + 1584*a^9*b^2*c^2*d^10 + 36*a^9*b^2*c^4*d^8 - 432*a^10*b*c*d^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4)*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4 - (((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) - (((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4)*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4 + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i))/b^4 + (16*tan(e/2 + (f*x)/2)*(216*a^12*d^12 + 8*a^4*b^8*d^12 + 82*a^6*b^6*d^12 + 126*a^8*b^4*d^12 - 432*a^10*b^2*d^12 - 8*a*b^11*c^3*d^9 - 192*a*b^11*c^5*d^7 - 1152*a*b^11*c^7*d^5 - 24*a^3*b^9*c*d^11 - 504*a^5*b^7*c*d^11 - 1488*a^7*b^5*c*d^11 + 3744*a^9*b^3*c*d^11 + 24*a^2*b^10*c^2*d^10 + 834*a^2*b^10*c^4*d^8 + 6576*a^2*b^10*c^6*d^6 + 288*a^2*b^10*c^8*d^4 - 1432*a^3*b^9*c^3*d^9 - 15744*a^3*b^9*c^5*d^7 + 384*a^3*b^9*c^7*d^5 + 1212*a^4*b^8*c^2*d^10 + 20406*a^4*b^8*c^4*d^8 - 7504*a^4*b^8*c^6*d^6 - 288*a^4*b^8*c^8*d^4 - 15360*a^5*b^7*c^3*d^9 + 22464*a^5*b^7*c^5*d^7 + 768*a^5*b^7*c^7*d^5 + 6636*a^6*b^6*c^2*d^10 - 32976*a^6*b^6*c^4*d^8 + 928*a^6*b^6*c^6*d^6 + 27808*a^7*b^5*c^3*d^9 - 6528*a^7*b^5*c^5*d^7 - 13776*a^8*b^4*c^2*d^10 + 11736*a^8*b^4*c^4*d^8 - 11008*a^9*b^3*c^3*d^9 + 5904*a^10*b^2*c^2*d^10 - 1728*a^11*b*c*d^11))/(b^13 - 2*a^2*b^11 + a^4*b^9)))*(a^2*d^4*3i + (b^2*d^2*(12*c^2 + d^2)*1i)/2 - a*b*c*d^3*8i)*2i)/(b^4*f) + (atan((((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9) - ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(54*a^11*d^12 + 4*a^5*b^6*d^12 + 9*a^7*b^4*d^12 - 81*a^9*b^2*d^12 - 32*a*b^10*c^6*d^6 - 384*a*b^10*c^8*d^4 - 12*a^4*b^7*c*d^11 - 60*a^6*b^5*c*d^11 + 648*a^8*b^3*c*d^11 - 4*a^2*b^9*c^3*d^9 + 96*a^2*b^9*c^5*d^7 + 2256*a^2*b^9*c^7*d^5 + 192*a^2*b^9*c^9*d^3 + 12*a^3*b^8*c^2*d^10 - 63*a^3*b^8*c^4*d^8 - 5784*a^3*b^8*c^6*d^6 - 690*a^3*b^8*c^8*d^4 - 24*a^3*b^8*c^10*d^2 - 76*a^4*b^7*c^3*d^9 + 8592*a^4*b^7*c^5*d^7 + 480*a^4*b^7*c^7*d^5 + 32*a^4*b^7*c^9*d^3 + 126*a^5*b^6*c^2*d^10 - 8277*a^5*b^6*c^4*d^8 + 1552*a^5*b^6*c^6*d^6 + 132*a^5*b^6*c^8*d^4 + 5424*a^6*b^5*c^3*d^9 - 4128*a^6*b^5*c^5*d^7 - 384*a^6*b^5*c^7*d^5 - 2394*a^7*b^4*c^2*d^10 + 4860*a^7*b^4*c^4*d^8 + 400*a^7*b^4*c^6*d^6 - 3472*a^8*b^3*c^3*d^9 - 192*a^8*b^3*c^5*d^7 + 1584*a^9*b^2*c^2*d^10 + 36*a^9*b^2*c^4*d^8 - 432*a^10*b*c*d^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (16*tan(e/2 + (f*x)/2)*(216*a^12*d^12 + 8*a^4*b^8*d^12 + 82*a^6*b^6*d^12 + 126*a^8*b^4*d^12 - 432*a^10*b^2*d^12 - 8*a*b^11*c^3*d^9 - 192*a*b^11*c^5*d^7 - 1152*a*b^11*c^7*d^5 - 24*a^3*b^9*c*d^11 - 504*a^5*b^7*c*d^11 - 1488*a^7*b^5*c*d^11 + 3744*a^9*b^3*c*d^11 + 24*a^2*b^10*c^2*d^10 + 834*a^2*b^10*c^4*d^8 + 6576*a^2*b^10*c^6*d^6 + 288*a^2*b^10*c^8*d^4 - 1432*a^3*b^9*c^3*d^9 - 15744*a^3*b^9*c^5*d^7 + 384*a^3*b^9*c^7*d^5 + 1212*a^4*b^8*c^2*d^10 + 20406*a^4*b^8*c^4*d^8 - 7504*a^4*b^8*c^6*d^6 - 288*a^4*b^8*c^8*d^4 - 15360*a^5*b^7*c^3*d^9 + 22464*a^5*b^7*c^5*d^7 + 768*a^5*b^7*c^7*d^5 + 6636*a^6*b^6*c^2*d^10 - 32976*a^6*b^6*c^4*d^8 + 928*a^6*b^6*c^6*d^6 + 27808*a^7*b^5*c^3*d^9 - 6528*a^7*b^5*c^5*d^7 - 13776*a^8*b^4*c^2*d^10 + 11736*a^8*b^4*c^4*d^8 - 11008*a^9*b^3*c^3*d^9 + 5904*a^10*b^2*c^2*d^10 - 1728*a^11*b*c*d^11))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9) + ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) + (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) - ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(a^2*b^11*d^8 + 10*a^4*b^9*d^8 + 13*a^6*b^7*d^8 - 60*a^8*b^5*d^8 + 36*a^10*b^3*d^8 - 32*a^3*b^10*c*d^7 - 128*a^5*b^8*c*d^7 + 352*a^7*b^6*c*d^7 - 192*a^9*b^4*c*d^7 + 24*a^2*b^11*c^2*d^6 + 144*a^2*b^11*c^4*d^4 - 384*a^3*b^10*c^3*d^5 + 352*a^4*b^9*c^2*d^6 - 288*a^4*b^9*c^4*d^4 + 768*a^5*b^8*c^3*d^5 - 776*a^6*b^7*c^2*d^6 + 144*a^6*b^7*c^4*d^4 - 384*a^7*b^6*c^3*d^5 + 400*a^8*b^5*c^2*d^6))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(2*a*b^13*d^8 - 4*a^3*b^11*c^8 + 19*a^3*b^11*d^8 + 16*a^5*b^9*d^8 - 197*a^7*b^7*d^8 + 228*a^9*b^5*d^8 - 72*a^11*b^3*d^8 + 48*a*b^13*c^2*d^6 + 288*a*b^13*c^4*d^4 - 64*a*b^13*c^6*d^2 - 64*a^2*b^12*c*d^7 + 32*a^2*b^12*c^7*d - 224*a^4*b^10*c*d^7 + 1216*a^6*b^8*c*d^7 - 1280*a^8*b^6*c*d^7 + 384*a^10*b^4*c*d^7 - 768*a^2*b^12*c^3*d^5 + 384*a^2*b^12*c^5*d^3 + 680*a^3*b^11*c^2*d^6 - 1680*a^3*b^11*c^4*d^4 - 96*a^3*b^11*c^6*d^2 + 3200*a^4*b^10*c^3*d^5 - 96*a^4*b^10*c^5*d^3 - 2864*a^5*b^9*c^2*d^6 + 1376*a^5*b^9*c^4*d^4 + 48*a^5*b^9*c^6*d^2 - 2976*a^6*b^8*c^3*d^5 - 64*a^6*b^8*c^5*d^3 + 2824*a^7*b^7*c^2*d^6 - 264*a^7*b^7*c^4*d^4 + 768*a^8*b^6*c^3*d^5 - 800*a^9*b^5*c^2*d^6))/(b^13 - 2*a^2*b^11 + a^4*b^9) - ((a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*a*b^14*d^4 + 4*a^3*b^12*c^4 - 4*a^5*b^10*c^4 + 6*a^3*b^12*d^4 - 14*a^5*b^10*d^4 + 6*a^7*b^8*d^4 + 24*a*b^14*c^2*d^2 - 32*a^2*b^13*c*d^3 - 16*a^2*b^13*c^3*d + 48*a^4*b^11*c*d^3 + 16*a^4*b^11*c^3*d - 16*a^6*b^9*c*d^3 - 24*a^3*b^12*c^2*d^2))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(8*a^2*b^14*c^4 - 8*a^4*b^12*c^4 + 32*a^4*b^12*d^4 - 56*a^6*b^10*d^4 + 24*a^8*b^8*d^4 - 96*a^3*b^13*c*d^3 + 32*a^3*b^13*c^3*d + 160*a^5*b^11*c*d^3 - 64*a^7*b^9*c*d^3 + 96*a^2*b^14*c^2*d^2 - 144*a^4*b^12*c^2*d^2 + 48*a^6*b^10*c^2*d^2 - 32*a*b^15*c^3*d))/(b^13 - 2*a^2*b^11 + a^4*b^9) - (((8*(4*a^2*b^15 - 8*a^4*b^13 + 4*a^6*b^11))/(b^12 - 2*a^2*b^10 + a^4*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17 - 32*a^3*b^15 + 28*a^5*b^13 - 8*a^7*b^11))/(b^13 - 2*a^2*b^11 + a^4*b^9))*(a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*a^2*d - 4*b^2*d + a*b*c))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(a*d - b*c)^3*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^2*d - 4*b^2*d + a*b*c)*2i)/(f*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
707,1,8953,205,17.830644,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + b*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(-2\,a^3\,d^3+3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+a\,b^2\,d^3+b^3\,c^3\right)}{b^2\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-2\,a^3\,d^3+3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+a\,b^2\,d^3+b^3\,c^3\right)}{b^2\,\left(a^2-b^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-3\,a^3\,d^3+3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+2\,a\,b^2\,d^3+b^3\,c^3\right)}{a\,b\,\left(a^2-b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{a\,b\,\left(a^2-b^2\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}+\frac{2\,d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}+\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}}{\frac{64\,\left(-4\,a^8\,d^9+4\,a^7\,b\,c^3\,d^6+24\,a^7\,b\,c\,d^8-12\,a^6\,b^2\,c^4\,d^5-57\,a^6\,b^2\,c^2\,d^7+6\,a^6\,b^2\,d^9+9\,a^5\,b^3\,c^5\,d^4+55\,a^5\,b^3\,c^3\,d^6-39\,a^5\,b^3\,c\,d^8+2\,a^4\,b^4\,c^6\,d^3+3\,a^4\,b^4\,c^4\,d^5+105\,a^4\,b^4\,c^2\,d^7-3\,a^3\,b^5\,c^7\,d^2-39\,a^3\,b^5\,c^5\,d^4-144\,a^3\,b^5\,c^3\,d^6+18\,a^2\,b^6\,c^6\,d^3+99\,a^2\,b^6\,c^4\,d^5-27\,a\,b^7\,c^5\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-16\,a^9\,d^9+72\,a^8\,b\,c\,d^8-108\,a^7\,b^2\,c^2\,d^7+40\,a^7\,b^2\,d^9+46\,a^6\,b^3\,c^3\,d^6-192\,a^6\,b^3\,c\,d^8+24\,a^5\,b^4\,c^4\,d^5+330\,a^5\,b^4\,c^2\,d^7-24\,a^5\,b^4\,d^9-18\,a^4\,b^5\,c^5\,d^4-226\,a^4\,b^5\,c^3\,d^6+120\,a^4\,b^5\,c\,d^8+30\,a^3\,b^6\,c^4\,d^5-222\,a^3\,b^6\,c^2\,d^7+18\,a^2\,b^7\,c^5\,d^4+180\,a^2\,b^7\,c^3\,d^6-54\,a\,b^8\,c^4\,d^5\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}-\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(2\,a\,d-3\,b\,c\right)\,\left(\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\left(2\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)\,\left(2\,a\,d-3\,b\,c\right)}{b^3\,f}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(-4\,a^8\,d^9+4\,a^7\,b\,c^3\,d^6+24\,a^7\,b\,c\,d^8-12\,a^6\,b^2\,c^4\,d^5-57\,a^6\,b^2\,c^2\,d^7+6\,a^6\,b^2\,d^9+9\,a^5\,b^3\,c^5\,d^4+55\,a^5\,b^3\,c^3\,d^6-39\,a^5\,b^3\,c\,d^8+2\,a^4\,b^4\,c^6\,d^3+3\,a^4\,b^4\,c^4\,d^5+105\,a^4\,b^4\,c^2\,d^7-3\,a^3\,b^5\,c^7\,d^2-39\,a^3\,b^5\,c^5\,d^4-144\,a^3\,b^5\,c^3\,d^6+18\,a^2\,b^6\,c^6\,d^3+99\,a^2\,b^6\,c^4\,d^5-27\,a\,b^7\,c^5\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-16\,a^9\,d^9+72\,a^8\,b\,c\,d^8-108\,a^7\,b^2\,c^2\,d^7+40\,a^7\,b^2\,d^9+46\,a^6\,b^3\,c^3\,d^6-192\,a^6\,b^3\,c\,d^8+24\,a^5\,b^4\,c^4\,d^5+330\,a^5\,b^4\,c^2\,d^7-24\,a^5\,b^4\,d^9-18\,a^4\,b^5\,c^5\,d^4-226\,a^4\,b^5\,c^3\,d^6+120\,a^4\,b^5\,c\,d^8+30\,a^3\,b^6\,c^4\,d^5-222\,a^3\,b^6\,c^2\,d^7+18\,a^2\,b^7\,c^5\,d^4+180\,a^2\,b^7\,c^3\,d^6-54\,a\,b^8\,c^4\,d^5\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}-\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(4\,a^8\,b^2\,d^6-12\,a^7\,b^3\,c\,d^5+9\,a^6\,b^4\,c^2\,d^4-8\,a^6\,b^4\,d^6+24\,a^5\,b^5\,c\,d^5-18\,a^4\,b^6\,c^2\,d^4+4\,a^4\,b^6\,d^6-12\,a^3\,b^7\,c\,d^5+9\,a^2\,b^8\,c^2\,d^4\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^9\,b^2\,d^6-24\,a^8\,b^3\,c\,d^5+18\,a^7\,b^4\,c^2\,d^4-28\,a^7\,b^4\,d^6+4\,a^6\,b^5\,c^3\,d^3+90\,a^6\,b^5\,c\,d^5-6\,a^5\,b^6\,c^4\,d^2-84\,a^5\,b^6\,c^2\,d^4+29\,a^5\,b^6\,d^6+12\,a^4\,b^7\,c^3\,d^3-96\,a^4\,b^7\,c\,d^5+a^3\,b^8\,c^6+12\,a^3\,b^8\,c^4\,d^2+99\,a^3\,b^8\,c^2\,d^4-8\,a^3\,b^8\,d^6-6\,a^2\,b^9\,c^5\,d-36\,a^2\,b^9\,c^3\,d^3+24\,a^2\,b^9\,c\,d^5+9\,a\,b^{10}\,c^4\,d^2-18\,a\,b^{10}\,c^2\,d^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b^6\,d^3+a^5\,b^7\,c^3-3\,a^4\,b^8\,c^2\,d-3\,a^4\,b^8\,d^3-a^3\,b^9\,c^3+3\,a^3\,b^9\,c\,d^2+3\,a^2\,b^{10}\,c^2\,d+2\,a^2\,b^{10}\,d^3-3\,a\,b^{11}\,c\,d^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,b^6\,d^3+6\,a^6\,b^7\,c\,d^2+10\,a^5\,b^8\,d^3-2\,a^4\,b^9\,c^3-18\,a^4\,b^9\,c\,d^2+6\,a^3\,b^{10}\,c^2\,d-6\,a^3\,b^{10}\,d^3+2\,a^2\,b^{11}\,c^3+12\,a^2\,b^{11}\,c\,d^2-6\,a\,b^{12}\,c^2\,d\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,d\,a^2+c\,a\,b-3\,d\,b^2\right)\,2{}\mathrm{i}}{f\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((2*(b^3*c^3 - 2*a^3*d^3 + a*b^2*d^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2))/(b^2*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)^2*(b^3*c^3 - 2*a^3*d^3 + a*b^2*d^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2))/(b^2*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)*(b^3*c^3 - 3*a^3*d^3 + 2*a*b^2*d^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2))/(a*b*(a^2 - b^2)) - (2*tan(e/2 + (f*x)/2)^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*b*(a^2 - b^2)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + 2*a*tan(e/2 + (f*x)/2)^2 + a*tan(e/2 + (f*x)/2)^4 + 2*b*tan(e/2 + (f*x)/2)^3)) + (2*d^2*atan(((d^2*(2*a*d - 3*b*c)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*(2*a*d - 3*b*c)*((32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (d^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a*d - 3*b*c)*1i)/b^3)*1i)/b^3))/b^3 + (d^2*(2*a*d - 3*b*c)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*(2*a*d - 3*b*c)*((32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a*d - 3*b*c)*1i)/b^3)*1i)/b^3))/b^3)/((64*(6*a^6*b^2*d^9 - 4*a^8*d^9 - 27*a*b^7*c^5*d^4 - 39*a^5*b^3*c*d^8 + 4*a^7*b*c^3*d^6 + 99*a^2*b^6*c^4*d^5 + 18*a^2*b^6*c^6*d^3 - 144*a^3*b^5*c^3*d^6 - 39*a^3*b^5*c^5*d^4 - 3*a^3*b^5*c^7*d^2 + 105*a^4*b^4*c^2*d^7 + 3*a^4*b^4*c^4*d^5 + 2*a^4*b^4*c^6*d^3 + 55*a^5*b^3*c^3*d^6 + 9*a^5*b^3*c^5*d^4 - 57*a^6*b^2*c^2*d^7 - 12*a^6*b^2*c^4*d^5 + 24*a^7*b*c*d^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (64*tan(e/2 + (f*x)/2)*(40*a^7*b^2*d^9 - 24*a^5*b^4*d^9 - 16*a^9*d^9 - 54*a*b^8*c^4*d^5 + 120*a^4*b^5*c*d^8 - 192*a^6*b^3*c*d^8 + 180*a^2*b^7*c^3*d^6 + 18*a^2*b^7*c^5*d^4 - 222*a^3*b^6*c^2*d^7 + 30*a^3*b^6*c^4*d^5 - 226*a^4*b^5*c^3*d^6 - 18*a^4*b^5*c^5*d^4 + 330*a^5*b^4*c^2*d^7 + 24*a^5*b^4*c^4*d^5 + 46*a^6*b^3*c^3*d^6 - 108*a^7*b^2*c^2*d^7 + 72*a^8*b*c*d^8))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*(2*a*d - 3*b*c)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*(2*a*d - 3*b*c)*((32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (d^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a*d - 3*b*c)*1i)/b^3)*1i)/b^3)*1i)/b^3 - (d^2*(2*a*d - 3*b*c)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*(2*a*d - 3*b*c)*((32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (d^2*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(2*a*d - 3*b*c)*1i)/b^3)*1i)/b^3)*1i)/b^3))*(2*a*d - 3*b*c))/(b^3*f) + (atan((((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(6*a^6*b^2*d^9 - 4*a^8*d^9 - 27*a*b^7*c^5*d^4 - 39*a^5*b^3*c*d^8 + 4*a^7*b*c^3*d^6 + 99*a^2*b^6*c^4*d^5 + 18*a^2*b^6*c^6*d^3 - 144*a^3*b^5*c^3*d^6 - 39*a^3*b^5*c^5*d^4 - 3*a^3*b^5*c^7*d^2 + 105*a^4*b^4*c^2*d^7 + 3*a^4*b^4*c^4*d^5 + 2*a^4*b^4*c^6*d^3 + 55*a^5*b^3*c^3*d^6 + 9*a^5*b^3*c^5*d^4 - 57*a^6*b^2*c^2*d^7 - 12*a^6*b^2*c^4*d^5 + 24*a^7*b*c*d^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (64*tan(e/2 + (f*x)/2)*(40*a^7*b^2*d^9 - 24*a^5*b^4*d^9 - 16*a^9*d^9 - 54*a*b^8*c^4*d^5 + 120*a^4*b^5*c*d^8 - 192*a^6*b^3*c*d^8 + 180*a^2*b^7*c^3*d^6 + 18*a^2*b^7*c^5*d^4 - 222*a^3*b^6*c^2*d^7 + 30*a^3*b^6*c^4*d^5 - 226*a^4*b^5*c^3*d^6 - 18*a^4*b^5*c^5*d^4 + 330*a^5*b^4*c^2*d^7 + 24*a^5*b^4*c^4*d^5 + 46*a^6*b^3*c^3*d^6 - 108*a^7*b^2*c^2*d^7 + 72*a^8*b*c*d^8))/(b^10 - 2*a^2*b^8 + a^4*b^6) + ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) - ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a^4*b^6*d^6 - 8*a^6*b^4*d^6 + 4*a^8*b^2*d^6 - 12*a^3*b^7*c*d^5 + 24*a^5*b^5*c*d^5 - 12*a^7*b^3*c*d^5 + 9*a^2*b^8*c^2*d^4 - 18*a^4*b^6*c^2*d^4 + 9*a^6*b^4*c^2*d^4))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^6 - 8*a^3*b^8*d^6 + 29*a^5*b^6*d^6 - 28*a^7*b^4*d^6 + 8*a^9*b^2*d^6 - 18*a*b^10*c^2*d^4 + 9*a*b^10*c^4*d^2 + 24*a^2*b^9*c*d^5 - 6*a^2*b^9*c^5*d - 96*a^4*b^7*c*d^5 + 90*a^6*b^5*c*d^5 - 24*a^8*b^3*c*d^5 - 36*a^2*b^9*c^3*d^3 + 99*a^3*b^8*c^2*d^4 + 12*a^3*b^8*c^4*d^2 + 12*a^4*b^7*c^3*d^3 - 84*a^5*b^6*c^2*d^4 - 6*a^5*b^6*c^4*d^2 + 4*a^6*b^5*c^3*d^3 + 18*a^7*b^4*c^2*d^4))/(b^10 - 2*a^2*b^8 + a^4*b^6) + ((a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^5*b^7*c^3 - a^3*b^9*c^3 + 2*a^2*b^10*d^3 - 3*a^4*b^8*d^3 + a^6*b^6*d^3 + 3*a^2*b^10*c^2*d + 3*a^3*b^9*c*d^2 - 3*a^4*b^8*c^2*d - 3*a*b^11*c*d^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(2*a^2*b^11*c^3 - 2*a^4*b^9*c^3 - 6*a^3*b^10*d^3 + 10*a^5*b^8*d^3 - 4*a^7*b^6*d^3 + 12*a^2*b^11*c*d^2 + 6*a^3*b^10*c^2*d - 18*a^4*b^9*c*d^2 + 6*a^6*b^7*c*d^2 - 6*a*b^12*c^2*d))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2*d - 3*b^2*d + a*b*c))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(a*d - b*c)^2*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^2*d - 3*b^2*d + a*b*c)*2i)/(f*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
708,1,5776,129,15.468841,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + b*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{b\,\left(a^2-b^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{a\,\left(a^2-b^2\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}-\frac{2\,d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{d^2\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{d^2\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}-\frac{d^2\,\left(\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{d^2\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}}{\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,d^6-2\,a^4\,b^2\,c^2\,d^4-6\,a^4\,b^2\,d^6+4\,a^3\,b^3\,c\,d^5+2\,a^2\,b^4\,c^2\,d^4+4\,a^2\,b^4\,d^6-4\,a\,b^5\,c\,d^5\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{64\,\left(-a^5\,c^2\,d^4-a^5\,d^6+2\,a^4\,b\,c\,d^5+a^3\,b^2\,c^4\,d^2+3\,a^3\,b^2\,c^2\,d^4+2\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^3\,d^3-6\,a^2\,b^3\,c\,d^5+4\,a\,b^4\,c^2\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{d^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{d^2\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{d^2\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{d^2\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{d^2\,\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}\right)}{b^2\,f}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}-\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,d^6-2\,a^4\,b^2\,c^2\,d^4-6\,a^4\,b^2\,d^6+4\,a^3\,b^3\,c\,d^5+2\,a^2\,b^4\,c^2\,d^4+4\,a^2\,b^4\,d^6-4\,a\,b^5\,c\,d^5\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{64\,\left(-a^5\,c^2\,d^4-a^5\,d^6+2\,a^4\,b\,c\,d^5+a^3\,b^2\,c^4\,d^2+3\,a^3\,b^2\,c^2\,d^4+2\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^3\,d^3-6\,a^2\,b^3\,c\,d^5+4\,a\,b^4\,c^2\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}+\frac{\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,b\,d^4-2\,a^5\,b^3\,c^2\,d^2-8\,a^5\,b^3\,d^4+4\,a^4\,b^4\,c\,d^3+a^3\,b^5\,c^4+4\,a^3\,b^5\,c^2\,d^2+9\,a^3\,b^5\,d^4-4\,a^2\,b^6\,c^3\,d-8\,a^2\,b^6\,c\,d^3+4\,a\,b^7\,c^2\,d^2-2\,a\,b^7\,d^4\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{32\,\left(a^6\,b\,d^4-2\,a^4\,b^3\,d^4+a^2\,b^5\,d^4\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^5\,b^4\,c^2+2\,a^4\,b^5\,c\,d+a^3\,b^6\,c^2-a^3\,b^6\,d^2-2\,a^2\,b^7\,c\,d+a\,b^8\,d^2\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^6\,b^4\,d^2-2\,a^4\,b^6\,c^2-6\,a^4\,b^6\,d^2+4\,a^3\,b^7\,c\,d+2\,a^2\,b^8\,c^2+4\,a^2\,b^8\,d^2-4\,a\,b^9\,c\,d\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}-\frac{\left(\frac{32\,\left(a^6\,b^5-2\,a^4\,b^7+a^2\,b^9\right)}{a^4\,b^2-2\,a^2\,b^4+b^6}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^5+7\,a^5\,b^7-8\,a^3\,b^9+3\,a\,b^{11}\right)}{a^4\,b^3-2\,a^2\,b^5+b^7}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(d\,a^2+c\,a\,b-2\,d\,b^2\right)\,2{}\mathrm{i}}{f\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"((2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(b*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*(a^2 - b^2)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2)) - (2*d^2*atan(((d^2*((32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (d^2*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) - (d^2*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2))/b^2 - (d^2*((32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) - (32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (d^2*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (d^2*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2))/b^2)/((64*tan(e/2 + (f*x)/2)*(2*a^6*d^6 + 4*a^2*b^4*d^6 - 6*a^4*b^2*d^6 + 4*a^3*b^3*c*d^5 + 2*a^2*b^4*c^2*d^4 - 2*a^4*b^2*c^2*d^4 - 4*a*b^5*c*d^5))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (64*(2*a^3*b^2*d^6 - a^5*d^6 - a^5*c^2*d^4 + 4*a*b^4*c^2*d^4 - 6*a^2*b^3*c*d^5 - 4*a^2*b^3*c^3*d^3 + 3*a^3*b^2*c^2*d^4 + a^3*b^2*c^4*d^2 + 2*a^4*b*c*d^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (d^2*((32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (d^2*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) - (d^2*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2)*1i)/b^2 + (d^2*((32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) - (32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (d^2*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (d^2*((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2 + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3))*1i)/b^2)*1i)/b^2)))/(b^2*f) + (atan((((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) - (32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) + ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) - ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) + ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*tan(e/2 + (f*x)/2)*(2*a^6*d^6 + 4*a^2*b^4*d^6 - 6*a^4*b^2*d^6 + 4*a^3*b^3*c*d^5 + 2*a^2*b^4*c^2*d^4 - 2*a^4*b^2*c^2*d^4 - 4*a*b^5*c*d^5))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (64*(2*a^3*b^2*d^6 - a^5*d^6 - a^5*c^2*d^4 + 4*a*b^4*c^2*d^4 - 6*a^2*b^3*c*d^5 - 4*a^2*b^3*c^3*d^3 + 3*a^3*b^2*c^2*d^4 + a^3*b^2*c^4*d^2 + 2*a^4*b*c*d^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) - (32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) + ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3) + (((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^7*b*d^4 - 2*a*b^7*d^4 + a^3*b^5*c^4 + 9*a^3*b^5*d^4 - 8*a^5*b^3*d^4 + 4*a*b^7*c^2*d^2 - 8*a^2*b^6*c*d^3 - 4*a^2*b^6*c^3*d + 4*a^4*b^4*c*d^3 + 4*a^3*b^5*c^2*d^2 - 2*a^5*b^3*c^2*d^2))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (32*(a^6*b*d^4 + a^2*b^5*d^4 - 2*a^4*b^3*d^4))/(b^6 - 2*a^2*b^4 + a^4*b^2) + ((a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^8*d^2 + a^3*b^6*c^2 - a^5*b^4*c^2 - a^3*b^6*d^2 - 2*a^2*b^7*c*d + 2*a^4*b^5*c*d))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(2*a^2*b^8*c^2 - 2*a^4*b^6*c^2 + 4*a^2*b^8*d^2 - 6*a^4*b^6*d^2 + 2*a^6*b^4*d^2 - 4*a*b^9*c*d + 4*a^3*b^7*c*d))/(b^7 - 2*a^2*b^5 + a^4*b^3) - (((32*(a^2*b^9 - 2*a^4*b^7 + a^6*b^5))/(b^6 - 2*a^2*b^4 + a^4*b^2) + (32*tan(e/2 + (f*x)/2)*(3*a*b^11 - 8*a^3*b^9 + 7*a^5*b^7 - 2*a^7*b^5))/(b^7 - 2*a^2*b^5 + a^4*b^3))*(a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(a^2*d - 2*b^2*d + a*b*c))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(a*d - b*c)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^2*d - 2*b^2*d + a*b*c)*2i)/(f*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))","B"
709,1,215,97,8.021134,"\text{Not used}","int((c + d*sin(e + f*x))/(a + b*sin(e + f*x))^2,x)","\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{2\,\left(a^2\,b-b^3\right)\,\left(a\,c-b\,d\right)}{{\left(a+b\right)}^{3/2}\,\left(a^2-b^2\right)\,{\left(a-b\right)}^{3/2}}+\frac{2\,a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c-b\,d\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}\right)\,\left(a^2-b^2\right)}{2\,\left(a\,c-b\,d\right)}\right)\,\left(a\,c-b\,d\right)}{f\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{\frac{2\,\left(a\,d-b\,c\right)}{a^2-b^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,d-b\,c\right)}{a\,\left(a^2-b^2\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}","Not used",1,"(2*atan((((2*(a^2*b - b^3)*(a*c - b*d))/((a + b)^(3/2)*(a^2 - b^2)*(a - b)^(3/2)) + (2*a*tan(e/2 + (f*x)/2)*(a*c - b*d))/((a + b)^(3/2)*(a - b)^(3/2)))*(a^2 - b^2))/(2*(a*c - b*d)))*(a*c - b*d))/(f*(a + b)^(3/2)*(a - b)^(3/2)) - ((2*(a*d - b*c))/(a^2 - b^2) + (2*b*tan(e/2 + (f*x)/2)*(a*d - b*c))/(a*(a^2 - b^2)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2))","B"
710,1,174,83,8.240039,"\text{Not used}","int(1/(a + b*sin(e + f*x))^2,x)","\frac{\frac{2\,b}{a^2-b^2}+\frac{2\,b^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{a\,\left(a^2-b^2\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}+\frac{2\,a\,\mathrm{atan}\left(\frac{\left(a^2-b^2\right)\,\left(\frac{2\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}+\frac{2\,a\,\left(a^2\,b-b^3\right)}{{\left(a+b\right)}^{3/2}\,\left(a^2-b^2\right)\,{\left(a-b\right)}^{3/2}}\right)}{2\,a}\right)}{f\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"((2*b)/(a^2 - b^2) + (2*b^2*tan(e/2 + (f*x)/2))/(a*(a^2 - b^2)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2)) + (2*a*atan(((a^2 - b^2)*((2*a^2*tan(e/2 + (f*x)/2))/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a*(a^2*b - b^3))/((a + b)^(3/2)*(a^2 - b^2)*(a - b)^(3/2))))/(2*a)))/(f*(a + b)^(3/2)*(a - b)^(3/2))","B"
711,1,24123,181,22.796890,"\text{Not used}","int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))),x)","-\frac{\frac{2\,b^2}{\left(a^2-b^2\right)\,\left(a\,d-b\,c\right)}+\frac{2\,b^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{a\,\left(a^2-b^2\right)\,\left(a\,d-b\,c\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}+\frac{d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)\,1{}\mathrm{i}}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}-\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)\,1{}\mathrm{i}}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}}{\frac{64\,\left(2\,a^5\,b\,c\,d^4-3\,a^4\,b^2\,c^2\,d^3+a^3\,b^3\,c^3\,d^2-3\,a^3\,b^3\,c\,d^4+2\,a^2\,b^4\,c^2\,d^3+a\,b^5\,c\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^4\,b^2\,c\,d^4+2\,a^3\,b^3\,c^2\,d^3+2\,a^2\,b^4\,c\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}-\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{d^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}\right)}{-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2}}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{f\,\left(-a^2\,c^2\,d^2+a^2\,d^4+2\,a\,b\,c^3\,d-2\,a\,b\,c\,d^3-b^2\,c^4+b^2\,c^2\,d^2\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{b\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)\,1{}\mathrm{i}}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{b\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)\,1{}\mathrm{i}}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}}{\frac{64\,\left(2\,a^5\,b\,c\,d^4-3\,a^4\,b^2\,c^2\,d^3+a^3\,b^3\,c^3\,d^2-3\,a^3\,b^3\,c\,d^4+2\,a^2\,b^4\,c^2\,d^3+a\,b^5\,c\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^4\,b^2\,c\,d^4+2\,a^3\,b^3\,c^2\,d^3+2\,a^2\,b^4\,c\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{b\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^7\,b\,c\,d^5-3\,a^6\,b^2\,c^2\,d^4+8\,a^5\,b^3\,c^3\,d^3+2\,a^5\,b^3\,c\,d^5-5\,a^4\,b^4\,c^4\,d^2+2\,a^4\,b^4\,c^2\,d^4+a^3\,b^5\,c^5\,d-6\,a^3\,b^5\,c^3\,d^3-a^3\,b^5\,c\,d^5+2\,a^2\,b^6\,c^4\,d^2+a\,b^7\,c^3\,d^3\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^8\,c\,d^5+a^7\,b\,c^2\,d^4-4\,a^6\,b^2\,c^3\,d^3+12\,a^6\,b^2\,c\,d^5+8\,a^5\,b^3\,c^4\,d^2-20\,a^5\,b^3\,c^2\,d^4-5\,a^4\,b^4\,c^5\,d+14\,a^4\,b^4\,c^3\,d^3-13\,a^4\,b^4\,c\,d^5+a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+17\,a^3\,b^5\,c^2\,d^4+2\,a^2\,b^6\,c^5\,d-5\,a^2\,b^6\,c^3\,d^3+4\,a^2\,b^6\,c\,d^5+a\,b^7\,c^4\,d^2-4\,a\,b^7\,c^2\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-5\,a^9\,b\,c^3\,d^4+2\,a^9\,b\,c\,d^6+10\,a^8\,b^2\,c^4\,d^3-10\,a^8\,b^2\,c^2\,d^5-10\,a^7\,b^3\,c^5\,d^2+21\,a^7\,b^3\,c^3\,d^4-3\,a^7\,b^3\,c\,d^6+5\,a^6\,b^4\,c^6\,d-24\,a^6\,b^4\,c^4\,d^3+13\,a^6\,b^4\,c^2\,d^5-a^5\,b^5\,c^7+16\,a^5\,b^5\,c^5\,d^2-22\,a^5\,b^5\,c^3\,d^4+a^5\,b^5\,c\,d^6-6\,a^4\,b^6\,c^6\,d+18\,a^4\,b^6\,c^4\,d^3-4\,a^4\,b^6\,c^2\,d^5+a^3\,b^7\,c^7-7\,a^3\,b^7\,c^5\,d^2+6\,a^3\,b^7\,c^3\,d^4+a^2\,b^8\,c^6\,d-4\,a^2\,b^8\,c^4\,d^3+a\,b^9\,c^5\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{10}\,c\,d^6-6\,a^9\,b\,c^2\,d^5+2\,a^8\,b^2\,c^3\,d^4-2\,a^8\,b^2\,c\,d^6+12\,a^7\,b^3\,c^4\,d^3+4\,a^7\,b^3\,c^2\,d^5-18\,a^6\,b^4\,c^5\,d^2+6\,a^6\,b^4\,c^3\,d^4+10\,a^5\,b^5\,c^6\,d-24\,a^5\,b^5\,c^4\,d^3+2\,a^5\,b^5\,c^2\,d^5-2\,a^4\,b^6\,c^7+26\,a^4\,b^6\,c^5\,d^2-8\,a^4\,b^6\,c^3\,d^4-12\,a^3\,b^7\,c^6\,d+12\,a^3\,b^7\,c^4\,d^3+2\,a^2\,b^8\,c^7-8\,a^2\,b^8\,c^5\,d^2+2\,a\,b^9\,c^6\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{b\,\left(\frac{32\,\left(a^{12}\,c^2\,d^6-4\,a^{11}\,b\,c^3\,d^5-a^{11}\,b\,c\,d^7+5\,a^{10}\,b^2\,c^4\,d^4+2\,a^{10}\,b^2\,c^2\,d^6+3\,a^9\,b^3\,c^3\,d^5+2\,a^9\,b^3\,c\,d^7-5\,a^8\,b^4\,c^6\,d^2-10\,a^8\,b^4\,c^4\,d^4-7\,a^8\,b^4\,c^2\,d^6+4\,a^7\,b^5\,c^7\,d+5\,a^7\,b^5\,c^5\,d^3+6\,a^7\,b^5\,c^3\,d^5-a^7\,b^5\,c\,d^7-a^6\,b^6\,c^8+6\,a^6\,b^6\,c^6\,d^2+5\,a^6\,b^6\,c^4\,d^4+4\,a^6\,b^6\,c^2\,d^6-7\,a^5\,b^7\,c^7\,d-10\,a^5\,b^7\,c^5\,d^3-5\,a^5\,b^7\,c^3\,d^5+2\,a^4\,b^8\,c^8+3\,a^4\,b^8\,c^6\,d^2+2\,a^3\,b^9\,c^7\,d+5\,a^3\,b^9\,c^5\,d^3-a^2\,b^{10}\,c^8-4\,a^2\,b^{10}\,c^6\,d^2+a\,b^{11}\,c^7\,d\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{12}\,c^3\,d^5-3\,a^{12}\,c\,d^7-10\,a^{11}\,b\,c^4\,d^4+15\,a^{11}\,b\,c^2\,d^6+20\,a^{10}\,b^2\,c^5\,d^3-37\,a^{10}\,b^2\,c^3\,d^5+10\,a^{10}\,b^2\,c\,d^7-20\,a^9\,b^3\,c^6\,d^2+65\,a^9\,b^3\,c^4\,d^4-50\,a^9\,b^3\,c^2\,d^6+10\,a^8\,b^4\,c^7\,d-85\,a^8\,b^4\,c^5\,d^3+108\,a^8\,b^4\,c^3\,d^5-11\,a^8\,b^4\,c\,d^7-2\,a^7\,b^5\,c^8+73\,a^7\,b^5\,c^6\,d^2-140\,a^7\,b^5\,c^4\,d^4+55\,a^7\,b^5\,c^2\,d^6-35\,a^6\,b^6\,c^7\,d+130\,a^6\,b^6\,c^5\,d^3-113\,a^6\,b^6\,c^3\,d^5+4\,a^6\,b^6\,c\,d^7+7\,a^5\,b^7\,c^8-90\,a^5\,b^7\,c^6\,d^2+125\,a^5\,b^7\,c^4\,d^4-20\,a^5\,b^7\,c^2\,d^6+40\,a^4\,b^8\,c^7\,d-85\,a^4\,b^8\,c^5\,d^3+40\,a^4\,b^8\,c^3\,d^5-8\,a^3\,b^9\,c^8+41\,a^3\,b^9\,c^6\,d^2-40\,a^3\,b^9\,c^4\,d^4-15\,a^2\,b^{10}\,c^7\,d+20\,a^2\,b^{10}\,c^5\,d^3+3\,a\,b^{11}\,c^8-4\,a\,b^{11}\,c^6\,d^2\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-2\,a^5\,b^2\,d^3-a^4\,b^3\,c^3+6\,a^4\,b^3\,c\,d^2-6\,a^3\,b^4\,c^2\,d+a^3\,b^4\,d^3+2\,a^2\,b^5\,c^3-3\,a^2\,b^5\,c\,d^2+3\,a\,b^6\,c^2\,d-b^7\,c^3}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}\right)\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)}{a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,d\,a^2+c\,a\,b+d\,b^2\right)\,2{}\mathrm{i}}{f\,\left(a^8\,d^2-2\,a^7\,b\,c\,d+a^6\,b^2\,c^2-3\,a^6\,b^2\,d^2+6\,a^5\,b^3\,c\,d-3\,a^4\,b^4\,c^2+3\,a^4\,b^4\,d^2-6\,a^3\,b^5\,c\,d+3\,a^2\,b^6\,c^2-a^2\,b^6\,d^2+2\,a\,b^7\,c\,d-b^8\,c^2\right)}","Not used",1,"(d^2*atan(((d^2*(d^2 - c^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (d^2*(d^2 - c^2)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (d^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d))*1i)/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d) - (d^2*(d^2 - c^2)^(1/2)*((32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (d^2*(d^2 - c^2)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (d^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d))*1i)/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d))/((64*(2*a^2*b^4*c^2*d^3 - 3*a^3*b^3*c*d^4 + a^3*b^3*c^3*d^2 - 3*a^4*b^2*c^2*d^3 + a*b^5*c*d^4 + 2*a^5*b*c*d^4))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (64*tan(e/2 + (f*x)/2)*(2*a^2*b^4*c*d^4 - 4*a^4*b^2*c*d^4 + 2*a^3*b^3*c^2*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (d^2*(d^2 - c^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (d^2*(d^2 - c^2)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (d^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d) - (d^2*(d^2 - c^2)^(1/2)*((32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (d^2*(d^2 - c^2)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (d^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))/(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)))*(d^2 - c^2)^(1/2)*2i)/(f*(a^2*d^4 - b^2*c^4 - a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 + 2*a*b*c^3*d)) - ((2*b^2)/((a^2 - b^2)*(a*d - b*c)) + (2*b^3*tan(e/2 + (f*x)/2))/(a*(a^2 - b^2)*(a*d - b*c)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2)) + (b*atan(((b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (b*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c)*1i)/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (b*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c)*1i)/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))/((64*(2*a^2*b^4*c^2*d^3 - 3*a^3*b^3*c*d^4 + a^3*b^3*c^3*d^2 - 3*a^4*b^2*c^2*d^3 + a*b^5*c*d^4 + 2*a^5*b*c*d^4))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (64*tan(e/2 + (f*x)/2)*(2*a^2*b^4*c*d^4 - 4*a^4*b^2*c*d^4 + 2*a^3*b^3*c^2*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (b*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^7*c^3*d^3 - a^3*b^5*c*d^5 + a^3*b^5*c^5*d + 2*a^5*b^3*c*d^5 + 2*a^2*b^6*c^4*d^2 - 6*a^3*b^5*c^3*d^3 + 2*a^4*b^4*c^2*d^4 - 5*a^4*b^4*c^4*d^2 + 8*a^5*b^3*c^3*d^3 - 3*a^6*b^2*c^2*d^4 - a^7*b*c*d^5))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(a^3*b^5*c^6 - a^8*c*d^5 - 4*a*b^7*c^2*d^4 + a*b^7*c^4*d^2 + 4*a^2*b^6*c*d^5 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c*d^5 - 5*a^4*b^4*c^5*d + 12*a^6*b^2*c*d^5 + a^7*b*c^2*d^4 - 5*a^2*b^6*c^3*d^3 + 17*a^3*b^5*c^2*d^4 - 8*a^3*b^5*c^4*d^2 + 14*a^4*b^4*c^3*d^3 - 20*a^5*b^3*c^2*d^4 + 8*a^5*b^3*c^4*d^2 - 4*a^6*b^2*c^3*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^3*b^7*c^7 - a^5*b^5*c^7 + a^10*c^2*d^5 + a*b^9*c^5*d^2 + a^2*b^8*c^6*d - 6*a^4*b^6*c^6*d + a^5*b^5*c*d^6 + 5*a^6*b^4*c^6*d - 3*a^7*b^3*c*d^6 - 5*a^9*b*c^3*d^4 - 4*a^2*b^8*c^4*d^3 + 6*a^3*b^7*c^3*d^4 - 7*a^3*b^7*c^5*d^2 - 4*a^4*b^6*c^2*d^5 + 18*a^4*b^6*c^4*d^3 - 22*a^5*b^5*c^3*d^4 + 16*a^5*b^5*c^5*d^2 + 13*a^6*b^4*c^2*d^5 - 24*a^6*b^4*c^4*d^3 + 21*a^7*b^3*c^3*d^4 - 10*a^7*b^3*c^5*d^2 - 10*a^8*b^2*c^2*d^5 + 10*a^8*b^2*c^4*d^3 + 2*a^9*b*c*d^6))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) + (32*tan(e/2 + (f*x)/2)*(2*a^10*c*d^6 + 2*a^2*b^8*c^7 - 2*a^4*b^6*c^7 - 12*a^3*b^7*c^6*d + 10*a^5*b^5*c^6*d - 2*a^8*b^2*c*d^6 - 6*a^9*b*c^2*d^5 - 8*a^2*b^8*c^5*d^2 + 12*a^3*b^7*c^4*d^3 - 8*a^4*b^6*c^3*d^4 + 26*a^4*b^6*c^5*d^2 + 2*a^5*b^5*c^2*d^5 - 24*a^5*b^5*c^4*d^3 + 6*a^6*b^4*c^3*d^4 - 18*a^6*b^4*c^5*d^2 + 4*a^7*b^3*c^2*d^5 + 12*a^7*b^3*c^4*d^3 + 2*a^8*b^2*c^3*d^4 + 2*a*b^9*c^6*d))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (b*((32*(2*a^4*b^8*c^8 - a^2*b^10*c^8 - a^6*b^6*c^8 + a^12*c^2*d^6 + 2*a^3*b^9*c^7*d - 7*a^5*b^7*c^7*d - a^7*b^5*c*d^7 + 4*a^7*b^5*c^7*d + 2*a^9*b^3*c*d^7 - 4*a^11*b*c^3*d^5 - 4*a^2*b^10*c^6*d^2 + 5*a^3*b^9*c^5*d^3 + 3*a^4*b^8*c^6*d^2 - 5*a^5*b^7*c^3*d^5 - 10*a^5*b^7*c^5*d^3 + 4*a^6*b^6*c^2*d^6 + 5*a^6*b^6*c^4*d^4 + 6*a^6*b^6*c^6*d^2 + 6*a^7*b^5*c^3*d^5 + 5*a^7*b^5*c^5*d^3 - 7*a^8*b^4*c^2*d^6 - 10*a^8*b^4*c^4*d^4 - 5*a^8*b^4*c^6*d^2 + 3*a^9*b^3*c^3*d^5 + 2*a^10*b^2*c^2*d^6 + 5*a^10*b^2*c^4*d^4 + a*b^11*c^7*d - a^11*b*c*d^7))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2) - (32*tan(e/2 + (f*x)/2)*(3*a*b^11*c^8 - 3*a^12*c*d^7 - 8*a^3*b^9*c^8 + 7*a^5*b^7*c^8 - 2*a^7*b^5*c^8 + 2*a^12*c^3*d^5 - 4*a*b^11*c^6*d^2 - 15*a^2*b^10*c^7*d + 40*a^4*b^8*c^7*d + 4*a^6*b^6*c*d^7 - 35*a^6*b^6*c^7*d - 11*a^8*b^4*c*d^7 + 10*a^8*b^4*c^7*d + 10*a^10*b^2*c*d^7 + 15*a^11*b*c^2*d^6 - 10*a^11*b*c^4*d^4 + 20*a^2*b^10*c^5*d^3 - 40*a^3*b^9*c^4*d^4 + 41*a^3*b^9*c^6*d^2 + 40*a^4*b^8*c^3*d^5 - 85*a^4*b^8*c^5*d^3 - 20*a^5*b^7*c^2*d^6 + 125*a^5*b^7*c^4*d^4 - 90*a^5*b^7*c^6*d^2 - 113*a^6*b^6*c^3*d^5 + 130*a^6*b^6*c^5*d^3 + 55*a^7*b^5*c^2*d^6 - 140*a^7*b^5*c^4*d^4 + 73*a^7*b^5*c^6*d^2 + 108*a^8*b^4*c^3*d^5 - 85*a^8*b^4*c^5*d^3 - 50*a^9*b^3*c^2*d^6 + 65*a^9*b^3*c^4*d^4 - 20*a^9*b^3*c^6*d^2 - 37*a^10*b^2*c^3*d^5 + 20*a^10*b^2*c^5*d^3))/(a^7*d^3 - b^7*c^3 + 2*a^2*b^5*c^3 - a^4*b^3*c^3 + a^3*b^4*d^3 - 2*a^5*b^2*d^3 - 3*a^2*b^5*c*d^2 - 6*a^3*b^4*c^2*d + 6*a^4*b^3*c*d^2 + 3*a^5*b^2*c^2*d + 3*a*b^6*c^2*d - 3*a^6*b*c*d^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))*(b^2*d - 2*a^2*d + a*b*c))/(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d)))*(-(a + b)^3*(a - b)^3)^(1/2)*(b^2*d - 2*a^2*d + a*b*c)*2i)/(f*(a^8*d^2 - b^8*c^2 + 3*a^2*b^6*c^2 - 3*a^4*b^4*c^2 + a^6*b^2*c^2 - a^2*b^6*d^2 + 3*a^4*b^4*d^2 - 3*a^6*b^2*d^2 + 2*a*b^7*c*d - 2*a^7*b*c*d - 6*a^3*b^5*c*d + 6*a^5*b^3*c*d))","B"
712,1,71320,290,30.890162,"\text{Not used}","int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^2),x)","\frac{\frac{2\,\left(a^3\,d^3-a\,b^2\,d^3+b^3\,c^3-b^3\,c\,d^2\right)}{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c^2-a^2\,d^2-b^2\,c^2+b^2\,d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^4\,d^4-a^2\,b^2\,d^4+b^4\,c^4-b^4\,c^2\,d^2\right)}{a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c^2-a^2\,d^2-b^2\,c^2+b^2\,d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,d^4+2\,a^3\,b\,c\,d^3-a^2\,b^2\,d^4+2\,a\,b^3\,c^3\,d-4\,a\,b^3\,c\,d^3+b^4\,c^4-b^4\,c^2\,d^2\right)}{a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c^2-a^2\,d^2-b^2\,c^2+b^2\,d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a\,c+2\,b\,d\right)\,\left(a^3\,d^3-a\,b^2\,d^3+b^3\,c^3-b^3\,c\,d^2\right)}{a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c^2-a^2\,d^2-b^2\,c^2+b^2\,d^2\right)}}{f\,\left(a\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+\left(2\,a\,d+2\,b\,c\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\left(2\,a\,c+4\,b\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(2\,a\,d+2\,b\,c\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,c\right)}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{13}\,c^4\,d^9-2\,a^{13}\,c^2\,d^{11}-16\,a^{12}\,b\,c^5\,d^8+20\,a^{12}\,b\,c^3\,d^{10}-4\,a^{12}\,b\,c\,d^{12}+50\,a^{11}\,b^2\,c^6\,d^7-76\,a^{11}\,b^2\,c^4\,d^9+26\,a^{11}\,b^2\,c^2\,d^{11}-74\,a^{10}\,b^3\,c^7\,d^6+150\,a^{10}\,b^3\,c^5\,d^8-82\,a^{10}\,b^3\,c^3\,d^{10}+6\,a^{10}\,b^3\,c\,d^{12}+38\,a^9\,b^4\,c^8\,d^5-164\,a^9\,b^4\,c^6\,d^7+160\,a^9\,b^4\,c^4\,d^9-34\,a^9\,b^4\,c^2\,d^{11}+38\,a^8\,b^5\,c^9\,d^4+72\,a^8\,b^5\,c^7\,d^6-188\,a^8\,b^5\,c^5\,d^8+80\,a^8\,b^5\,c^3\,d^{10}-2\,a^8\,b^5\,c\,d^{12}-74\,a^7\,b^6\,c^{10}\,d^3+72\,a^7\,b^6\,c^8\,d^5+88\,a^7\,b^6\,c^6\,d^7-96\,a^7\,b^6\,c^4\,d^9+10\,a^7\,b^6\,c^2\,d^{11}+50\,a^6\,b^7\,c^{11}\,d^2-164\,a^6\,b^7\,c^9\,d^4+88\,a^6\,b^7\,c^7\,d^6+44\,a^6\,b^7\,c^5\,d^8-18\,a^6\,b^7\,c^3\,d^{10}-16\,a^5\,b^8\,c^{12}\,d+150\,a^5\,b^8\,c^{10}\,d^3-188\,a^5\,b^8\,c^8\,d^5+44\,a^5\,b^8\,c^6\,d^7+10\,a^5\,b^8\,c^4\,d^9+2\,a^4\,b^9\,c^{13}-76\,a^4\,b^9\,c^{11}\,d^2+160\,a^4\,b^9\,c^9\,d^4-96\,a^4\,b^9\,c^7\,d^6+10\,a^4\,b^9\,c^5\,d^8+20\,a^3\,b^{10}\,c^{12}\,d-82\,a^3\,b^{10}\,c^{10}\,d^3+80\,a^3\,b^{10}\,c^8\,d^5-18\,a^3\,b^{10}\,c^6\,d^7-2\,a^2\,b^{11}\,c^{13}+26\,a^2\,b^{11}\,c^{11}\,d^2-34\,a^2\,b^{11}\,c^9\,d^4+10\,a^2\,b^{11}\,c^7\,d^6-4\,a\,b^{12}\,c^{12}\,d+6\,a\,b^{12}\,c^{10}\,d^3-2\,a\,b^{12}\,c^8\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\left(-a^{13}\,c^5\,d^8+a^{13}\,c^3\,d^{10}+8\,a^{12}\,b\,c^6\,d^7-10\,a^{12}\,b\,c^4\,d^9+2\,a^{12}\,b\,c^2\,d^{11}-28\,a^{11}\,b^2\,c^7\,d^6+47\,a^{11}\,b^2\,c^5\,d^8-22\,a^{11}\,b^2\,c^3\,d^{10}+3\,a^{11}\,b^2\,c\,d^{12}+56\,a^{10}\,b^3\,c^8\,d^5-132\,a^{10}\,b^3\,c^6\,d^7+98\,a^{10}\,b^3\,c^4\,d^9-22\,a^{10}\,b^3\,c^2\,d^{11}-70\,a^9\,b^4\,c^9\,d^4+240\,a^9\,b^4\,c^7\,d^6-248\,a^9\,b^4\,c^5\,d^8+83\,a^9\,b^4\,c^3\,d^{10}-5\,a^9\,b^4\,c\,d^{12}+56\,a^8\,b^5\,c^{10}\,d^3-292\,a^8\,b^5\,c^8\,d^5+412\,a^8\,b^5\,c^6\,d^7-208\,a^8\,b^5\,c^4\,d^9+32\,a^8\,b^5\,c^2\,d^{11}-28\,a^7\,b^6\,c^{11}\,d^2+240\,a^7\,b^6\,c^9\,d^4-484\,a^7\,b^6\,c^7\,d^6+362\,a^7\,b^6\,c^5\,d^8-92\,a^7\,b^6\,c^3\,d^{10}+2\,a^7\,b^6\,c\,d^{12}+8\,a^6\,b^7\,c^{12}\,d-132\,a^6\,b^7\,c^{10}\,d^3+412\,a^6\,b^7\,c^8\,d^5-436\,a^6\,b^7\,c^6\,d^7+160\,a^6\,b^7\,c^4\,d^9-12\,a^6\,b^7\,c^2\,d^{11}-a^5\,b^8\,c^{13}+47\,a^5\,b^8\,c^{11}\,d^2-248\,a^5\,b^8\,c^9\,d^4+362\,a^5\,b^8\,c^7\,d^6-190\,a^5\,b^8\,c^5\,d^8+30\,a^5\,b^8\,c^3\,d^{10}-10\,a^4\,b^9\,c^{12}\,d+98\,a^4\,b^9\,c^{10}\,d^3-208\,a^4\,b^9\,c^8\,d^5+160\,a^4\,b^9\,c^6\,d^7-40\,a^4\,b^9\,c^4\,d^9+a^3\,b^{10}\,c^{13}-22\,a^3\,b^{10}\,c^{11}\,d^2+83\,a^3\,b^{10}\,c^9\,d^4-92\,a^3\,b^{10}\,c^7\,d^6+30\,a^3\,b^{10}\,c^5\,d^8+2\,a^2\,b^{11}\,c^{12}\,d-22\,a^2\,b^{11}\,c^{10}\,d^3+32\,a^2\,b^{11}\,c^8\,d^5-12\,a^2\,b^{11}\,c^6\,d^7+3\,a\,b^{12}\,c^{11}\,d^2-5\,a\,b^{12}\,c^9\,d^4+2\,a\,b^{12}\,c^7\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{b^2\,\left(\frac{32\,\left(a^{15}\,c^6\,d^9-2\,a^{15}\,c^4\,d^{11}+a^{15}\,c^2\,d^{13}-7\,a^{14}\,b\,c^7\,d^8+13\,a^{14}\,b\,c^5\,d^{10}-5\,a^{14}\,b\,c^3\,d^{12}-a^{14}\,b\,c\,d^{14}+20\,a^{13}\,b^2\,c^8\,d^7-35\,a^{13}\,b^2\,c^6\,d^9+10\,a^{13}\,b^2\,c^4\,d^{11}+5\,a^{13}\,b^2\,c^2\,d^{13}-28\,a^{12}\,b^3\,c^9\,d^6+50\,a^{12}\,b^3\,c^7\,d^8-14\,a^{12}\,b^3\,c^5\,d^{10}-10\,a^{12}\,b^3\,c^3\,d^{12}+2\,a^{12}\,b^3\,c\,d^{14}+14\,a^{11}\,b^4\,c^{10}\,d^5-40\,a^{11}\,b^4\,c^8\,d^7+25\,a^{11}\,b^4\,c^6\,d^9+14\,a^{11}\,b^4\,c^4\,d^{11}-13\,a^{11}\,b^4\,c^2\,d^{13}+14\,a^{10}\,b^5\,c^{11}\,d^4+14\,a^{10}\,b^5\,c^9\,d^6-37\,a^{10}\,b^5\,c^7\,d^8-25\,a^{10}\,b^5\,c^5\,d^{10}+35\,a^{10}\,b^5\,c^3\,d^{12}-a^{10}\,b^5\,c\,d^{14}-28\,a^9\,b^6\,c^{12}\,d^3+14\,a^9\,b^6\,c^{10}\,d^5+20\,a^9\,b^6\,c^8\,d^7+37\,a^9\,b^6\,c^6\,d^9-50\,a^9\,b^6\,c^4\,d^{11}+7\,a^9\,b^6\,c^2\,d^{13}+20\,a^8\,b^7\,c^{13}\,d^2-40\,a^8\,b^7\,c^{11}\,d^4+20\,a^8\,b^7\,c^9\,d^6-20\,a^8\,b^7\,c^7\,d^8+40\,a^8\,b^7\,c^5\,d^{10}-20\,a^8\,b^7\,c^3\,d^{12}-7\,a^7\,b^8\,c^{14}\,d+50\,a^7\,b^8\,c^{12}\,d^3-37\,a^7\,b^8\,c^{10}\,d^5-20\,a^7\,b^8\,c^8\,d^7-14\,a^7\,b^8\,c^6\,d^9+28\,a^7\,b^8\,c^4\,d^{11}+a^6\,b^9\,c^{15}-35\,a^6\,b^9\,c^{13}\,d^2+25\,a^6\,b^9\,c^{11}\,d^4+37\,a^6\,b^9\,c^9\,d^6-14\,a^6\,b^9\,c^7\,d^8-14\,a^6\,b^9\,c^5\,d^{10}+13\,a^5\,b^{10}\,c^{14}\,d-14\,a^5\,b^{10}\,c^{12}\,d^3-25\,a^5\,b^{10}\,c^{10}\,d^5+40\,a^5\,b^{10}\,c^8\,d^7-14\,a^5\,b^{10}\,c^6\,d^9-2\,a^4\,b^{11}\,c^{15}+10\,a^4\,b^{11}\,c^{13}\,d^2+14\,a^4\,b^{11}\,c^{11}\,d^4-50\,a^4\,b^{11}\,c^9\,d^6+28\,a^4\,b^{11}\,c^7\,d^8-5\,a^3\,b^{12}\,c^{14}\,d-10\,a^3\,b^{12}\,c^{12}\,d^3+35\,a^3\,b^{12}\,c^{10}\,d^5-20\,a^3\,b^{12}\,c^8\,d^7+a^2\,b^{13}\,c^{15}+5\,a^2\,b^{13}\,c^{13}\,d^2-13\,a^2\,b^{13}\,c^{11}\,d^4+7\,a^2\,b^{13}\,c^9\,d^6-a\,b^{14}\,c^{14}\,d+2\,a\,b^{14}\,c^{12}\,d^3-a\,b^{14}\,c^{10}\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{15}\,c^7\,d^8-7\,a^{15}\,c^5\,d^{10}+8\,a^{15}\,c^3\,d^{12}-3\,a^{15}\,c\,d^{14}-16\,a^{14}\,b\,c^8\,d^7+56\,a^{14}\,b\,c^6\,d^9-64\,a^{14}\,b\,c^4\,d^{11}+24\,a^{14}\,b\,c^2\,d^{13}+56\,a^{13}\,b^2\,c^9\,d^6-203\,a^{13}\,b^2\,c^7\,d^8+248\,a^{13}\,b^2\,c^5\,d^{10}-111\,a^{13}\,b^2\,c^3\,d^{12}+10\,a^{13}\,b^2\,c\,d^{14}-112\,a^{12}\,b^3\,c^{10}\,d^5+448\,a^{12}\,b^3\,c^8\,d^7-640\,a^{12}\,b^3\,c^6\,d^9+384\,a^{12}\,b^3\,c^4\,d^{11}-80\,a^{12}\,b^3\,c^2\,d^{13}+140\,a^{11}\,b^4\,c^{11}\,d^4-686\,a^{11}\,b^4\,c^9\,d^6+1240\,a^{11}\,b^4\,c^7\,d^8-993\,a^{11}\,b^4\,c^5\,d^{10}+310\,a^{11}\,b^4\,c^3\,d^{12}-11\,a^{11}\,b^4\,c\,d^{14}-112\,a^{10}\,b^5\,c^{12}\,d^3+784\,a^{10}\,b^5\,c^{10}\,d^5-1856\,a^{10}\,b^5\,c^8\,d^7+1896\,a^{10}\,b^5\,c^6\,d^9-800\,a^{10}\,b^5\,c^4\,d^{11}+88\,a^{10}\,b^5\,c^2\,d^{13}+56\,a^9\,b^6\,c^{13}\,d^2-686\,a^9\,b^6\,c^{11}\,d^4+2128\,a^9\,b^6\,c^9\,d^6-2733\,a^9\,b^6\,c^7\,d^8+1550\,a^9\,b^6\,c^5\,d^{10}-319\,a^9\,b^6\,c^3\,d^{12}+4\,a^9\,b^6\,c\,d^{14}-16\,a^8\,b^7\,c^{14}\,d+448\,a^8\,b^7\,c^{12}\,d^3-1856\,a^8\,b^7\,c^{10}\,d^5+3072\,a^8\,b^7\,c^8\,d^7-2320\,a^8\,b^7\,c^6\,d^9+704\,a^8\,b^7\,c^4\,d^{11}-32\,a^8\,b^7\,c^2\,d^{13}+2\,a^7\,b^8\,c^{15}-203\,a^7\,b^8\,c^{13}\,d^2+1240\,a^7\,b^8\,c^{11}\,d^4-2733\,a^7\,b^8\,c^9\,d^6+2660\,a^7\,b^8\,c^7\,d^8-1078\,a^7\,b^8\,c^5\,d^{10}+112\,a^7\,b^8\,c^3\,d^{12}+56\,a^6\,b^9\,c^{14}\,d-640\,a^6\,b^9\,c^{12}\,d^3+1896\,a^6\,b^9\,c^{10}\,d^5-2320\,a^6\,b^9\,c^8\,d^7+1232\,a^6\,b^9\,c^6\,d^9-224\,a^6\,b^9\,c^4\,d^{11}-7\,a^5\,b^{10}\,c^{15}+248\,a^5\,b^{10}\,c^{13}\,d^2-993\,a^5\,b^{10}\,c^{11}\,d^4+1550\,a^5\,b^{10}\,c^9\,d^6-1078\,a^5\,b^{10}\,c^7\,d^8+280\,a^5\,b^{10}\,c^5\,d^{10}-64\,a^4\,b^{11}\,c^{14}\,d+384\,a^4\,b^{11}\,c^{12}\,d^3-800\,a^4\,b^{11}\,c^{10}\,d^5+704\,a^4\,b^{11}\,c^8\,d^7-224\,a^4\,b^{11}\,c^6\,d^9+8\,a^3\,b^{12}\,c^{15}-111\,a^3\,b^{12}\,c^{13}\,d^2+310\,a^3\,b^{12}\,c^{11}\,d^4-319\,a^3\,b^{12}\,c^9\,d^6+112\,a^3\,b^{12}\,c^7\,d^8+24\,a^2\,b^{13}\,c^{14}\,d-80\,a^2\,b^{13}\,c^{12}\,d^3+88\,a^2\,b^{13}\,c^{10}\,d^5-32\,a^2\,b^{13}\,c^8\,d^7-3\,a\,b^{14}\,c^{15}+10\,a\,b^{14}\,c^{13}\,d^2-11\,a\,b^{14}\,c^{11}\,d^4+4\,a\,b^{14}\,c^9\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}\right)\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}\right)\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)\,1{}\mathrm{i}}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d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\,d^7-3\,a\,b^{14}\,c^{15}+10\,a\,b^{14}\,c^{13}\,d^2-11\,a\,b^{14}\,c^{11}\,d^4+4\,a\,b^{14}\,c^9\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}\right)\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}\right)\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)\,1{}\mathrm{i}}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}}{\frac{64\,\left(3\,a^7\,b^2\,c^3\,d^6-16\,a^6\,b^3\,c^4\,d^5+12\,a^6\,b^3\,c^2\,d^7+26\,a^5\,b^4\,c^5\,d^4-42\,a^5\,b^4\,c^3\,d^6+12\,a^5\,b^4\,c\,d^8-16\,a^4\,b^5\,c^6\,d^3+52\,a^4\,b^5\,c^4\,d^5-30\,a^4\,b^5\,c^2\,d^7+3\,a^3\,b^6\,c^7\,d^2-42\,a^3\,b^6\,c^5\,d^4+60\,a^3\,b^6\,c^3\,d^6-20\,a^3\,b^6\,c\,d^8+12\,a^2\,b^7\,c^6\,d^3-30\,a^2\,b^7\,c^4\,d^5+16\,a^2\,b^7\,c^2\,d^7+12\,a\,b^8\,c^5\,d^4-20\,a\,b^8\,c^3\,d^6+8\,a\,b^8\,c\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,a^6\,b^3\,c^3\,d^6-14\,a^5\,b^4\,c^4\,d^5+6\,a^5\,b^4\,c^2\,d^7-14\,a^4\,b^5\,c^5\,d^4+18\,a^4\,b^5\,c^3\,d^6-12\,a^4\,b^5\,c\,d^8+6\,a^3\,b^6\,c^6\,d^3+18\,a^3\,b^6\,c^4\,d^5-12\,a^3\,b^6\,c^2\,d^7+6\,a^2\,b^7\,c^5\,d^4-12\,a^2\,b^7\,c^3\,d^6+8\,a^2\,b^7\,c\,d^8-12\,a\,b^8\,c^4\,d^5+8\,a\,b^8\,c^2\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\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^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}-\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(-a^{13}\,c^5\,d^8+a^{13}\,c^3\,d^{10}+8\,a^{12}\,b\,c^6\,d^7-10\,a^{12}\,b\,c^4\,d^9+2\,a^{12}\,b\,c^2\,d^{11}-28\,a^{11}\,b^2\,c^7\,d^6+47\,a^{11}\,b^2\,c^5\,d^8-22\,a^{11}\,b^2\,c^3\,d^{10}+3\,a^{11}\,b^2\,c\,d^{12}+56\,a^{10}\,b^3\,c^8\,d^5-132\,a^{10}\,b^3\,c^6\,d^7+98\,a^{10}\,b^3\,c^4\,d^9-22\,a^{10}\,b^3\,c^2\,d^{11}-70\,a^9\,b^4\,c^9\,d^4+240\,a^9\,b^4\,c^7\,d^6-248\,a^9\,b^4\,c^5\,d^8+83\,a^9\,b^4\,c^3\,d^{10}-5\,a^9\,b^4\,c\,d^{12}+56\,a^8\,b^5\,c^{10}\,d^3-292\,a^8\,b^5\,c^8\,d^5+412\,a^8\,b^5\,c^6\,d^7-208\,a^8\,b^5\,c^4\,d^9+32\,a^8\,b^5\,c^2\,d^{11}-28\,a^7\,b^6\,c^{11}\,d^2+240\,a^7\,b^6\,c^9\,d^4-484\,a^7\,b^6\,c^7\,d^6+362\,a^7\,b^6\,c^5\,d^8-92\,a^7\,b^6\,c^3\,d^{10}+2\,a^7\,b^6\,c\,d^{12}+8\,a^6\,b^7\,c^{12}\,d-132\,a^6\,b^7\,c^{10}\,d^3+412\,a^6\,b^7\,c^8\,d^5-436\,a^6\,b^7\,c^6\,d^7+160\,a^6\,b^7\,c^4\,d^9-12\,a^6\,b^7\,c^2\,d^{11}-a^5\,b^8\,c^{13}+47\,a^5\,b^8\,c^{11}\,d^2-248\,a^5\,b^8\,c^9\,d^4+362\,a^5\,b^8\,c^7\,d^6-190\,a^5\,b^8\,c^5\,d^8+30\,a^5\,b^8\,c^3\,d^{10}-10\,a^4\,b^9\,c^{12}\,d+98\,a^4\,b^9\,c^{10}\,d^3-208\,a^4\,b^9\,c^8\,d^5+160\,a^4\,b^9\,c^6\,d^7-40\,a^4\,b^9\,c^4\,d^9+a^3\,b^{10}\,c^{13}-22\,a^3\,b^{10}\,c^{11}\,d^2+83\,a^3\,b^{10}\,c^9\,d^4-92\,a^3\,b^{10}\,c^7\,d^6+30\,a^3\,b^{10}\,c^5\,d^8+2\,a^2\,b^{11}\,c^{12}\,d-22\,a^2\,b^{11}\,c^{10}\,d^3+32\,a^2\,b^{11}\,c^8\,d^5-12\,a^2\,b^{11}\,c^6\,d^7+3\,a\,b^{12}\,c^{11}\,d^2-5\,a\,b^{12}\,c^9\,d^4+2\,a\,b^{12}\,c^7\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{13}\,c^4\,d^9-2\,a^{13}\,c^2\,d^{11}-16\,a^{12}\,b\,c^5\,d^8+20\,a^{12}\,b\,c^3\,d^{10}-4\,a^{12}\,b\,c\,d^{12}+50\,a^{11}\,b^2\,c^6\,d^7-76\,a^{11}\,b^2\,c^4\,d^9+26\,a^{11}\,b^2\,c^2\,d^{11}-74\,a^{10}\,b^3\,c^7\,d^6+150\,a^{10}\,b^3\,c^5\,d^8-82\,a^{10}\,b^3\,c^3\,d^{10}+6\,a^{10}\,b^3\,c\,d^{12}+38\,a^9\,b^4\,c^8\,d^5-164\,a^9\,b^4\,c^6\,d^7+160\,a^9\,b^4\,c^4\,d^9-34\,a^9\,b^4\,c^2\,d^{11}+38\,a^8\,b^5\,c^9\,d^4+72\,a^8\,b^5\,c^7\,d^6-188\,a^8\,b^5\,c^5\,d^8+80\,a^8\,b^5\,c^3\,d^{10}-2\,a^8\,b^5\,c\,d^{12}-74\,a^7\,b^6\,c^{10}\,d^3+72\,a^7\,b^6\,c^8\,d^5+88\,a^7\,b^6\,c^6\,d^7-96\,a^7\,b^6\,c^4\,d^9+10\,a^7\,b^6\,c^2\,d^{11}+50\,a^6\,b^7\,c^{11}\,d^2-164\,a^6\,b^7\,c^9\,d^4+88\,a^6\,b^7\,c^7\,d^6+44\,a^6\,b^7\,c^5\,d^8-18\,a^6\,b^7\,c^3\,d^{10}-16\,a^5\,b^8\,c^{12}\,d+150\,a^5\,b^8\,c^{10}\,d^3-188\,a^5\,b^8\,c^8\,d^5+44\,a^5\,b^8\,c^6\,d^7+10\,a^5\,b^8\,c^4\,d^9+2\,a^4\,b^9\,c^{13}-76\,a^4\,b^9\,c^{11}\,d^2+160\,a^4\,b^9\,c^9\,d^4-96\,a^4\,b^9\,c^7\,d^6+10\,a^4\,b^9\,c^5\,d^8+20\,a^3\,b^{10}\,c^{12}\,d-82\,a^3\,b^{10}\,c^{10}\,d^3+80\,a^3\,b^{10}\,c^8\,d^5-18\,a^3\,b^{10}\,c^6\,d^7-2\,a^2\,b^{11}\,c^{13}+26\,a^2\,b^{11}\,c^{11}\,d^2-34\,a^2\,b^{11}\,c^9\,d^4+10\,a^2\,b^{11}\,c^7\,d^6-4\,a\,b^{12}\,c^{12}\,d+6\,a\,b^{12}\,c^{10}\,d^3-2\,a\,b^{12}\,c^8\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{b^2\,\left(\frac{32\,\left(a^{15}\,c^6\,d^9-2\,a^{15}\,c^4\,d^{11}+a^{15}\,c^2\,d^{13}-7\,a^{14}\,b\,c^7\,d^8+13\,a^{14}\,b\,c^5\,d^{10}-5\,a^{14}\,b\,c^3\,d^{12}-a^{14}\,b\,c\,d^{14}+20\,a^{13}\,b^2\,c^8\,d^7-35\,a^{13}\,b^2\,c^6\,d^9+10\,a^{13}\,b^2\,c^4\,d^{11}+5\,a^{13}\,b^2\,c^2\,d^{13}-28\,a^{12}\,b^3\,c^9\,d^6+50\,a^{12}\,b^3\,c^7\,d^8-14\,a^{12}\,b^3\,c^5\,d^{10}-10\,a^{12}\,b^3\,c^3\,d^{12}+2\,a^{12}\,b^3\,c\,d^{14}+14\,a^{11}\,b^4\,c^{10}\,d^5-40\,a^{11}\,b^4\,c^8\,d^7+25\,a^{11}\,b^4\,c^6\,d^9+14\,a^{11}\,b^4\,c^4\,d^{11}-13\,a^{11}\,b^4\,c^2\,d^{13}+14\,a^{10}\,b^5\,c^{11}\,d^4+14\,a^{10}\,b^5\,c^9\,d^6-37\,a^{10}\,b^5\,c^7\,d^8-25\,a^{10}\,b^5\,c^5\,d^{10}+35\,a^{10}\,b^5\,c^3\,d^{12}-a^{10}\,b^5\,c\,d^{14}-28\,a^9\,b^6\,c^{12}\,d^3+14\,a^9\,b^6\,c^{10}\,d^5+20\,a^9\,b^6\,c^8\,d^7+37\,a^9\,b^6\,c^6\,d^9-50\,a^9\,b^6\,c^4\,d^{11}+7\,a^9\,b^6\,c^2\,d^{13}+20\,a^8\,b^7\,c^{13}\,d^2-40\,a^8\,b^7\,c^{11}\,d^4+20\,a^8\,b^7\,c^9\,d^6-20\,a^8\,b^7\,c^7\,d^8+40\,a^8\,b^7\,c^5\,d^{10}-20\,a^8\,b^7\,c^3\,d^{12}-7\,a^7\,b^8\,c^{14}\,d+50\,a^7\,b^8\,c^{12}\,d^3-37\,a^7\,b^8\,c^{10}\,d^5-20\,a^7\,b^8\,c^8\,d^7-14\,a^7\,b^8\,c^6\,d^9+28\,a^7\,b^8\,c^4\,d^{11}+a^6\,b^9\,c^{15}-35\,a^6\,b^9\,c^{13}\,d^2+25\,a^6\,b^9\,c^{11}\,d^4+37\,a^6\,b^9\,c^9\,d^6-14\,a^6\,b^9\,c^7\,d^8-14\,a^6\,b^9\,c^5\,d^{10}+13\,a^5\,b^{10}\,c^{14}\,d-14\,a^5\,b^{10}\,c^{12}\,d^3-25\,a^5\,b^{10}\,c^{10}\,d^5+40\,a^5\,b^{10}\,c^8\,d^7-14\,a^5\,b^{10}\,c^6\,d^9-2\,a^4\,b^{11}\,c^{15}+10\,a^4\,b^{11}\,c^{13}\,d^2+14\,a^4\,b^{11}\,c^{11}\,d^4-50\,a^4\,b^{11}\,c^9\,d^6+28\,a^4\,b^{11}\,c^7\,d^8-5\,a^3\,b^{12}\,c^{14}\,d-10\,a^3\,b^{12}\,c^{12}\,d^3+35\,a^3\,b^{12}\,c^{10}\,d^5-20\,a^3\,b^{12}\,c^8\,d^7+a^2\,b^{13}\,c^{15}+5\,a^2\,b^{13}\,c^{13}\,d^2-13\,a^2\,b^{13}\,c^{11}\,d^4+7\,a^2\,b^{13}\,c^9\,d^6-a\,b^{14}\,c^{14}\,d+2\,a\,b^{14}\,c^{12}\,d^3-a\,b^{14}\,c^{10}\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{15}\,c^7\,d^8-7\,a^{15}\,c^5\,d^{10}+8\,a^{15}\,c^3\,d^{12}-3\,a^{15}\,c\,d^{14}-16\,a^{14}\,b\,c^8\,d^7+56\,a^{14}\,b\,c^6\,d^9-64\,a^{14}\,b\,c^4\,d^{11}+24\,a^{14}\,b\,c^2\,d^{13}+56\,a^{13}\,b^2\,c^9\,d^6-203\,a^{13}\,b^2\,c^7\,d^8+248\,a^{13}\,b^2\,c^5\,d^{10}-111\,a^{13}\,b^2\,c^3\,d^{12}+10\,a^{13}\,b^2\,c\,d^{14}-112\,a^{12}\,b^3\,c^{10}\,d^5+448\,a^{12}\,b^3\,c^8\,d^7-640\,a^{12}\,b^3\,c^6\,d^9+384\,a^{12}\,b^3\,c^4\,d^{11}-80\,a^{12}\,b^3\,c^2\,d^{13}+140\,a^{11}\,b^4\,c^{11}\,d^4-686\,a^{11}\,b^4\,c^9\,d^6+1240\,a^{11}\,b^4\,c^7\,d^8-993\,a^{11}\,b^4\,c^5\,d^{10}+310\,a^{11}\,b^4\,c^3\,d^{12}-11\,a^{11}\,b^4\,c\,d^{14}-112\,a^{10}\,b^5\,c^{12}\,d^3+784\,a^{10}\,b^5\,c^{10}\,d^5-1856\,a^{10}\,b^5\,c^8\,d^7+1896\,a^{10}\,b^5\,c^6\,d^9-800\,a^{10}\,b^5\,c^4\,d^{11}+88\,a^{10}\,b^5\,c^2\,d^{13}+56\,a^9\,b^6\,c^{13}\,d^2-686\,a^9\,b^6\,c^{11}\,d^4+2128\,a^9\,b^6\,c^9\,d^6-2733\,a^9\,b^6\,c^7\,d^8+1550\,a^9\,b^6\,c^5\,d^{10}-319\,a^9\,b^6\,c^3\,d^{12}+4\,a^9\,b^6\,c\,d^{14}-16\,a^8\,b^7\,c^{14}\,d+448\,a^8\,b^7\,c^{12}\,d^3-1856\,a^8\,b^7\,c^{10}\,d^5+3072\,a^8\,b^7\,c^8\,d^7-2320\,a^8\,b^7\,c^6\,d^9+704\,a^8\,b^7\,c^4\,d^{11}-32\,a^8\,b^7\,c^2\,d^{13}+2\,a^7\,b^8\,c^{15}-203\,a^7\,b^8\,c^{13}\,d^2+1240\,a^7\,b^8\,c^{11}\,d^4-2733\,a^7\,b^8\,c^9\,d^6+2660\,a^7\,b^8\,c^7\,d^8-1078\,a^7\,b^8\,c^5\,d^{10}+112\,a^7\,b^8\,c^3\,d^{12}+56\,a^6\,b^9\,c^{14}\,d-640\,a^6\,b^9\,c^{12}\,d^3+1896\,a^6\,b^9\,c^{10}\,d^5-2320\,a^6\,b^9\,c^8\,d^7+1232\,a^6\,b^9\,c^6\,d^9-224\,a^6\,b^9\,c^4\,d^{11}-7\,a^5\,b^{10}\,c^{15}+248\,a^5\,b^{10}\,c^{13}\,d^2-993\,a^5\,b^{10}\,c^{11}\,d^4+1550\,a^5\,b^{10}\,c^9\,d^6-1078\,a^5\,b^{10}\,c^7\,d^8+280\,a^5\,b^{10}\,c^5\,d^{10}-64\,a^4\,b^{11}\,c^{14}\,d+384\,a^4\,b^{11}\,c^{12}\,d^3-800\,a^4\,b^{11}\,c^{10}\,d^5+704\,a^4\,b^{11}\,c^8\,d^7-224\,a^4\,b^{11}\,c^6\,d^9+8\,a^3\,b^{12}\,c^{15}-111\,a^3\,b^{12}\,c^{13}\,d^2+310\,a^3\,b^{12}\,c^{11}\,d^4-319\,a^3\,b^{12}\,c^9\,d^6+112\,a^3\,b^{12}\,c^7\,d^8+24\,a^2\,b^{13}\,c^{14}\,d-80\,a^2\,b^{13}\,c^{12}\,d^3+88\,a^2\,b^{13}\,c^{10}\,d^5-32\,a^2\,b^{13}\,c^8\,d^7-3\,a\,b^{14}\,c^{15}+10\,a\,b^{14}\,c^{13}\,d^2-11\,a\,b^{14}\,c^{11}\,d^4+4\,a\,b^{14}\,c^9\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}\right)\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}\right)\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)}{a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-3\,d\,a^2+c\,a\,b+2\,d\,b^2\right)\,2{}\mathrm{i}}{f\,\left(a^9\,d^3-3\,a^8\,b\,c\,d^2+3\,a^7\,b^2\,c^2\,d-3\,a^7\,b^2\,d^3-a^6\,b^3\,c^3+9\,a^6\,b^3\,c\,d^2-9\,a^5\,b^4\,c^2\,d+3\,a^5\,b^4\,d^3+3\,a^4\,b^5\,c^3-9\,a^4\,b^5\,c\,d^2+9\,a^3\,b^6\,c^2\,d-a^3\,b^6\,d^3-3\,a^2\,b^7\,c^3+3\,a^2\,b^7\,c\,d^2-3\,a\,b^8\,c^2\,d+b^9\,c^3\right)}-\frac{d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{13}\,c^4\,d^9-2\,a^{13}\,c^2\,d^{11}-16\,a^{12}\,b\,c^5\,d^8+20\,a^{12}\,b\,c^3\,d^{10}-4\,a^{12}\,b\,c\,d^{12}+50\,a^{11}\,b^2\,c^6\,d^7-76\,a^{11}\,b^2\,c^4\,d^9+26\,a^{11}\,b^2\,c^2\,d^{11}-74\,a^{10}\,b^3\,c^7\,d^6+150\,a^{10}\,b^3\,c^5\,d^8-82\,a^{10}\,b^3\,c^3\,d^{10}+6\,a^{10}\,b^3\,c\,d^{12}+38\,a^9\,b^4\,c^8\,d^5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\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)\,1{}\mathrm{i}}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}+\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^{13}\,c^5\,d^8+a^{13}\,c^3\,d^{10}+8\,a^{12}\,b\,c^6\,d^7-10\,a^{12}\,b\,c^4\,d^9+2\,a^{12}\,b\,c^2\,d^{11}-28\,a^{11}\,b^2\,c^7\,d^6+47\,a^{11}\,b^2\,c^5\,d^8-22\,a^{11}\,b^2\,c^3\,d^{10}+3\,a^{11}\,b^2\,c\,d^{12}+56\,a^{10}\,b^3\,c^8\,d^5-132\,a^{10}\,b^3\,c^6\,d^7+98\,a^{10}\,b^3\,c^4\,d^9-22\,a^{10}\,b^3\,c^2\,d^{11}-70\,a^9\,b^4\,c^9\,d^4+240\,a^9\,b^4\,c^7\,d^6-248\,a^9\,b^4\,c^5\,d^8+83\,a^9\,b^4\,c^3\,d^{10}-5\,a^9\,b^4\,c\,d^{12}+56\,a^8\,b^5\,c^{10}\,d^3-292\,a^8\,b^5\,c^8\,d^5+412\,a^8\,b^5\,c^6\,d^7-208\,a^8\,b^5\,c^4\,d^9+32\,a^8\,b^5\,c^2\,d^{11}-28\,a^7\,b^6\,c^{11}\,d^2+240\,a^7\,b^6\,c^9\,d^4-484\,a^7\,b^6\,c^7\,d^6+362\,a^7\,b^6\,c^5\,d^8-92\,a^7\,b^6\,c^3\,d^{10}+2\,a^7\,b^6\,c\,d^{12}+8\,a^6\,b^7\,c^{12}\,d-132\,a^6\,b^7\,c^{10}\,d^3+412\,a^6\,b^7\,c^8\,d^5-436\,a^6\,b^7\,c^6\,d^7+160\,a^6\,b^7\,c^4\,d^9-12\,a^6\,b^7\,c^2\,d^{11}-a^5\,b^8\,c^{13}+47\,a^5\,b^8\,c^{11}\,d^2-248\,a^5\,b^8\,c^9\,d^4+362\,a^5\,b^8\,c^7\,d^6-190\,a^5\,b^8\,c^5\,d^8+30\,a^5\,b^8\,c^3\,d^{10}-10\,a^4\,b^9\,c^{12}\,d+98\,a^4\,b^9\,c^{10}\,d^3-208\,a^4\,b^9\,c^8\,d^5+160\,a^4\,b^9\,c^6\,d^7-40\,a^4\,b^9\,c^4\,d^9+a^3\,b^{10}\,c^{13}-22\,a^3\,b^{10}\,c^{11}\,d^2+83\,a^3\,b^{10}\,c^9\,d^4-92\,a^3\,b^{10}\,c^7\,d^6+30\,a^3\,b^{10}\,c^5\,d^8+2\,a^2\,b^{11}\,c^{12}\,d-22\,a^2\,b^{11}\,c^{10}\,d^3+32\,a^2\,b^{11}\,c^8\,d^5-12\,a^2\,b^{11}\,c^6\,d^7+3\,a\,b^{12}\,c^{11}\,d^2-5\,a\,b^{12}\,c^9\,d^4+2\,a\,b^{12}\,c^7\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{13}\,c^4\,d^9-2\,a^{13}\,c^2\,d^{11}-16\,a^{12}\,b\,c^5\,d^8+20\,a^{12}\,b\,c^3\,d^{10}-4\,a^{12}\,b\,c\,d^{12}+50\,a^{11}\,b^2\,c^6\,d^7-76\,a^{11}\,b^2\,c^4\,d^9+26\,a^{11}\,b^2\,c^2\,d^{11}-74\,a^{10}\,b^3\,c^7\,d^6+150\,a^{10}\,b^3\,c^5\,d^8-82\,a^{10}\,b^3\,c^3\,d^{10}+6\,a^{10}\,b^3\,c\,d^{12}+38\,a^9\,b^4\,c^8\,d^5-164\,a^9\,b^4\,c^6\,d^7+160\,a^9\,b^4\,c^4\,d^9-34\,a^9\,b^4\,c^2\,d^{11}+38\,a^8\,b^5\,c^9\,d^4+72\,a^8\,b^5\,c^7\,d^6-188\,a^8\,b^5\,c^5\,d^8+80\,a^8\,b^5\,c^3\,d^{10}-2\,a^8\,b^5\,c\,d^{12}-74\,a^7\,b^6\,c^{10}\,d^3+72\,a^7\,b^6\,c^8\,d^5+88\,a^7\,b^6\,c^6\,d^7-96\,a^7\,b^6\,c^4\,d^9+10\,a^7\,b^6\,c^2\,d^{11}+50\,a^6\,b^7\,c^{11}\,d^2-164\,a^6\,b^7\,c^9\,d^4+88\,a^6\,b^7\,c^7\,d^6+44\,a^6\,b^7\,c^5\,d^8-18\,a^6\,b^7\,c^3\,d^{10}-16\,a^5\,b^8\,c^{12}\,d+150\,a^5\,b^8\,c^{10}\,d^3-188\,a^5\,b^8\,c^8\,d^5+44\,a^5\,b^8\,c^6\,d^7+10\,a^5\,b^8\,c^4\,d^9+2\,a^4\,b^9\,c^{13}-76\,a^4\,b^9\,c^{11}\,d^2+160\,a^4\,b^9\,c^9\,d^4-96\,a^4\,b^9\,c^7\,d^6+10\,a^4\,b^9\,c^5\,d^8+20\,a^3\,b^{10}\,c^{12}\,d-82\,a^3\,b^{10}\,c^{10}\,d^3+80\,a^3\,b^{10}\,c^8\,d^5-18\,a^3\,b^{10}\,c^6\,d^7-2\,a^2\,b^{11}\,c^{13}+26\,a^2\,b^{11}\,c^{11}\,d^2-34\,a^2\,b^{11}\,c^9\,d^4+10\,a^2\,b^{11}\,c^7\,d^6-4\,a\,b^{12}\,c^{12}\,d+6\,a\,b^{12}\,c^{10}\,d^3-2\,a\,b^{12}\,c^8\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\left(\frac{32\,\left(a^{15}\,c^6\,d^9-2\,a^{15}\,c^4\,d^{11}+a^{15}\,c^2\,d^{13}-7\,a^{14}\,b\,c^7\,d^8+13\,a^{14}\,b\,c^5\,d^{10}-5\,a^{14}\,b\,c^3\,d^{12}-a^{14}\,b\,c\,d^{14}+20\,a^{13}\,b^2\,c^8\,d^7-35\,a^{13}\,b^2\,c^6\,d^9+10\,a^{13}\,b^2\,c^4\,d^{11}+5\,a^{13}\,b^2\,c^2\,d^{13}-28\,a^{12}\,b^3\,c^9\,d^6+50\,a^{12}\,b^3\,c^7\,d^8-14\,a^{12}\,b^3\,c^5\,d^{10}-10\,a^{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b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)\,1{}\mathrm{i}}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}}{\frac{64\,\left(3\,a^7\,b^2\,c^3\,d^6-16\,a^6\,b^3\,c^4\,d^5+12\,a^6\,b^3\,c^2\,d^7+26\,a^5\,b^4\,c^5\,d^4-42\,a^5\,b^4\,c^3\,d^6+12\,a^5\,b^4\,c\,d^8-16\,a^4\,b^5\,c^6\,d^3+52\,a^4\,b^5\,c^4\,d^5-30\,a^4\,b^5\,c^2\,d^7+3\,a^3\,b^6\,c^7\,d^2-42\,a^3\,b^6\,c^5\,d^4+60\,a^3\,b^6\,c^3\,d^6-20\,a^3\,b^6\,c\,d^8+12\,a^2\,b^7\,c^6\,d^3-30\,a^2\,b^7\,c^4\,d^5+16\,a^2\,b^7\,c^2\,d^7+12\,a\,b^8\,c^5\,d^4-20\,a\,b^8\,c^3\,d^6+8\,a\,b^8\,c\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,a^6\,b^3\,c^3\,d^6-14\,a^5\,b^4\,c^4\,d^5+6\,a^5\,b^4\,c^2\,d^7-14\,a^4\,b^5\,c^5\,d^4+18\,a^4\,b^5\,c^3\,d^6-12\,a^4\,b^5\,c\,d^8+6\,a^3\,b^6\,c^6\,d^3+18\,a^3\,b^6\,c^4\,d^5-12\,a^3\,b^6\,c^2\,d^7+6\,a^2\,b^7\,c^5\,d^4-12\,a^2\,b^7\,c^3\,d^6+8\,a^2\,b^7\,c\,d^8-12\,a\,b^8\,c^4\,d^5+8\,a\,b^8\,c^2\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{13}\,c^4\,d^9-2\,a^{13}\,c^2\,d^{11}-16\,a^{12}\,b\,c^5\,d^8+20\,a^{12}\,b\,c^3\,d^{10}-4\,a^{12}\,b\,c\,d^{12}+50\,a^{11}\,b^2\,c^6\,d^7-76\,a^{11}\,b^2\,c^4\,d^9+26\,a^{11}\,b^2\,c^2\,d^{11}-74\,a^{10}\,b^3\,c^7\,d^6+150\,a^{10}\,b^3\,c^5\,d^8-82\,a^{10}\,b^3\,c^3\,d^{10}+6\,a^{10}\,b^3\,c\,d^{12}+38\,a^9\,b^4\,c^8\,d^5-164\,a^9\,b^4\,c^6\,d^7+160\,a^9\,b^4\,c^4\,d^9-34\,a^9\,b^4\,c^2\,d^{11}+38\,a^8\,b^5\,c^9\,d^4+72\,a^8\,b^5\,c^7\,d^6-188\,a^8\,b^5\,c^5\,d^8+80\,a^8\,b^5\,c^3\,d^{10}-2\,a^8\,b^5\,c\,d^{12}-74\,a^7\,b^6\,c^{10}\,d^3+72\,a^7\,b^6\,c^8\,d^5+88\,a^7\,b^6\,c^6\,d^7-96\,a^7\,b^6\,c^4\,d^9+10\,a^7\,b^6\,c^2\,d^{11}+50\,a^6\,b^7\,c^{11}\,d^2-164\,a^6\,b^7\,c^9\,d^4+88\,a^6\,b^7\,c^7\,d^6+44\,a^6\,b^7\,c^5\,d^8-18\,a^6\,b^7\,c^3\,d^{10}-16\,a^5\,b^8\,c^{12}\,d+150\,a^5\,b^8\,c^{10}\,d^3-188\,a^5\,b^8\,c^8\,d^5+44\,a^5\,b^8\,c^6\,d^7+10\,a^5\,b^8\,c^4\,d^9+2\,a^4\,b^9\,c^{13}-76\,a^4\,b^9\,c^{11}\,d^2+160\,a^4\,b^9\,c^9\,d^4-96\,a^4\,b^9\,c^7\,d^6+10\,a^4\,b^9\,c^5\,d^8+20\,a^3\,b^{10}\,c^{12}\,d-82\,a^3\,b^{10}\,c^{10}\,d^3+80\,a^3\,b^{10}\,c^8\,d^5-18\,a^3\,b^{10}\,c^6\,d^7-2\,a^2\,b^{11}\,c^{13}+26\,a^2\,b^{11}\,c^{11}\,d^2-34\,a^2\,b^{11}\,c^9\,d^4+10\,a^2\,b^{11}\,c^7\,d^6-4\,a\,b^{12}\,c^{12}\,d+6\,a\,b^{12}\,c^{10}\,d^3-2\,a\,b^{12}\,c^8\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-4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,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{15}\,c^7\,d^8-7\,a^{15}\,c^5\,d^{10}+8\,a^{15}\,c^3\,d^{12}-3\,a^{15}\,c\,d^{14}-16\,a^{14}\,b\,c^8\,d^7+56\,a^{14}\,b\,c^6\,d^9-64\,a^{14}\,b\,c^4\,d^{11}+24\,a^{14}\,b\,c^2\,d^{13}+56\,a^{13}\,b^2\,c^9\,d^6-203\,a^{13}\,b^2\,c^7\,d^8+248\,a^{13}\,b^2\,c^5\,d^{10}-111\,a^{13}\,b^2\,c^3\,d^{12}+10\,a^{13}\,b^2\,c\,d^{14}-112\,a^{12}\,b^3\,c^{10}\,d^5+448\,a^{12}\,b^3\,c^8\,d^7-640\,a^{12}\,b^3\,c^6\,d^9+384\,a^{12}\,b^3\,c^4\,d^{11}-80\,a^{12}\,b^3\,c^2\,d^{13}+140\,a^{11}\,b^4\,c^{11}\,d^4-686\,a^{11}\,b^4\,c^9\,d^6+1240\,a^{11}\,b^4\,c^7\,d^8-993\,a^{11}\,b^4\,c^5\,d^{10}+310\,a^{11}\,b^4\,c^3\,d^{12}-11\,a^{11}\,b^4\,c\,d^{14}-112\,a^{10}\,b^5\,c^{12}\,d^3+784\,a^{10}\,b^5\,c^{10}\,d^5-1856\,a^{10}\,b^5\,c^8\,d^7+1896\,a^{10}\,b^5\,c^6\,d^9-800\,a^{10}\,b^5\,c^4\,d^{11}+88\,a^{10}\,b^5\,c^2\,d^{13}+56\,a^9\,b^6\,c^{13}\,d^2-686\,a^9\,b^6\,c^{11}\,d^4+2128\,a^9\,b^6\,c^9\,d^6-2733\,a^9\,b^6\,c^7\,d^8+1550\,a^9\,b^6\,c^5\,d^{10}-319\,a^9\,b^6\,c^3\,d^{12}+4\,a^9\,b^6\,c\,d^{14}-16\,a^8\,b^7\,c^{14}\,d+448\,a^8\,b^7\,c^{12}\,d^3-1856\,a^8\,b^7\,c^{10}\,d^5+3072\,a^8\,b^7\,c^8\,d^7-2320\,a^8\,b^7\,c^6\,d^9+704\,a^8\,b^7\,c^4\,d^{11}-32\,a^8\,b^7\,c^2\,d^{13}+2\,a^7\,b^8\,c^{15}-203\,a^7\,b^8\,c^{13}\,d^2+1240\,a^7\,b^8\,c^{11}\,d^4-2733\,a^7\,b^8\,c^9\,d^6+2660\,a^7\,b^8\,c^7\,d^8-1078\,a^7\,b^8\,c^5\,d^{10}+112\,a^7\,b^8\,c^3\,d^{12}+56\,a^6\,b^9\,c^{14}\,d-640\,a^6\,b^9\,c^{12}\,d^3+1896\,a^6\,b^9\,c^{10}\,d^5-2320\,a^6\,b^9\,c^8\,d^7+1232\,a^6\,b^9\,c^6\,d^9-224\,a^6\,b^9\,c^4\,d^{11}-7\,a^5\,b^{10}\,c^{15}+248\,a^5\,b^{10}\,c^{13}\,d^2-993\,a^5\,b^{10}\,c^{11}\,d^4+1550\,a^5\,b^{10}\,c^9\,d^6-1078\,a^5\,b^{10}\,c^7\,d^8+280\,a^5\,b^{10}\,c^5\,d^{10}-64\,a^4\,b^{11}\,c^{14}\,d+384\,a^4\,b^{11}\,c^{12}\,d^3-800\,a^4\,b^{11}\,c^{10}\,d^5+704\,a^4\,b^{11}\,c^8\,d^7-224\,a^4\,b^{11}\,c^6\,d^9+8\,a^3\,b^{12}\,c^{15}-111\,a^3\,b^{12}\,c^{13}\,d^2+310\,a^3\,b^{12}\,c^{11}\,d^4-319\,a^3\,b^{12}\,c^9\,d^6+112\,a^3\,b^{12}\,c^7\,d^8+24\,a^2\,b^{13}\,c^{14}\,d-80\,a^2\,b^{13}\,c^{12}\,d^3+88\,a^2\,b^{13}\,c^{10}\,d^5-32\,a^2\,b^{13}\,c^8\,d^7-3\,a\,b^{14}\,c^{15}+10\,a\,b^{14}\,c^{13}\,d^2-11\,a\,b^{14}\,c^{11}\,d^4+4\,a\,b^{14}\,c^9\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}-\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(a^{10}\,b\,c^3\,d^8-8\,a^9\,b^2\,c^4\,d^7+4\,a^9\,b^2\,c^2\,d^9+22\,a^8\,b^3\,c^5\,d^6-22\,a^8\,b^3\,c^3\,d^8+4\,a^8\,b^3\,c\,d^{10}-15\,a^7\,b^4\,c^6\,d^5+26\,a^7\,b^4\,c^4\,d^7-7\,a^7\,b^4\,c^2\,d^9-15\,a^6\,b^5\,c^7\,d^4-8\,a^6\,b^5\,c^5\,d^6+21\,a^6\,b^5\,c^3\,d^8-8\,a^6\,b^5\,c\,d^{10}+22\,a^5\,b^6\,c^8\,d^3-8\,a^5\,b^6\,c^6\,d^5-18\,a^5\,b^6\,c^4\,d^7+8\,a^5\,b^6\,c^2\,d^9-8\,a^4\,b^7\,c^9\,d^2+26\,a^4\,b^7\,c^7\,d^4-18\,a^4\,b^7\,c^5\,d^6+4\,a^4\,b^7\,c\,d^{10}+a^3\,b^8\,c^{10}\,d-22\,a^3\,b^8\,c^8\,d^3+21\,a^3\,b^8\,c^6\,d^5-4\,a^3\,b^8\,c^2\,d^9+4\,a^2\,b^9\,c^9\,d^2-7\,a^2\,b^9\,c^7\,d^4+8\,a^2\,b^9\,c^5\,d^6-4\,a^2\,b^9\,c^3\,d^8+4\,a\,b^{10}\,c^8\,d^3-8\,a\,b^{10}\,c^6\,d^5+4\,a\,b^{10}\,c^4\,d^7\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^{11}\,c^3\,d^8-8\,a^{10}\,b\,c^4\,d^7+4\,a^{10}\,b\,c^2\,d^9+22\,a^9\,b^2\,c^5\,d^6-24\,a^9\,b^2\,c^3\,d^8+4\,a^9\,b^2\,c\,d^{10}-24\,a^8\,b^3\,c^6\,d^5+60\,a^8\,b^3\,c^4\,d^7-24\,a^8\,b^3\,c^2\,d^9+18\,a^7\,b^4\,c^7\,d^4-136\,a^7\,b^4\,c^5\,d^6+134\,a^7\,b^4\,c^3\,d^8-34\,a^7\,b^4\,c\,d^{10}-24\,a^6\,b^5\,c^8\,d^3+192\,a^6\,b^5\,c^6\,d^5-272\,a^6\,b^5\,c^4\,d^7+100\,a^6\,b^5\,c^2\,d^9+22\,a^5\,b^6\,c^9\,d^2-136\,a^5\,b^6\,c^7\,d^4+316\,a^5\,b^6\,c^5\,d^6-222\,a^5\,b^6\,c^3\,d^8+44\,a^5\,b^6\,c\,d^{10}-8\,a^4\,b^7\,c^{10}\,d+60\,a^4\,b^7\,c^8\,d^3-272\,a^4\,b^7\,c^6\,d^5+312\,a^4\,b^7\,c^4\,d^7-104\,a^4\,b^7\,c^2\,d^9+a^3\,b^8\,c^{11}-24\,a^3\,b^8\,c^9\,d^2+134\,a^3\,b^8\,c^7\,d^4-222\,a^3\,b^8\,c^5\,d^6+120\,a^3\,b^8\,c^3\,d^8-16\,a^3\,b^8\,c\,d^{10}+4\,a^2\,b^9\,c^{10}\,d-24\,a^2\,b^9\,c^8\,d^3+100\,a^2\,b^9\,c^6\,d^5-104\,a^2\,b^9\,c^4\,d^7+32\,a^2\,b^9\,c^2\,d^9+4\,a\,b^{10}\,c^9\,d^2-34\,a\,b^{10}\,c^7\,d^4+44\,a\,b^{10}\,c^5\,d^6-16\,a\,b^{10}\,c^3\,d^8\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(-a^{13}\,c^5\,d^8+a^{13}\,c^3\,d^{10}+8\,a^{12}\,b\,c^6\,d^7-10\,a^{12}\,b\,c^4\,d^9+2\,a^{12}\,b\,c^2\,d^{11}-28\,a^{11}\,b^2\,c^7\,d^6+47\,a^{11}\,b^2\,c^5\,d^8-22\,a^{11}\,b^2\,c^3\,d^{10}+3\,a^{11}\,b^2\,c\,d^{12}+56\,a^{10}\,b^3\,c^8\,d^5-132\,a^{10}\,b^3\,c^6\,d^7+98\,a^{10}\,b^3\,c^4\,d^9-22\,a^{10}\,b^3\,c^2\,d^{11}-70\,a^9\,b^4\,c^9\,d^4+240\,a^9\,b^4\,c^7\,d^6-248\,a^9\,b^4\,c^5\,d^8+83\,a^9\,b^4\,c^3\,d^{10}-5\,a^9\,b^4\,c\,d^{12}+56\,a^8\,b^5\,c^{10}\,d^3-292\,a^8\,b^5\,c^8\,d^5+412\,a^8\,b^5\,c^6\,d^7-208\,a^8\,b^5\,c^4\,d^9+32\,a^8\,b^5\,c^2\,d^{11}-28\,a^7\,b^6\,c^{11}\,d^2+240\,a^7\,b^6\,c^9\,d^4-484\,a^7\,b^6\,c^7\,d^6+362\,a^7\,b^6\,c^5\,d^8-92\,a^7\,b^6\,c^3\,d^{10}+2\,a^7\,b^6\,c\,d^{12}+8\,a^6\,b^7\,c^{12}\,d-132\,a^6\,b^7\,c^{10}\,d^3+412\,a^6\,b^7\,c^8\,d^5-436\,a^6\,b^7\,c^6\,d^7+160\,a^6\,b^7\,c^4\,d^9-12\,a^6\,b^7\,c^2\,d^{11}-a^5\,b^8\,c^{13}+47\,a^5\,b^8\,c^{11}\,d^2-248\,a^5\,b^8\,c^9\,d^4+362\,a^5\,b^8\,c^7\,d^6-190\,a^5\,b^8\,c^5\,d^8+30\,a^5\,b^8\,c^3\,d^{10}-10\,a^4\,b^9\,c^{12}\,d+98\,a^4\,b^9\,c^{10}\,d^3-208\,a^4\,b^9\,c^8\,d^5+160\,a^4\,b^9\,c^6\,d^7-40\,a^4\,b^9\,c^4\,d^9+a^3\,b^{10}\,c^{13}-22\,a^3\,b^{10}\,c^{11}\,d^2+83\,a^3\,b^{10}\,c^9\,d^4-92\,a^3\,b^{10}\,c^7\,d^6+30\,a^3\,b^{10}\,c^5\,d^8+2\,a^2\,b^{11}\,c^{12}\,d-22\,a^2\,b^{11}\,c^{10}\,d^3+32\,a^2\,b^{11}\,c^8\,d^5-12\,a^2\,b^{11}\,c^6\,d^7+3\,a\,b^{12}\,c^{11}\,d^2-5\,a\,b^{12}\,c^9\,d^4+2\,a\,b^{12}\,c^7\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{13}\,c^4\,d^9-2\,a^{13}\,c^2\,d^{11}-16\,a^{12}\,b\,c^5\,d^8+20\,a^{12}\,b\,c^3\,d^{10}-4\,a^{12}\,b\,c\,d^{12}+50\,a^{11}\,b^2\,c^6\,d^7-76\,a^{11}\,b^2\,c^4\,d^9+26\,a^{11}\,b^2\,c^2\,d^{11}-74\,a^{10}\,b^3\,c^7\,d^6+150\,a^{10}\,b^3\,c^5\,d^8-82\,a^{10}\,b^3\,c^3\,d^{10}+6\,a^{10}\,b^3\,c\,d^{12}+38\,a^9\,b^4\,c^8\,d^5-164\,a^9\,b^4\,c^6\,d^7+160\,a^9\,b^4\,c^4\,d^9-34\,a^9\,b^4\,c^2\,d^{11}+38\,a^8\,b^5\,c^9\,d^4+72\,a^8\,b^5\,c^7\,d^6-188\,a^8\,b^5\,c^5\,d^8+80\,a^8\,b^5\,c^3\,d^{10}-2\,a^8\,b^5\,c\,d^{12}-74\,a^7\,b^6\,c^{10}\,d^3+72\,a^7\,b^6\,c^8\,d^5+88\,a^7\,b^6\,c^6\,d^7-96\,a^7\,b^6\,c^4\,d^9+10\,a^7\,b^6\,c^2\,d^{11}+50\,a^6\,b^7\,c^{11}\,d^2-164\,a^6\,b^7\,c^9\,d^4+88\,a^6\,b^7\,c^7\,d^6+44\,a^6\,b^7\,c^5\,d^8-18\,a^6\,b^7\,c^3\,d^{10}-16\,a^5\,b^8\,c^{12}\,d+150\,a^5\,b^8\,c^{10}\,d^3-188\,a^5\,b^8\,c^8\,d^5+44\,a^5\,b^8\,c^6\,d^7+10\,a^5\,b^8\,c^4\,d^9+2\,a^4\,b^9\,c^{13}-76\,a^4\,b^9\,c^{11}\,d^2+160\,a^4\,b^9\,c^9\,d^4-96\,a^4\,b^9\,c^7\,d^6+10\,a^4\,b^9\,c^5\,d^8+20\,a^3\,b^{10}\,c^{12}\,d-82\,a^3\,b^{10}\,c^{10}\,d^3+80\,a^3\,b^{10}\,c^8\,d^5-18\,a^3\,b^{10}\,c^6\,d^7-2\,a^2\,b^{11}\,c^{13}+26\,a^2\,b^{11}\,c^{11}\,d^2-34\,a^2\,b^{11}\,c^9\,d^4+10\,a^2\,b^{11}\,c^7\,d^6-4\,a\,b^{12}\,c^{12}\,d+6\,a\,b^{12}\,c^{10}\,d^3-2\,a\,b^{12}\,c^8\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}+\frac{d^2\,\left(\frac{32\,\left(a^{15}\,c^6\,d^9-2\,a^{15}\,c^4\,d^{11}+a^{15}\,c^2\,d^{13}-7\,a^{14}\,b\,c^7\,d^8+13\,a^{14}\,b\,c^5\,d^{10}-5\,a^{14}\,b\,c^3\,d^{12}-a^{14}\,b\,c\,d^{14}+20\,a^{13}\,b^2\,c^8\,d^7-35\,a^{13}\,b^2\,c^6\,d^9+10\,a^{13}\,b^2\,c^4\,d^{11}+5\,a^{13}\,b^2\,c^2\,d^{13}-28\,a^{12}\,b^3\,c^9\,d^6+50\,a^{12}\,b^3\,c^7\,d^8-14\,a^{12}\,b^3\,c^5\,d^{10}-10\,a^{12}\,b^3\,c^3\,d^{12}+2\,a^{12}\,b^3\,c\,d^{14}+14\,a^{11}\,b^4\,c^{10}\,d^5-40\,a^{11}\,b^4\,c^8\,d^7+25\,a^{11}\,b^4\,c^6\,d^9+14\,a^{11}\,b^4\,c^4\,d^{11}-13\,a^{11}\,b^4\,c^2\,d^{13}+14\,a^{10}\,b^5\,c^{11}\,d^4+14\,a^{10}\,b^5\,c^9\,d^6-37\,a^{10}\,b^5\,c^7\,d^8-25\,a^{10}\,b^5\,c^5\,d^{10}+35\,a^{10}\,b^5\,c^3\,d^{12}-a^{10}\,b^5\,c\,d^{14}-28\,a^9\,b^6\,c^{12}\,d^3+14\,a^9\,b^6\,c^{10}\,d^5+20\,a^9\,b^6\,c^8\,d^7+37\,a^9\,b^6\,c^6\,d^9-50\,a^9\,b^6\,c^4\,d^{11}+7\,a^9\,b^6\,c^2\,d^{13}+20\,a^8\,b^7\,c^{13}\,d^2-40\,a^8\,b^7\,c^{11}\,d^4+20\,a^8\,b^7\,c^9\,d^6-20\,a^8\,b^7\,c^7\,d^8+40\,a^8\,b^7\,c^5\,d^{10}-20\,a^8\,b^7\,c^3\,d^{12}-7\,a^7\,b^8\,c^{14}\,d+50\,a^7\,b^8\,c^{12}\,d^3-37\,a^7\,b^8\,c^{10}\,d^5-20\,a^7\,b^8\,c^8\,d^7-14\,a^7\,b^8\,c^6\,d^9+28\,a^7\,b^8\,c^4\,d^{11}+a^6\,b^9\,c^{15}-35\,a^6\,b^9\,c^{13}\,d^2+25\,a^6\,b^9\,c^{11}\,d^4+37\,a^6\,b^9\,c^9\,d^6-14\,a^6\,b^9\,c^7\,d^8-14\,a^6\,b^9\,c^5\,d^{10}+13\,a^5\,b^{10}\,c^{14}\,d-14\,a^5\,b^{10}\,c^{12}\,d^3-25\,a^5\,b^{10}\,c^{10}\,d^5+40\,a^5\,b^{10}\,c^8\,d^7-14\,a^5\,b^{10}\,c^6\,d^9-2\,a^4\,b^{11}\,c^{15}+10\,a^4\,b^{11}\,c^{13}\,d^2+14\,a^4\,b^{11}\,c^{11}\,d^4-50\,a^4\,b^{11}\,c^9\,d^6+28\,a^4\,b^{11}\,c^7\,d^8-5\,a^3\,b^{12}\,c^{14}\,d-10\,a^3\,b^{12}\,c^{12}\,d^3+35\,a^3\,b^{12}\,c^{10}\,d^5-20\,a^3\,b^{12}\,c^8\,d^7+a^2\,b^{13}\,c^{15}+5\,a^2\,b^{13}\,c^{13}\,d^2-13\,a^2\,b^{13}\,c^{11}\,d^4+7\,a^2\,b^{13}\,c^9\,d^6-a\,b^{14}\,c^{14}\,d+2\,a\,b^{14}\,c^{12}\,d^3-a\,b^{14}\,c^{10}\,d^5\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^{15}\,c^7\,d^8-7\,a^{15}\,c^5\,d^{10}+8\,a^{15}\,c^3\,d^{12}-3\,a^{15}\,c\,d^{14}-16\,a^{14}\,b\,c^8\,d^7+56\,a^{14}\,b\,c^6\,d^9-64\,a^{14}\,b\,c^4\,d^{11}+24\,a^{14}\,b\,c^2\,d^{13}+56\,a^{13}\,b^2\,c^9\,d^6-203\,a^{13}\,b^2\,c^7\,d^8+248\,a^{13}\,b^2\,c^5\,d^{10}-111\,a^{13}\,b^2\,c^3\,d^{12}+10\,a^{13}\,b^2\,c\,d^{14}-112\,a^{12}\,b^3\,c^{10}\,d^5+448\,a^{12}\,b^3\,c^8\,d^7-640\,a^{12}\,b^3\,c^6\,d^9+384\,a^{12}\,b^3\,c^4\,d^{11}-80\,a^{12}\,b^3\,c^2\,d^{13}+140\,a^{11}\,b^4\,c^{11}\,d^4-686\,a^{11}\,b^4\,c^9\,d^6+1240\,a^{11}\,b^4\,c^7\,d^8-993\,a^{11}\,b^4\,c^5\,d^{10}+310\,a^{11}\,b^4\,c^3\,d^{12}-11\,a^{11}\,b^4\,c\,d^{14}-112\,a^{10}\,b^5\,c^{12}\,d^3+784\,a^{10}\,b^5\,c^{10}\,d^5-1856\,a^{10}\,b^5\,c^8\,d^7+1896\,a^{10}\,b^5\,c^6\,d^9-800\,a^{10}\,b^5\,c^4\,d^{11}+88\,a^{10}\,b^5\,c^2\,d^{13}+56\,a^9\,b^6\,c^{13}\,d^2-686\,a^9\,b^6\,c^{11}\,d^4+2128\,a^9\,b^6\,c^9\,d^6-2733\,a^9\,b^6\,c^7\,d^8+1550\,a^9\,b^6\,c^5\,d^{10}-319\,a^9\,b^6\,c^3\,d^{12}+4\,a^9\,b^6\,c\,d^{14}-16\,a^8\,b^7\,c^{14}\,d+448\,a^8\,b^7\,c^{12}\,d^3-1856\,a^8\,b^7\,c^{10}\,d^5+3072\,a^8\,b^7\,c^8\,d^7-2320\,a^8\,b^7\,c^6\,d^9+704\,a^8\,b^7\,c^4\,d^{11}-32\,a^8\,b^7\,c^2\,d^{13}+2\,a^7\,b^8\,c^{15}-203\,a^7\,b^8\,c^{13}\,d^2+1240\,a^7\,b^8\,c^{11}\,d^4-2733\,a^7\,b^8\,c^9\,d^6+2660\,a^7\,b^8\,c^7\,d^8-1078\,a^7\,b^8\,c^5\,d^{10}+112\,a^7\,b^8\,c^3\,d^{12}+56\,a^6\,b^9\,c^{14}\,d-640\,a^6\,b^9\,c^{12}\,d^3+1896\,a^6\,b^9\,c^{10}\,d^5-2320\,a^6\,b^9\,c^8\,d^7+1232\,a^6\,b^9\,c^6\,d^9-224\,a^6\,b^9\,c^4\,d^{11}-7\,a^5\,b^{10}\,c^{15}+248\,a^5\,b^{10}\,c^{13}\,d^2-993\,a^5\,b^{10}\,c^{11}\,d^4+1550\,a^5\,b^{10}\,c^9\,d^6-1078\,a^5\,b^{10}\,c^7\,d^8+280\,a^5\,b^{10}\,c^5\,d^{10}-64\,a^4\,b^{11}\,c^{14}\,d+384\,a^4\,b^{11}\,c^{12}\,d^3-800\,a^4\,b^{11}\,c^{10}\,d^5+704\,a^4\,b^{11}\,c^8\,d^7-224\,a^4\,b^{11}\,c^6\,d^9+8\,a^3\,b^{12}\,c^{15}-111\,a^3\,b^{12}\,c^{13}\,d^2+310\,a^3\,b^{12}\,c^{11}\,d^4-319\,a^3\,b^{12}\,c^9\,d^6+112\,a^3\,b^{12}\,c^7\,d^8+24\,a^2\,b^{13}\,c^{14}\,d-80\,a^2\,b^{13}\,c^{12}\,d^3+88\,a^2\,b^{13}\,c^{10}\,d^5-32\,a^2\,b^{13}\,c^8\,d^7-3\,a\,b^{14}\,c^{15}+10\,a\,b^{14}\,c^{13}\,d^2-11\,a\,b^{14}\,c^{11}\,d^4+4\,a\,b^{14}\,c^9\,d^6\right)}{a^{10}\,c^4\,d^6-2\,a^{10}\,c^2\,d^8+a^{10}\,d^{10}-6\,a^9\,b\,c^5\,d^5+12\,a^9\,b\,c^3\,d^7-6\,a^9\,b\,c\,d^9+15\,a^8\,b^2\,c^6\,d^4-32\,a^8\,b^2\,c^4\,d^6+19\,a^8\,b^2\,c^2\,d^8-2\,a^8\,b^2\,d^{10}-20\,a^7\,b^3\,c^7\,d^3+52\,a^7\,b^3\,c^5\,d^5-44\,a^7\,b^3\,c^3\,d^7+12\,a^7\,b^3\,c\,d^9+15\,a^6\,b^4\,c^8\,d^2-60\,a^6\,b^4\,c^6\,d^4+76\,a^6\,b^4\,c^4\,d^6-32\,a^6\,b^4\,c^2\,d^8+a^6\,b^4\,d^{10}-6\,a^5\,b^5\,c^9\,d+52\,a^5\,b^5\,c^7\,d^3-92\,a^5\,b^5\,c^5\,d^5+52\,a^5\,b^5\,c^3\,d^7-6\,a^5\,b^5\,c\,d^9+a^4\,b^6\,c^{10}-32\,a^4\,b^6\,c^8\,d^2+76\,a^4\,b^6\,c^6\,d^4-60\,a^4\,b^6\,c^4\,d^6+15\,a^4\,b^6\,c^2\,d^8+12\,a^3\,b^7\,c^9\,d-44\,a^3\,b^7\,c^7\,d^3+52\,a^3\,b^7\,c^5\,d^5-20\,a^3\,b^7\,c^3\,d^7-2\,a^2\,b^8\,c^{10}+19\,a^2\,b^8\,c^8\,d^2-32\,a^2\,b^8\,c^6\,d^4+15\,a^2\,b^8\,c^4\,d^6-6\,a\,b^9\,c^9\,d+12\,a\,b^9\,c^7\,d^3-6\,a\,b^9\,c^5\,d^5+b^{10}\,c^{10}-2\,b^{10}\,c^8\,d^2+b^{10}\,c^6\,d^4}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}\right)\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)}{-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-3\,b\,c^2+a\,c\,d+2\,b\,d^2\right)\,2{}\mathrm{i}}{f\,\left(-a^3\,c^6\,d^3+3\,a^3\,c^4\,d^5-3\,a^3\,c^2\,d^7+a^3\,d^9+3\,a^2\,b\,c^7\,d^2-9\,a^2\,b\,c^5\,d^4+9\,a^2\,b\,c^3\,d^6-3\,a^2\,b\,c\,d^8-3\,a\,b^2\,c^8\,d+9\,a\,b^2\,c^6\,d^3-9\,a\,b^2\,c^4\,d^5+3\,a\,b^2\,c^2\,d^7+b^3\,c^9-3\,b^3\,c^7\,d^2+3\,b^3\,c^5\,d^4-b^3\,c^3\,d^6\right)}","Not used",1,"((2*(a^3*d^3 + b^3*c^3 - a*b^2*d^3 - b^3*c*d^2))/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c^2 - a^2*d^2 - b^2*c^2 + b^2*d^2)) + (2*tan(e/2 + (f*x)/2)^3*(a^4*d^4 + b^4*c^4 - a^2*b^2*d^4 - b^4*c^2*d^2))/(a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c^2 - a^2*d^2 - b^2*c^2 + b^2*d^2)) + (2*tan(e/2 + (f*x)/2)*(a^4*d^4 + b^4*c^4 - a^2*b^2*d^4 - b^4*c^2*d^2 - 4*a*b^3*c*d^3 + 2*a*b^3*c^3*d + 2*a^3*b*c*d^3))/(a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c^2 - a^2*d^2 - b^2*c^2 + b^2*d^2)) + (2*tan(e/2 + (f*x)/2)^2*(a*c + 2*b*d)*(a^3*d^3 + b^3*c^3 - a*b^2*d^3 - b^3*c*d^2))/(a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c^2 - a^2*d^2 - b^2*c^2 + b^2*d^2)))/(f*(a*c + tan(e/2 + (f*x)/2)^3*(2*a*d + 2*b*c) + tan(e/2 + (f*x)/2)^2*(2*a*c + 4*b*d) + tan(e/2 + (f*x)/2)*(2*a*d + 2*b*c) + a*c*tan(e/2 + (f*x)/2)^4)) - (b^2*atan(((b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c)*1i)/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c)*1i)/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))/((64*(12*a*b^8*c^5*d^4 - 20*a*b^8*c^3*d^6 - 20*a^3*b^6*c*d^8 + 12*a^5*b^4*c*d^8 + 16*a^2*b^7*c^2*d^7 - 30*a^2*b^7*c^4*d^5 + 12*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^3*d^6 - 42*a^3*b^6*c^5*d^4 + 3*a^3*b^6*c^7*d^2 - 30*a^4*b^5*c^2*d^7 + 52*a^4*b^5*c^4*d^5 - 16*a^4*b^5*c^6*d^3 - 42*a^5*b^4*c^3*d^6 + 26*a^5*b^4*c^5*d^4 + 12*a^6*b^3*c^2*d^7 - 16*a^6*b^3*c^4*d^5 + 3*a^7*b^2*c^3*d^6 + 8*a*b^8*c*d^8))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (64*tan(e/2 + (f*x)/2)*(8*a*b^8*c^2*d^7 - 12*a*b^8*c^4*d^5 + 8*a^2*b^7*c*d^8 - 12*a^4*b^5*c*d^8 - 12*a^2*b^7*c^3*d^6 + 6*a^2*b^7*c^5*d^4 - 12*a^3*b^6*c^2*d^7 + 18*a^3*b^6*c^4*d^5 + 6*a^3*b^6*c^6*d^3 + 18*a^4*b^5*c^3*d^6 - 14*a^4*b^5*c^5*d^4 + 6*a^5*b^4*c^2*d^7 - 14*a^5*b^4*c^4*d^5 + 6*a^6*b^3*c^3*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2) - (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (b^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2))*(2*b^2*d - 3*a^2*d + a*b*c))/(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*b^2*d - 3*a^2*d + a*b*c)*2i)/(f*(a^9*d^3 + b^9*c^3 - 3*a^2*b^7*c^3 + 3*a^4*b^5*c^3 - a^6*b^3*c^3 - a^3*b^6*d^3 + 3*a^5*b^4*d^3 - 3*a^7*b^2*d^3 + 3*a^2*b^7*c*d^2 + 9*a^3*b^6*c^2*d - 9*a^4*b^5*c*d^2 - 9*a^5*b^4*c^2*d + 9*a^6*b^3*c*d^2 + 3*a^7*b^2*c^2*d - 3*a*b^8*c^2*d - 3*a^8*b*c*d^2)) - (d^2*atan(((d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d)*1i)/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8) + (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d)*1i)/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))/((64*(12*a*b^8*c^5*d^4 - 20*a*b^8*c^3*d^6 - 20*a^3*b^6*c*d^8 + 12*a^5*b^4*c*d^8 + 16*a^2*b^7*c^2*d^7 - 30*a^2*b^7*c^4*d^5 + 12*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^3*d^6 - 42*a^3*b^6*c^5*d^4 + 3*a^3*b^6*c^7*d^2 - 30*a^4*b^5*c^2*d^7 + 52*a^4*b^5*c^4*d^5 - 16*a^4*b^5*c^6*d^3 - 42*a^5*b^4*c^3*d^6 + 26*a^5*b^4*c^5*d^4 + 12*a^6*b^3*c^2*d^7 - 16*a^6*b^3*c^4*d^5 + 3*a^7*b^2*c^3*d^6 + 8*a*b^8*c*d^8))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (64*tan(e/2 + (f*x)/2)*(8*a*b^8*c^2*d^7 - 12*a*b^8*c^4*d^5 + 8*a^2*b^7*c*d^8 - 12*a^4*b^5*c*d^8 - 12*a^2*b^7*c^3*d^6 + 6*a^2*b^7*c^5*d^4 - 12*a^3*b^6*c^2*d^7 + 18*a^3*b^6*c^4*d^5 + 6*a^3*b^6*c^6*d^3 + 18*a^4*b^5*c^3*d^6 - 14*a^4*b^5*c^5*d^4 + 6*a^5*b^4*c^2*d^7 - 14*a^5*b^4*c^4*d^5 + 6*a^6*b^3*c^3*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8) - (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(4*a*b^10*c^4*d^7 - 8*a*b^10*c^6*d^5 + 4*a*b^10*c^8*d^3 + a^3*b^8*c^10*d + 4*a^4*b^7*c*d^10 - 8*a^6*b^5*c*d^10 + 4*a^8*b^3*c*d^10 + a^10*b*c^3*d^8 - 4*a^2*b^9*c^3*d^8 + 8*a^2*b^9*c^5*d^6 - 7*a^2*b^9*c^7*d^4 + 4*a^2*b^9*c^9*d^2 - 4*a^3*b^8*c^2*d^9 + 21*a^3*b^8*c^6*d^5 - 22*a^3*b^8*c^8*d^3 - 18*a^4*b^7*c^5*d^6 + 26*a^4*b^7*c^7*d^4 - 8*a^4*b^7*c^9*d^2 + 8*a^5*b^6*c^2*d^9 - 18*a^5*b^6*c^4*d^7 - 8*a^5*b^6*c^6*d^5 + 22*a^5*b^6*c^8*d^3 + 21*a^6*b^5*c^3*d^8 - 8*a^6*b^5*c^5*d^6 - 15*a^6*b^5*c^7*d^4 - 7*a^7*b^4*c^2*d^9 + 26*a^7*b^4*c^4*d^7 - 15*a^7*b^4*c^6*d^5 - 22*a^8*b^3*c^3*d^8 + 22*a^8*b^3*c^5*d^6 + 4*a^9*b^2*c^2*d^9 - 8*a^9*b^2*c^4*d^7))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(a^3*b^8*c^11 + a^11*c^3*d^8 - 16*a*b^10*c^3*d^8 + 44*a*b^10*c^5*d^6 - 34*a*b^10*c^7*d^4 + 4*a*b^10*c^9*d^2 + 4*a^2*b^9*c^10*d - 16*a^3*b^8*c*d^10 - 8*a^4*b^7*c^10*d + 44*a^5*b^6*c*d^10 - 34*a^7*b^4*c*d^10 + 4*a^9*b^2*c*d^10 + 4*a^10*b*c^2*d^9 - 8*a^10*b*c^4*d^7 + 32*a^2*b^9*c^2*d^9 - 104*a^2*b^9*c^4*d^7 + 100*a^2*b^9*c^6*d^5 - 24*a^2*b^9*c^8*d^3 + 120*a^3*b^8*c^3*d^8 - 222*a^3*b^8*c^5*d^6 + 134*a^3*b^8*c^7*d^4 - 24*a^3*b^8*c^9*d^2 - 104*a^4*b^7*c^2*d^9 + 312*a^4*b^7*c^4*d^7 - 272*a^4*b^7*c^6*d^5 + 60*a^4*b^7*c^8*d^3 - 222*a^5*b^6*c^3*d^8 + 316*a^5*b^6*c^5*d^6 - 136*a^5*b^6*c^7*d^4 + 22*a^5*b^6*c^9*d^2 + 100*a^6*b^5*c^2*d^9 - 272*a^6*b^5*c^4*d^7 + 192*a^6*b^5*c^6*d^5 - 24*a^6*b^5*c^8*d^3 + 134*a^7*b^4*c^3*d^8 - 136*a^7*b^4*c^5*d^6 + 18*a^7*b^4*c^7*d^4 - 24*a^8*b^3*c^2*d^9 + 60*a^8*b^3*c^4*d^7 - 24*a^8*b^3*c^6*d^5 - 24*a^9*b^2*c^3*d^8 + 22*a^9*b^2*c^5*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(a^3*b^10*c^13 - a^5*b^8*c^13 + a^13*c^3*d^10 - a^13*c^5*d^8 + 2*a*b^12*c^7*d^6 - 5*a*b^12*c^9*d^4 + 3*a*b^12*c^11*d^2 + 2*a^2*b^11*c^12*d - 10*a^4*b^9*c^12*d + 8*a^6*b^7*c^12*d + 2*a^7*b^6*c*d^12 - 5*a^9*b^4*c*d^12 + 3*a^11*b^2*c*d^12 + 2*a^12*b*c^2*d^11 - 10*a^12*b*c^4*d^9 + 8*a^12*b*c^6*d^7 - 12*a^2*b^11*c^6*d^7 + 32*a^2*b^11*c^8*d^5 - 22*a^2*b^11*c^10*d^3 + 30*a^3*b^10*c^5*d^8 - 92*a^3*b^10*c^7*d^6 + 83*a^3*b^10*c^9*d^4 - 22*a^3*b^10*c^11*d^2 - 40*a^4*b^9*c^4*d^9 + 160*a^4*b^9*c^6*d^7 - 208*a^4*b^9*c^8*d^5 + 98*a^4*b^9*c^10*d^3 + 30*a^5*b^8*c^3*d^10 - 190*a^5*b^8*c^5*d^8 + 362*a^5*b^8*c^7*d^6 - 248*a^5*b^8*c^9*d^4 + 47*a^5*b^8*c^11*d^2 - 12*a^6*b^7*c^2*d^11 + 160*a^6*b^7*c^4*d^9 - 436*a^6*b^7*c^6*d^7 + 412*a^6*b^7*c^8*d^5 - 132*a^6*b^7*c^10*d^3 - 92*a^7*b^6*c^3*d^10 + 362*a^7*b^6*c^5*d^8 - 484*a^7*b^6*c^7*d^6 + 240*a^7*b^6*c^9*d^4 - 28*a^7*b^6*c^11*d^2 + 32*a^8*b^5*c^2*d^11 - 208*a^8*b^5*c^4*d^9 + 412*a^8*b^5*c^6*d^7 - 292*a^8*b^5*c^8*d^5 + 56*a^8*b^5*c^10*d^3 + 83*a^9*b^4*c^3*d^10 - 248*a^9*b^4*c^5*d^8 + 240*a^9*b^4*c^7*d^6 - 70*a^9*b^4*c^9*d^4 - 22*a^10*b^3*c^2*d^11 + 98*a^10*b^3*c^4*d^9 - 132*a^10*b^3*c^6*d^7 + 56*a^10*b^3*c^8*d^5 - 22*a^11*b^2*c^3*d^10 + 47*a^11*b^2*c^5*d^8 - 28*a^11*b^2*c^7*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(2*a^4*b^9*c^13 - 2*a^2*b^11*c^13 - 2*a^13*c^2*d^11 + 2*a^13*c^4*d^9 - 2*a*b^12*c^8*d^5 + 6*a*b^12*c^10*d^3 + 20*a^3*b^10*c^12*d - 16*a^5*b^8*c^12*d - 2*a^8*b^5*c*d^12 + 6*a^10*b^3*c*d^12 + 20*a^12*b*c^3*d^10 - 16*a^12*b*c^5*d^8 + 10*a^2*b^11*c^7*d^6 - 34*a^2*b^11*c^9*d^4 + 26*a^2*b^11*c^11*d^2 - 18*a^3*b^10*c^6*d^7 + 80*a^3*b^10*c^8*d^5 - 82*a^3*b^10*c^10*d^3 + 10*a^4*b^9*c^5*d^8 - 96*a^4*b^9*c^7*d^6 + 160*a^4*b^9*c^9*d^4 - 76*a^4*b^9*c^11*d^2 + 10*a^5*b^8*c^4*d^9 + 44*a^5*b^8*c^6*d^7 - 188*a^5*b^8*c^8*d^5 + 150*a^5*b^8*c^10*d^3 - 18*a^6*b^7*c^3*d^10 + 44*a^6*b^7*c^5*d^8 + 88*a^6*b^7*c^7*d^6 - 164*a^6*b^7*c^9*d^4 + 50*a^6*b^7*c^11*d^2 + 10*a^7*b^6*c^2*d^11 - 96*a^7*b^6*c^4*d^9 + 88*a^7*b^6*c^6*d^7 + 72*a^7*b^6*c^8*d^5 - 74*a^7*b^6*c^10*d^3 + 80*a^8*b^5*c^3*d^10 - 188*a^8*b^5*c^5*d^8 + 72*a^8*b^5*c^7*d^6 + 38*a^8*b^5*c^9*d^4 - 34*a^9*b^4*c^2*d^11 + 160*a^9*b^4*c^4*d^9 - 164*a^9*b^4*c^6*d^7 + 38*a^9*b^4*c^8*d^5 - 82*a^10*b^3*c^3*d^10 + 150*a^10*b^3*c^5*d^8 - 74*a^10*b^3*c^7*d^6 + 26*a^11*b^2*c^2*d^11 - 76*a^11*b^2*c^4*d^9 + 50*a^11*b^2*c^6*d^7 - 4*a*b^12*c^12*d - 4*a^12*b*c*d^12))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) + (d^2*((32*(a^2*b^13*c^15 - 2*a^4*b^11*c^15 + a^6*b^9*c^15 + a^15*c^2*d^13 - 2*a^15*c^4*d^11 + a^15*c^6*d^9 - a*b^14*c^10*d^5 + 2*a*b^14*c^12*d^3 - 5*a^3*b^12*c^14*d + 13*a^5*b^10*c^14*d - 7*a^7*b^8*c^14*d - a^10*b^5*c*d^14 + 2*a^12*b^3*c*d^14 - 5*a^14*b*c^3*d^12 + 13*a^14*b*c^5*d^10 - 7*a^14*b*c^7*d^8 + 7*a^2*b^13*c^9*d^6 - 13*a^2*b^13*c^11*d^4 + 5*a^2*b^13*c^13*d^2 - 20*a^3*b^12*c^8*d^7 + 35*a^3*b^12*c^10*d^5 - 10*a^3*b^12*c^12*d^3 + 28*a^4*b^11*c^7*d^8 - 50*a^4*b^11*c^9*d^6 + 14*a^4*b^11*c^11*d^4 + 10*a^4*b^11*c^13*d^2 - 14*a^5*b^10*c^6*d^9 + 40*a^5*b^10*c^8*d^7 - 25*a^5*b^10*c^10*d^5 - 14*a^5*b^10*c^12*d^3 - 14*a^6*b^9*c^5*d^10 - 14*a^6*b^9*c^7*d^8 + 37*a^6*b^9*c^9*d^6 + 25*a^6*b^9*c^11*d^4 - 35*a^6*b^9*c^13*d^2 + 28*a^7*b^8*c^4*d^11 - 14*a^7*b^8*c^6*d^9 - 20*a^7*b^8*c^8*d^7 - 37*a^7*b^8*c^10*d^5 + 50*a^7*b^8*c^12*d^3 - 20*a^8*b^7*c^3*d^12 + 40*a^8*b^7*c^5*d^10 - 20*a^8*b^7*c^7*d^8 + 20*a^8*b^7*c^9*d^6 - 40*a^8*b^7*c^11*d^4 + 20*a^8*b^7*c^13*d^2 + 7*a^9*b^6*c^2*d^13 - 50*a^9*b^6*c^4*d^11 + 37*a^9*b^6*c^6*d^9 + 20*a^9*b^6*c^8*d^7 + 14*a^9*b^6*c^10*d^5 - 28*a^9*b^6*c^12*d^3 + 35*a^10*b^5*c^3*d^12 - 25*a^10*b^5*c^5*d^10 - 37*a^10*b^5*c^7*d^8 + 14*a^10*b^5*c^9*d^6 + 14*a^10*b^5*c^11*d^4 - 13*a^11*b^4*c^2*d^13 + 14*a^11*b^4*c^4*d^11 + 25*a^11*b^4*c^6*d^9 - 40*a^11*b^4*c^8*d^7 + 14*a^11*b^4*c^10*d^5 - 10*a^12*b^3*c^3*d^12 - 14*a^12*b^3*c^5*d^10 + 50*a^12*b^3*c^7*d^8 - 28*a^12*b^3*c^9*d^6 + 5*a^13*b^2*c^2*d^13 + 10*a^13*b^2*c^4*d^11 - 35*a^13*b^2*c^6*d^9 + 20*a^13*b^2*c^8*d^7 - a*b^14*c^14*d - a^14*b*c*d^14))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9) - (32*tan(e/2 + (f*x)/2)*(8*a^3*b^12*c^15 - 3*a^15*c*d^14 - 3*a*b^14*c^15 - 7*a^5*b^10*c^15 + 2*a^7*b^8*c^15 + 8*a^15*c^3*d^12 - 7*a^15*c^5*d^10 + 2*a^15*c^7*d^8 + 4*a*b^14*c^9*d^6 - 11*a*b^14*c^11*d^4 + 10*a*b^14*c^13*d^2 + 24*a^2*b^13*c^14*d - 64*a^4*b^11*c^14*d + 56*a^6*b^9*c^14*d - 16*a^8*b^7*c^14*d + 4*a^9*b^6*c*d^14 - 11*a^11*b^4*c*d^14 + 10*a^13*b^2*c*d^14 + 24*a^14*b*c^2*d^13 - 64*a^14*b*c^4*d^11 + 56*a^14*b*c^6*d^9 - 16*a^14*b*c^8*d^7 - 32*a^2*b^13*c^8*d^7 + 88*a^2*b^13*c^10*d^5 - 80*a^2*b^13*c^12*d^3 + 112*a^3*b^12*c^7*d^8 - 319*a^3*b^12*c^9*d^6 + 310*a^3*b^12*c^11*d^4 - 111*a^3*b^12*c^13*d^2 - 224*a^4*b^11*c^6*d^9 + 704*a^4*b^11*c^8*d^7 - 800*a^4*b^11*c^10*d^5 + 384*a^4*b^11*c^12*d^3 + 280*a^5*b^10*c^5*d^10 - 1078*a^5*b^10*c^7*d^8 + 1550*a^5*b^10*c^9*d^6 - 993*a^5*b^10*c^11*d^4 + 248*a^5*b^10*c^13*d^2 - 224*a^6*b^9*c^4*d^11 + 1232*a^6*b^9*c^6*d^9 - 2320*a^6*b^9*c^8*d^7 + 1896*a^6*b^9*c^10*d^5 - 640*a^6*b^9*c^12*d^3 + 112*a^7*b^8*c^3*d^12 - 1078*a^7*b^8*c^5*d^10 + 2660*a^7*b^8*c^7*d^8 - 2733*a^7*b^8*c^9*d^6 + 1240*a^7*b^8*c^11*d^4 - 203*a^7*b^8*c^13*d^2 - 32*a^8*b^7*c^2*d^13 + 704*a^8*b^7*c^4*d^11 - 2320*a^8*b^7*c^6*d^9 + 3072*a^8*b^7*c^8*d^7 - 1856*a^8*b^7*c^10*d^5 + 448*a^8*b^7*c^12*d^3 - 319*a^9*b^6*c^3*d^12 + 1550*a^9*b^6*c^5*d^10 - 2733*a^9*b^6*c^7*d^8 + 2128*a^9*b^6*c^9*d^6 - 686*a^9*b^6*c^11*d^4 + 56*a^9*b^6*c^13*d^2 + 88*a^10*b^5*c^2*d^13 - 800*a^10*b^5*c^4*d^11 + 1896*a^10*b^5*c^6*d^9 - 1856*a^10*b^5*c^8*d^7 + 784*a^10*b^5*c^10*d^5 - 112*a^10*b^5*c^12*d^3 + 310*a^11*b^4*c^3*d^12 - 993*a^11*b^4*c^5*d^10 + 1240*a^11*b^4*c^7*d^8 - 686*a^11*b^4*c^9*d^6 + 140*a^11*b^4*c^11*d^4 - 80*a^12*b^3*c^2*d^13 + 384*a^12*b^3*c^4*d^11 - 640*a^12*b^3*c^6*d^9 + 448*a^12*b^3*c^8*d^7 - 112*a^12*b^3*c^10*d^5 - 111*a^13*b^2*c^3*d^12 + 248*a^13*b^2*c^5*d^10 - 203*a^13*b^2*c^7*d^8 + 56*a^13*b^2*c^9*d^6))/(a^10*d^10 + b^10*c^10 - 2*a^2*b^8*c^10 + a^4*b^6*c^10 + a^6*b^4*d^10 - 2*a^8*b^2*d^10 - 2*a^10*c^2*d^8 + a^10*c^4*d^6 + b^10*c^6*d^4 - 2*b^10*c^8*d^2 - 6*a*b^9*c^5*d^5 + 12*a*b^9*c^7*d^3 + 12*a^3*b^7*c^9*d - 6*a^5*b^5*c*d^9 - 6*a^5*b^5*c^9*d + 12*a^7*b^3*c*d^9 + 12*a^9*b*c^3*d^7 - 6*a^9*b*c^5*d^5 + 15*a^2*b^8*c^4*d^6 - 32*a^2*b^8*c^6*d^4 + 19*a^2*b^8*c^8*d^2 - 20*a^3*b^7*c^3*d^7 + 52*a^3*b^7*c^5*d^5 - 44*a^3*b^7*c^7*d^3 + 15*a^4*b^6*c^2*d^8 - 60*a^4*b^6*c^4*d^6 + 76*a^4*b^6*c^6*d^4 - 32*a^4*b^6*c^8*d^2 + 52*a^5*b^5*c^3*d^7 - 92*a^5*b^5*c^5*d^5 + 52*a^5*b^5*c^7*d^3 - 32*a^6*b^4*c^2*d^8 + 76*a^6*b^4*c^4*d^6 - 60*a^6*b^4*c^6*d^4 + 15*a^6*b^4*c^8*d^2 - 44*a^7*b^3*c^3*d^7 + 52*a^7*b^3*c^5*d^5 - 20*a^7*b^3*c^7*d^3 + 19*a^8*b^2*c^2*d^8 - 32*a^8*b^2*c^4*d^6 + 15*a^8*b^2*c^6*d^4 - 6*a*b^9*c^9*d - 6*a^9*b*c*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))*(2*b*d^2 - 3*b*c^2 + a*c*d))/(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8)))*(-(c + d)^3*(c - d)^3)^(1/2)*(2*b*d^2 - 3*b*c^2 + a*c*d)*2i)/(f*(a^3*d^9 + b^3*c^9 - 3*a^3*c^2*d^7 + 3*a^3*c^4*d^5 - a^3*c^6*d^3 - b^3*c^3*d^6 + 3*b^3*c^5*d^4 - 3*b^3*c^7*d^2 + 3*a*b^2*c^2*d^7 - 9*a*b^2*c^4*d^5 + 9*a*b^2*c^6*d^3 + 9*a^2*b*c^3*d^6 - 9*a^2*b*c^5*d^4 + 3*a^2*b*c^7*d^2 - 3*a*b^2*c^8*d - 3*a^2*b*c*d^8))","B"
713,1,137274,458,45.339295,"\text{Not used}","int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^3),x)","-\frac{\frac{-4\,a^4\,c^2\,d^4+a^4\,d^6+8\,a^3\,b\,c^3\,d^3-5\,a^3\,b\,c\,d^5+4\,a^2\,b^2\,c^2\,d^4-a^2\,b^2\,d^6-8\,a\,b^3\,c^3\,d^3+5\,a\,b^3\,c\,d^5+2\,b^4\,c^6-4\,b^4\,c^4\,d^2+2\,b^4\,c^2\,d^4}{\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^2\,c^4-2\,a^2\,c^2\,d^2+a^2\,d^4-b^2\,c^4+2\,b^2\,c^2\,d^2-b^2\,d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(4\,a^5\,c^4\,d^4+7\,a^5\,c^2\,d^6-2\,a^5\,d^8-8\,a^4\,b\,c^5\,d^3-a^4\,b\,c^3\,d^5+6\,a^4\,b\,c\,d^7-22\,a^3\,b^2\,c^4\,d^4+5\,a^3\,b^2\,c^2\,d^6+2\,a^3\,b^2\,d^8+8\,a^2\,b^3\,c^5\,d^3+a^2\,b^3\,c^3\,d^5-6\,a^2\,b^3\,c\,d^7-2\,a\,b^4\,c^8+4\,a\,b^4\,c^6\,d^2+16\,a\,b^4\,c^4\,d^4-12\,a\,b^4\,c^2\,d^6-8\,b^5\,c^7\,d+16\,b^5\,c^5\,d^3-8\,b^5\,c^3\,d^5\right)}{a\,c^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^2\,c^4-2\,a^2\,c^2\,d^2+a^2\,d^4-b^2\,c^4+2\,b^2\,c^2\,d^2-b^2\,d^4\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-11\,a^5\,c^2\,d^5+2\,a^5\,d^7+15\,a^4\,b\,c^3\,d^4-12\,a^4\,b\,c\,d^6+16\,a^3\,b^2\,c^4\,d^3+a^3\,b^2\,c^2\,d^5-2\,a^3\,b^2\,d^7-15\,a^2\,b^3\,c^3\,d^4+12\,a^2\,b^3\,c\,d^6+8\,a\,b^4\,c^6\,d-32\,a\,b^4\,c^4\,d^3+18\,a\,b^4\,c^2\,d^5+2\,b^5\,c^7-4\,b^5\,c^5\,d^2+2\,b^5\,c^3\,d^4\right)}{a\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^2\,c^4-2\,a^2\,c^2\,d^2+a^2\,d^4-b^2\,c^4+2\,b^2\,c^2\,d^2-b^2\,d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-5\,a^5\,c^2\,d^5+2\,a^5\,d^7+9\,a^4\,b\,c^3\,d^4-6\,a^4\,b\,c\,d^6+5\,a^3\,b^2\,c^2\,d^5-2\,a^3\,b^2\,d^7-9\,a^2\,b^3\,c^3\,d^4+6\,a^2\,b^3\,c\,d^6+2\,b^5\,c^7-4\,b^5\,c^5\,d^2+2\,b^5\,c^3\,d^4\right)}{a\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^2\,c^4-2\,a^2\,c^2\,d^2+a^2\,d^4-b^2\,c^4+2\,b^2\,c^2\,d^2-b^2\,d^4\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-4\,a^5\,c^4\,d^4-3\,a^5\,c^2\,d^6+a^5\,d^8+8\,a^4\,b\,c^5\,d^3-8\,a^4\,b\,c^3\,d^5-3\,a^4\,b\,c\,d^7+27\,a^3\,b^2\,c^4\,d^4-11\,a^3\,b^2\,c^2\,d^6-a^3\,b^2\,d^8-8\,a^2\,b^3\,c^5\,d^3+8\,a^2\,b^3\,c^3\,d^5+3\,a^2\,b^3\,c\,d^7+2\,a\,b^4\,c^8-29\,a\,b^4\,c^4\,d^4+18\,a\,b^4\,c^2\,d^6+4\,b^5\,c^7\,d-8\,b^5\,c^5\,d^3+4\,b^5\,c^3\,d^5\right)}{a\,c^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^2\,c^4-2\,a^2\,c^2\,d^2+a^2\,d^4-b^2\,c^4+2\,b^2\,c^2\,d^2-b^2\,d^4\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(b\,c^2+2\,a\,c\,d+2\,b\,d^2\right)\,\left(-4\,a^4\,c^2\,d^4+a^4\,d^6+8\,a^3\,b\,c^3\,d^3-5\,a^3\,b\,c\,d^5+4\,a^2\,b^2\,c^2\,d^4-a^2\,b^2\,d^6-8\,a\,b^3\,c^3\,d^3+5\,a\,b^3\,c\,d^5+2\,b^4\,c^6-4\,b^4\,c^4\,d^2+2\,b^4\,c^2\,d^4\right)}{a\,c^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^2\,c^4-2\,a^2\,c^2\,d^2+a^2\,d^4-b^2\,c^4+2\,b^2\,c^2\,d^2-b^2\,d^4\right)}}{f\,\left(a\,c^2+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,a\,c^2+8\,b\,c\,d+4\,a\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a\,c^2+8\,b\,c\,d+4\,a\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,b\,c^2+8\,a\,c\,d+8\,b\,d^2\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,b\,c^2+4\,a\,d\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,b\,c^2+4\,a\,d\,c\right)+a\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\right)}+\frac{d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^{14}\,c^5\,d^{11}-4\,a^{14}\,c^3\,d^{13}-a^{14}\,c\,d^{15}+44\,a^{13}\,b\,c^6\,d^{10}+20\,a^{13}\,b\,c^4\,d^{12}-a^{13}\,b\,c^2\,d^{14}-220\,a^{12}\,b^2\,c^7\,d^9+48\,a^{12}\,b^2\,c^5\,d^{11}+27\,a^{12}\,b^2\,c^3\,d^{13}-8\,a^{12}\,b^2\,c\,d^{15}+628\,a^{11}\,b^3\,c^8\,d^8-640\,a^{11}\,b^3\,c^6\,d^{10}+59\,a^{11}\,b^3\,c^4\,d^{12}+16\,a^{11}\,b^3\,c^2\,d^{14}-1088\,a^{10}\,b^4\,c^9\,d^7+2300\,a^{10}\,b^4\,c^7\,d^9-975\,a^{10}\,b^4\,c^5\,d^{11}+152\,a^{10}\,b^4\,c^3\,d^{13}+7\,a^{10}\,b^4\,c\,d^{15}+1120\,a^9\,b^5\,c^{10}\,d^6-4524\,a^9\,b^5\,c^8\,d^8+3649\,a^9\,b^5\,c^6\,d^{10}-1056\,a^9\,b^5\,c^4\,d^{12}+55\,a^9\,b^5\,c^2\,d^{14}-688\,a^8\,b^6\,c^{11}\,d^5+6104\,a^8\,b^6\,c^9\,d^7-8939\,a^8\,b^6\,c^7\,d^9+5064\,a^8\,b^6\,c^5\,d^{11}-1485\,a^8\,b^6\,c^3\,d^{13}+214\,a^8\,b^6\,c\,d^{15}+368\,a^7\,b^7\,c^{12}\,d^4-6184\,a^7\,b^7\,c^{10}\,d^6+14693\,a^7\,b^7\,c^8\,d^8-12464\,a^7\,b^7\,c^6\,d^{10}+5107\,a^7\,b^7\,c^4\,d^{12}-818\,a^7\,b^7\,c^2\,d^{14}-292\,a^6\,b^8\,c^{13}\,d^3+4344\,a^6\,b^8\,c^{11}\,d^5-15576\,a^6\,b^8\,c^9\,d^7+18608\,a^6\,b^8\,c^7\,d^9-10619\,a^6\,b^8\,c^5\,d^{11}+2938\,a^6\,b^8\,c^3\,d^{13}-348\,a^6\,b^8\,c\,d^{15}+172\,a^5\,b^9\,c^{14}\,d^2-1920\,a^5\,b^9\,c^{12}\,d^4+11320\,a^5\,b^9\,c^{10}\,d^6-19912\,a^5\,b^9\,c^8\,d^8+16053\,a^5\,b^9\,c^6\,d^{10}-6574\,a^5\,b^9\,c^4\,d^{12}+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2}\,d^5-36\,a\,b^{12}\,c^{10}\,d^7+9\,a\,b^{12}\,c^8\,d^9-b^{13}\,c^{17}+4\,b^{13}\,c^{15}\,d^2-6\,b^{13}\,c^{13}\,d^4+4\,b^{13}\,c^{11}\,d^6-b^{13}\,c^9\,d^8}\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-8\,a\,b\,c^3\,d+2\,a\,b\,c\,d^3+12\,b^2\,c^4-15\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-a^4\,c^{10}\,d^4+5\,a^4\,c^8\,d^6-10\,a^4\,c^6\,d^8+10\,a^4\,c^4\,d^{10}-5\,a^4\,c^2\,d^{12}+a^4\,d^{14}+4\,a^3\,b\,c^{11}\,d^3-20\,a^3\,b\,c^9\,d^5+40\,a^3\,b\,c^7\,d^7-40\,a^3\,b\,c^5\,d^9+20\,a^3\,b\,c^3\,d^{11}-4\,a^3\,b\,c\,d^{13}-6\,a^2\,b^2\,c^{12}\,d^2+30\,a^2\,b^2\,c^{10}\,d^4-60\,a^2\,b^2\,c^8\,d^6+60\,a^2\,b^2\,c^6\,d^8-30\,a^2\,b^2\,c^4\,d^{10}+6\,a^2\,b^2\,c^2\,d^{12}+4\,a\,b^3\,c^{13}\,d-20\,a\,b^3\,c^{11}\,d^3+40\,a\,b^3\,c^9\,d^5-40\,a\,b^3\,c^7\,d^7+20\,a\,b^3\,c^5\,d^9-4\,a\,b^3\,c^3\,d^{11}-b^4\,c^{14}+5\,b^4\,c^{12}\,d^2-10\,b^4\,c^{10}\,d^4+10\,b^4\,c^8\,d^6-5\,b^4\,c^6\,d^8+b^4\,c^4\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-8\,a\,b\,c^3\,d+2\,a\,b\,c\,d^3+12\,b^2\,c^4-15\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-a^4\,c^{10}\,d^4+5\,a^4\,c^8\,d^6-10\,a^4\,c^6\,d^8+10\,a^4\,c^4\,d^{10}-5\,a^4\,c^2\,d^{12}+a^4\,d^{14}+4\,a^3\,b\,c^{11}\,d^3-20\,a^3\,b\,c^9\,d^5+40\,a^3\,b\,c^7\,d^7-40\,a^3\,b\,c^5\,d^9+20\,a^3\,b\,c^3\,d^{11}-4\,a^3\,b\,c\,d^{13}-6\,a^2\,b^2\,c^{12}\,d^2+30\,a^2\,b^2\,c^{10}\,d^4-60\,a^2\,b^2\,c^8\,d^6+60\,a^2\,b^2\,c^6\,d^8-30\,a^2\,b^2\,c^4\,d^{10}+6\,a^2\,b^2\,c^2\,d^{12}+4\,a\,b^3\,c^{13}\,d-20\,a\,b^3\,c^{11}\,d^3+40\,a\,b^3\,c^9\,d^5-40\,a\,b^3\,c^7\,d^7+20\,a\,b^3\,c^5\,d^9-4\,a\,b^3\,c^3\,d^{11}-b^4\,c^{14}+5\,b^4\,c^{12}\,d^2-10\,b^4\,c^{10}\,d^4+10\,b^4\,c^8\,d^6-5\,b^4\,c^6\,d^8+b^4\,c^4\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-8\,a\,b\,c^3\,d+2\,a\,b\,c\,d^3+12\,b^2\,c^4-15\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)\,1{}\mathrm{i}}{2\,\left(-a^4\,c^{10}\,d^4+5\,a^4\,c^8\,d^6-10\,a^4\,c^6\,d^8+10\,a^4\,c^4\,d^{10}-5\,a^4\,c^2\,d^{12}+a^4\,d^{14}+4\,a^3\,b\,c^{11}\,d^3-20\,a^3\,b\,c^9\,d^5+40\,a^3\,b\,c^7\,d^7-40\,a^3\,b\,c^5\,d^9+20\,a^3\,b\,c^3\,d^{11}-4\,a^3\,b\,c\,d^{13}-6\,a^2\,b^2\,c^{12}\,d^2+30\,a^2\,b^2\,c^{10}\,d^4-60\,a^2\,b^2\,c^8\,d^6+60\,a^2\,b^2\,c^6\,d^8-30\,a^2\,b^2\,c^4\,d^{10}+6\,a^2\,b^2\,c^2\,d^{12}+4\,a\,b^3\,c^{13}\,d-20\,a\,b^3\,c^{11}\,d^3+40\,a\,b^3\,c^9\,d^5-40\,a\,b^3\,c^7\,d^7+20\,a\,b^3\,c^5\,d^9-4\,a\,b^3\,c^3\,d^{11}-b^4\,c^{14}+5\,b^4\,c^{12}\,d^2-10\,b^4\,c^{10}\,d^4+10\,b^4\,c^8\,d^6-5\,b^4\,c^6\,d^8+b^4\,c^4\,d^{10}\right)}-\frac{d^2\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(-4\,a^{13}\,b\,c^5\,d^{11}-4\,a^{13}\,b\,c^3\,d^{13}-a^{13}\,b\,c\,d^{15}+44\,a^{12}\,b^2\,c^6\,d^{10}+20\,a^{12}\,b^2\,c^4\,d^{12}-a^{12}\,b^2\,c^2\,d^{14}-220\,a^{11}\,b^3\,c^7\,d^9+40\,a^{11}\,b^3\,c^5\,d^{11}+19\,a^{11}\,b^3\,c^3\,d^{13}-10\,a^{11}\,b^3\,c\,d^{15}+628\,a^{10}\,b^4\,c^8\,d^8-552\,a^{10}\,b^4\,c^6\,d^{10}+99\,a^{10}\,b^4\,c^4\,d^{12}+14\,a^{10}\,b^4\,c^2\,d^{14}-1088\,a^9\,b^5\,c^9\,d^7+1860\,a^9\,b^5\,c^7\,d^9-895\,a^9\,b^5\,c^5\,d^{11}+190\,a^9\,b^5\,c^3\,d^{13}-13\,a^9\,b^5\,c\,d^{15}+1056\,a^8\,b^6\,c^{10}\,d^6-3012\,a^8\,b^6\,c^8\,d^8+2161\,a^8\,b^6\,c^6\,d^{10}-602\,a^8\,b^6\,c^4\,d^{12}+19\,a^8\,b^6\,c^2\,d^{14}-400\,a^7\,b^7\,c^{11}\,d^5+2648\,a^7\,b^7\,c^9\,d^7-2979\,a^7\,b^7\,c^7\,d^9+1354\,a^7\,b^7\,c^5\,d^{11}-305\,a^7\,b^7\,c^3\,d^{13}+60\,a^7\,b^7\,c\,d^{15}-148\,a^6\,b^8\,c^{12}\,d^4-1336\,a^6\,b^8\,c^{10}\,d^6+2885\,a^6\,b^8\,c^8\,d^8-2046\,a^6\,b^8\,c^6\,d^{10}+699\,a^6\,b^8\,c^4\,d^{12}-108\,a^6\,b^8\,c^2\,d^{14}+172\,a^5\,b^9\,c^{13}\,d^3+248\,a^5\,b^9\,c^{11}\,d^5-1544\,a^5\,b^9\,c^9\,d^7+1386\,a^5\,b^9\,c^7\,d^9-535\,a^5\,b^9\,c^5\,d^{11}+120\,a^5\,b^9\,c^3\,d^{13}-36\,a^5\,b^9\,c\,d^{15}-44\,a^4\,b^{10}\,c^{14}\,d^2+248\,a^4\,b^{10}\,c^{12}\,d^4+100\,a^4\,b^{10}\,c^{10}\,d^6-270\,a^4\,b^{10}\,c^8\,d^8+233\,a^4\,b^{10}\,c^6\,d^{10}-168\,a^4\,b^{10}\,c^4\,d^{12}+72\,a^4\,b^{10}\,c^2\,d^{14}+4\,a^3\,b^{11}\,c^{15}\,d-184\,a^3\,b^{11}\,c^{13}\,d^3+180\,a^3\,b^{11}\,c^{11}\,d^5-88\,a^3\,b^{11}\,c^9\,d^7+61\,a^3\,b^{11}\,c^7\,d^9-36\,a^3\,b^{11}\,c^5\,d^{11}+24\,a^2\,b^{12}\,c^{14}\,d^2-60\,a^2\,b^{12}\,c^{12}\,d^4+216\,a^2\,b^{12}\,c^{10}\,d^6-375\,a^2\,b^{12}\,c^8\,d^8+276\,a^2\,b^{12}\,c^6\,d^{10}-72\,a^2\,b^{12}\,c^4\,d^{12}+36\,a\,b^{13}\,c^{13}\,d^3-144\,a\,b^{13}\,c^{11}\,d^5+216\,a\,b^{13}\,c^9\,d^7-144\,a\,b^{13}\,c^7\,d^9+36\,a\,b^{13}\,c^5\,d^{11}\right)}{a^{13}\,c^8\,d^9-4\,a^{13}\,c^6\,d^{11}+6\,a^{13}\,c^4\,d^{13}-4\,a^{13}\,c^2\,d^{15}+a^{13}\,d^{17}-9\,a^{12}\,b\,c^9\,d^8+36\,a^{12}\,b\,c^7\,d^{10}-54\,a^{12}\,b\,c^5\,d^{12}+36\,a^{12}\,b\,c^3\,d^{14}-9\,a^{12}\,b\,c\,d^{16}+36\,a^{11}\,b^2\,c^{10}\,d^7-146\,a^{11}\,b^2\,c^8\,d^9+224\,a^{11}\,b^2\,c^6\,d^{11}-156\,a^{11}\,b^2\,c^4\,d^{13}+44\,a^{11}\,b^2\,c^2\,d^{15}-2\,a^{11}\,b^2\,d^{17}-84\,a^{10}\,b^3\,c^{11}\,d^6+354\,a^{10}\,b^3\,c^9\,d^8-576\,a^{10}\,b^3\,c^7\,d^{10}+444\,a^{10}\,b^3\,c^5\,d^{12}-156\,a^{10}\,b^3\,c^3\,d^{14}+18\,a^{10}\,b^3\,c\,d^{16}+126\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^8+b^4\,c^4\,d^{10}\right)}\right)\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-8\,a\,b\,c^3\,d+2\,a\,b\,c\,d^3+12\,b^2\,c^4-15\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)}{2\,\left(-a^4\,c^{10}\,d^4+5\,a^4\,c^8\,d^6-10\,a^4\,c^6\,d^8+10\,a^4\,c^4\,d^{10}-5\,a^4\,c^2\,d^{12}+a^4\,d^{14}+4\,a^3\,b\,c^{11}\,d^3-20\,a^3\,b\,c^9\,d^5+40\,a^3\,b\,c^7\,d^7-40\,a^3\,b\,c^5\,d^9+20\,a^3\,b\,c^3\,d^{11}-4\,a^3\,b\,c\,d^{13}-6\,a^2\,b^2\,c^{12}\,d^2+30\,a^2\,b^2\,c^{10}\,d^4-60\,a^2\,b^2\,c^8\,d^6+60\,a^2\,b^2\,c^6\,d^8-30\,a^2\,b^2\,c^4\,d^{10}+6\,a^2\,b^2\,c^2\,d^{12}+4\,a\,b^3\,c^{13}\,d-20\,a\,b^3\,c^{11}\,d^3+40\,a\,b^3\,c^9\,d^5-40\,a\,b^3\,c^7\,d^7+20\,a\,b^3\,c^5\,d^9-4\,a\,b^3\,c^3\,d^{11}-b^4\,c^{14}+5\,b^4\,c^{12}\,d^2-10\,b^4\,c^{10}\,d^4+10\,b^4\,c^8\,d^6-5\,b^4\,c^6\,d^8+b^4\,c^4\,d^{10}\right)}}\right)\,\sqrt{-{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(2\,a^2\,c^2\,d^2+a^2\,d^4-8\,a\,b\,c^3\,d+2\,a\,b\,c\,d^3+12\,b^2\,c^4-15\,b^2\,c^2\,d^2+6\,b^2\,d^4\right)\,1{}\mathrm{i}}{f\,\left(-a^4\,c^{10}\,d^4+5\,a^4\,c^8\,d^6-10\,a^4\,c^6\,d^8+10\,a^4\,c^4\,d^{10}-5\,a^4\,c^2\,d^{12}+a^4\,d^{14}+4\,a^3\,b\,c^{11}\,d^3-20\,a^3\,b\,c^9\,d^5+40\,a^3\,b\,c^7\,d^7-40\,a^3\,b\,c^5\,d^9+20\,a^3\,b\,c^3\,d^{11}-4\,a^3\,b\,c\,d^{13}-6\,a^2\,b^2\,c^{12}\,d^2+30\,a^2\,b^2\,c^{10}\,d^4-60\,a^2\,b^2\,c^8\,d^6+60\,a^2\,b^2\,c^6\,d^8-30\,a^2\,b^2\,c^4\,d^{10}+6\,a^2\,b^2\,c^2\,d^{12}+4\,a\,b^3\,c^{13}\,d-20\,a\,b^3\,c^{11}\,d^3+40\,a\,b^3\,c^9\,d^5-40\,a\,b^3\,c^7\,d^7+20\,a\,b^3\,c^5\,d^9-4\,a\,b^3\,c^3\,d^{11}-b^4\,c^{14}+5\,b^4\,c^{12}\,d^2-10\,b^4\,c^{10}\,d^4+10\,b^4\,c^8\,d^6-5\,b^4\,c^6\,d^8+b^4\,c^4\,d^{10}\right)}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(-4\,a^{13}\,b\,c^5\,d^{11}-4\,a^{13}\,b\,c^3\,d^{13}-a^{13}\,b\,c\,d^{15}+44\,a^{12}\,b^2\,c^6\,d^{10}+20\,a^{12}\,b^2\,c^4\,d^{12}-a^{12}\,b^2\,c^2\,d^{14}-220\,a^{11}\,b^3\,c^7\,d^9+40\,a^{11}\,b^3\,c^5\,d^{11}+19\,a^{11}\,b^3\,c^3\,d^{13}-10\,a^{11}\,b^3\,c\,d^{15}+628\,a^{10}\,b^4\,c^8\,d^8-552\,a^{10}\,b^4\,c^6\,d^{10}+99\,a^{10}\,b^4\,c^4\,d^{12}+14\,a^{10}\,b^4\,c^2\,d^{14}-1088\,a^9\,b^5\,c^9\,d^7+1860\,a^9\,b^5\,c^7\,d^9-895\,a^9\,b^5\,c^5\,d^{11}+190\,a^9\,b^5\,c^3\,d^{13}-13\,a^9\,b^5\,c\,d^{15}+1056\,a^8\,b^6\,c^{10}\,d^6-3012\,a^8\,b^6\,c^8\,d^8+2161\,a^8\,b^6\,c^6\,d^{10}-602\,a^8\,b^6\,c^4\,d^{12}+19\,a^8\,b^6\,c^2\,d^{14}-400\,a^7\,b^7\,c^{11}\,d^5+2648\,a^7\,b^7\,c^9\,d^7-2979\,a^7\,b^7\,c^7\,d^9+1354\,a^7\,b^7\,c^5\,d^{11}-305\,a^7\,b^7\,c^3\,d^{13}+60\,a^7\,b^7\,c\,d^{15}-148\,a^6\,b^8\,c^{12}\,d^4-1336\,a^6\,b^8\,c^{10}\,d^6+2885\,a^6\,b^8\,c^8\,d^8-2046\,a^6\,b^8\,c^6\,d^{10}+699\,a^6\,b^8\,c^4\,d^{12}-108\,a^6\,b^8\,c^2\,d^{14}+172\,a^5\,b^9\,c^{13}\,d^3+248\,a^5\,b^9\,c^{11}\,d^5-1544\,a^5\,b^9\,c^9\,d^7+1386\,a^5\,b^9\,c^7\,d^9-535\,a^5\,b^9\,c^5\,d^{11}+120\,a^5\,b^9\,c^3\,d^{13}-36\,a^5\,b^9\,c\,d^{15}-44\,a^4\,b^{10}\,c^{14}\,d^2+248\,a^4\,b^{10}\,c^{12}\,d^4+100\,a^4\,b^{10}\,c^{10}\,d^6-270\,a^4\,b^{10}\,c^8\,d^8+233\,a^4\,b^{10}\,c^6\,d^{10}-168\,a^4\,b^{10}\,c^4\,d^{12}+72\,a^4\,b^{10}\,c^2\,d^{14}+4\,a^3\,b^{11}\,c^{15}\,d-184\,a^3\,b^{11}\,c^{13}\,d^3+180\,a^3\,b^{11}\,c^{11}\,d^5-88\,a^3\,b^{11}\,c^9\,d^7+61\,a^3\,b^{11}\,c^7\,d^9-36\,a^3\,b^{11}\,c^5\,d^{11}+24\,a^2\,b^{12}\,c^{14}\,d^2-60\,a^2\,b^{12}\,c^{12}\,d^4+216\,a^2\,b^{12}\,c^{10}\,d^6-375\,a^2\,b^{12}\,c^8\,d^8+276\,a^2\,b^{12}\,c^6\,d^{10}-72\,a^2\,b^{12}\,c^4\,d^{12}+36\,a\,b^{13}\,c^{13}\,d^3-144\,a\,b^{13}\,c^{11}\,d^5+216\,a\,b^{13}\,c^9\,d^7-144\,a\,b^{13}\,c^7\,d^9+36\,a\,b^{13}\,c^5\,d^{11}\right)}{a^{13}\,c^8\,d^9-4\,a^{13}\,c^6\,d^{11}+6\,a^{13}\,c^4\,d^{13}-4\,a^{13}\,c^2\,d^{15}+a^{13}\,d^{17}-9\,a^{12}\,b\,c^9\,d^8+36\,a^{12}\,b\,c^7\,d^{10}-54\,a^{12}\,b\,c^5\,d^{12}+36\,a^{12}\,b\,c^3\,d^{14}-9\,a^{12}\,b\,c\,d^{16}+36\,a^{11}\,b^2\,c^{10}\,d^7-146\,a^{11}\,b^2\,c^8\,d^9+224\,a^{11}\,b^2\,c^6\,d^{11}-156\,a^{11}\,b^2\,c^4\,d^{13}+44\,a^{11}\,b^2\,c^2\,d^{15}-2\,a^{11}\,b^2\,d^{17}-84\,a^{10}\,b^3\,c^{11}\,d^6+354\,a^{10}\,b^3\,c^9\,d^8-576\,a^{10}\,b^3\,c^7\,d^{10}+444\,a^{10}\,b^3\,c^5\,d^{12}-156\,a^{10}\,b^3\,c^3\,d^{14}+18\,a^{10}\,b^3\,c\,d^{16}+126\,a^9\,b^4\,c^{12}\,d^5-576\,a^9\,b^4\,c^{10}\,d^7+1045\,a^9\,b^4\,c^8\,d^9-940\,a^9\,b^4\,c^6\,d^{11}+420\,a^9\,b^4\,c^4\,d^{13}-76\,a^9\,b^4\,c^2\,d^{15}+a^9\,b^4\,d^{17}-126\,a^8\,b^5\,c^{13}\,d^4+672\,a^8\,b^5\,c^{11}\,d^6-1437\,a^8\,b^5\,c^9\,d^8+1548\,a^8\,b^5\,c^7\,d^{10}-852\,a^8\,b^5\,c^5\,d^{12}+204\,a^8\,b^5\,c^3\,d^{14}-9\,a^8\,b^5\,c\,d^{16}+84\,a^7\,b^6\,c^{14}\,d^3-588\,a^7\,b^6\,c^{12}\,d^5+1548\,a^7\,b^6\,c^{10}\,d^7-1992\,a^7\,b^6\,c^8\,d^9+1308\,a^7\,b^6\,c^6\,d^{11}-396\,a^7\,b^6\,c^4\,d^{13}+36\,a^7\,b^6\,c^2\,d^{15}-36\,a^6\,b^7\,c^{15}\,d^2+396\,a^6\,b^7\,c^{13}\,d^4-1308\,a^6\,b^7\,c^{11}\,d^6+1992\,a^6\,b^7\,c^9\,d^8-1548\,a^6\,b^7\,c^7\,d^{10}+588\,a^6\,b^7\,c^5\,d^{12}-84\,a^6\,b^7\,c^3\,d^{14}+9\,a^5\,b^8\,c^{16}\,d-204\,a^5\,b^8\,c^{14}\,d^3+852\,a^5\,b^8\,c^{12}\,d^5-1548\,a^5\,b^8\,c^{10}\,d^7+1437\,a^5\,b^8\,c^8\,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{12}\,c^{21}\,d+6952\,a^6\,b^{12}\,c^{19}\,d^3-37532\,a^6\,b^{12}\,c^{17}\,d^5+94160\,a^6\,b^{12}\,c^{15}\,d^7-129580\,a^6\,b^{12}\,c^{13}\,d^9+101288\,a^6\,b^{12}\,c^{11}\,d^{11}-42372\,a^6\,b^{12}\,c^9\,d^{13}+7392\,a^6\,b^{12}\,c^7\,d^{15}+28\,a^5\,b^{13}\,c^{22}-1912\,a^5\,b^{13}\,c^{20}\,d^2+13748\,a^5\,b^{13}\,c^{18}\,d^4-41712\,a^5\,b^{13}\,c^{16}\,d^6+66628\,a^5\,b^{13}\,c^{14}\,d^8-59000\,a^5\,b^{13}\,c^{12}\,d^{10}+27500\,a^5\,b^{13}\,c^{10}\,d^{12}-5280\,a^5\,b^{13}\,c^8\,d^{14}+352\,a^4\,b^{14}\,c^{21}\,d-3872\,a^4\,b^{14}\,c^{19}\,d^3+14608\,a^4\,b^{14}\,c^{17}\,d^5-26752\,a^4\,b^{14}\,c^{15}\,d^7+26048\,a^4\,b^{14}\,c^{13}\,d^9-13024\,a^4\,b^{14}\,c^{11}\,d^{11}+2640\,a^4\,b^{14}\,c^9\,d^{13}-32\,a^3\,b^{15}\,c^{22}+832\,a^3\,b^{15}\,c^{20}\,d^2-3888\,a^3\,b^{15}\,c^{18}\,d^4+7872\,a^3\,b^{15}\,c^{16}\,d^6-8128\,a^3\,b^{15}\,c^{14}\,d^8+4224\,a^3\,b^{15}\,c^{12}\,d^{10}-880\,a^3\,b^{15}\,c^{10}\,d^{12}-132\,a^2\,b^{16}\,c^{21}\,d+704\,a^2\,b^{16}\,c^{19}\,d^3-1496\,a^2\,b^{16}\,c^{17}\,d^5+1584\,a^2\,b^{16}\,c^{15}\,d^7-836\,a^2\,b^{16}\,c^{13}\,d^9+176\,a^2\,b^{16}\,c^{11}\,d^{11}+12\,a\,b^{17}\,c^{22}-64\,a\,b^{17}\,c^{20}\,d^2+136\,a\,b^{17}\,c^{18}\,d^4-144\,a\,b^{17}\,c^{16}\,d^6+76\,a\,b^{17}\,c^{14}\,d^8-16\,a\,b^{17}\,c^{12}\,d^{10}\right)}{a^{13}\,c^8\,d^9-4\,a^{13}\,c^6\,d^{11}+6\,a^{13}\,c^4\,d^{13}-4\,a^{13}\,c^2\,d^{15}+a^{13}\,d^{17}-9\,a^{12}\,b\,c^9\,d^8+36\,a^{12}\,b\,c^7\,d^{10}-54\,a^{12}\,b\,c^5\,d^{12}+36\,a^{12}\,b\,c^3\,d^{14}-9\,a^{12}\,b\,c\,d^{16}+36\,a^{11}\,b^2\,c^{10}\,d^7-146\,a^{11}\,b^2\,c^8\,d^9+224\,a^{11}\,b^2\,c^6\,d^{11}-156\,a^{11}\,b^2\,c^4\,d^{13}+44\,a^{11}\,b^2\,c^2\,d^{15}-2\,a^{11}\,b^2\,d^{17}-84\,a^{10}\,b^3\,c^{11}\,d^6+354\,a^{10}\,b^3\,c^9\,d^8-576\,a^{10}\,b^3\,c^7\,d^{10}+444\,a^{10}\,b^3\,c^5\,d^{12}-156\,a^{10}\,b^3\,c^3\,d^{14}+18\,a^{10}\,b^3\,c\,d^{16}+126\,a^9\,b^4\,c^{12}\,d^5-576\,a^9\,b^4\,c^{10}\,d^7+1045\,a^9\,b^4\,c^8\,d^9-940\,a^9\,b^4\,c^6\,d^{11}+420\,a^9\,b^4\,c^4\,d^{13}-76\,a^9\,b^4\,c^2\,d^{15}+a^9\,b^4\,d^{17}-126\,a^8\,b^5\,c^{13}\,d^4+672\,a^8\,b^5\,c^{11}\,d^6-1437\,a^8\,b^5\,c^9\,d^8+1548\,a^8\,b^5\,c^7\,d^{10}-852\,a^8\,b^5\,c^5\,d^{12}+204\,a^8\,b^5\,c^3\,d^{14}-9\,a^8\,b^5\,c\,d^{16}+84\,a^7\,b^6\,c^{14}\,d^3-588\,a^7\,b^6\,c^{12}\,d^5+1548\,a^7\,b^6\,c^{10}\,d^7-1992\,a^7\,b^6\,c^8\,d^9+1308\,a^7\,b^6\,c^6\,d^{11}-396\,a^7\,b^6\,c^4\,d^{13}+36\,a^7\,b^6\,c^2\,d^{15}-36\,a^6\,b^7\,c^{15}\,d^2+396\,a^6\,b^7\,c^{13}\,d^4-1308\,a^6\,b^7\,c^{11}\,d^6+1992\,a^6\,b^7\,c^9\,d^8-1548\,a^6\,b^7\,c^7\,d^{10}+588\,a^6\,b^7\,c^5\,d^{12}-84\,a^6\,b^7\,c^3\,d^{14}+9\,a^5\,b^8\,c^{16}\,d-204\,a^5\,b^8\,c^{14}\,d^3+852\,a^5\,b^8\,c^{12}\,d^5-1548\,a^5\,b^8\,c^{10}\,d^7+1437\,a^5\,b^8\,c^8\,d^9-672\,a^5\,b^8\,c^6\,d^{11}+126\,a^5\,b^8\,c^4\,d^{13}-a^4\,b^9\,c^{17}+76\,a^4\,b^9\,c^{15}\,d^2-420\,a^4\,b^9\,c^{13}\,d^4+940\,a^4\,b^9\,c^{11}\,d^6-1045\,a^4\,b^9\,c^9\,d^8+576\,a^4\,b^9\,c^7\,d^{10}-126\,a^4\,b^9\,c^5\,d^{12}-18\,a^3\,b^{10}\,c^{16}\,d+156\,a^3\,b^{10}\,c^{14}\,d^3-444\,a^3\,b^{10}\,c^{12}\,d^5+576\,a^3\,b^{10}\,c^{10}\,d^7-354\,a^3\,b^{10}\,c^8\,d^9+84\,a^3\,b^{10}\,c^6\,d^{11}+2\,a^2\,b^{11}\,c^{17}-44\,a^2\,b^{11}\,c^{15}\,d^2+156\,a^2\,b^{11}\,c^{13}\,d^4-224\,a^2\,b^{11}\,c^{11}\,d^6+146\,a^2\,b^{11}\,c^9\,d^8-36\,a^2\,b^{11}\,c^7\,d^{10}+9\,a\,b^{12}\,c^{16}\,d-36\,a\,b^{12}\,c^{14}\,d^3+54\,a\,b^{12}\,c^{12}\,d^5-36\,a\,b^{12}\,c^{10}\,d^7+9\,a\,b^{12}\,c^8\,d^9-b^{13}\,c^{17}+4\,b^{13}\,c^{15}\,d^2-6\,b^{13}\,c^{13}\,d^4+4\,b^{13}\,c^{11}\,d^6-b^{13}\,c^9\,d^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-4\,d\,a^2+c\,a\,b+3\,d\,b^2\right)}{a^{10}\,d^4-4\,a^9\,b\,c\,d^3+6\,a^8\,b^2\,c^2\,d^2-3\,a^8\,b^2\,d^4-4\,a^7\,b^3\,c^3\,d+12\,a^7\,b^3\,c\,d^3+a^6\,b^4\,c^4-18\,a^6\,b^4\,c^2\,d^2+3\,a^6\,b^4\,d^4+12\,a^5\,b^5\,c^3\,d-12\,a^5\,b^5\,c\,d^3-3\,a^4\,b^6\,c^4+18\,a^4\,b^6\,c^2\,d^2-a^4\,b^6\,d^4-12\,a^3\,b^7\,c^3\,d+4\,a^3\,b^7\,c\,d^3+3\,a^2\,b^8\,c^4-6\,a^2\,b^8\,c^2\,d^2+4\,a\,b^9\,c^3\,d-b^{10}\,c^4}\right)\,\left(-4\,d\,a^2+c\,a\,b+3\,d\,b^2\right)}{a^{10}\,d^4-4\,a^9\,b\,c\,d^3+6\,a^8\,b^2\,c^2\,d^2-3\,a^8\,b^2\,d^4-4\,a^7\,b^3\,c^3\,d+12\,a^7\,b^3\,c\,d^3+a^6\,b^4\,c^4-18\,a^6\,b^4\,c^2\,d^2+3\,a^6\,b^4\,d^4+12\,a^5\,b^5\,c^3\,d-12\,a^5\,b^5\,c\,d^3-3\,a^4\,b^6\,c^4+18\,a^4\,b^6\,c^2\,d^2-a^4\,b^6\,d^4-12\,a^3\,b^7\,c^3\,d+4\,a^3\,b^7\,c\,d^3+3\,a^2\,b^8\,c^4-6\,a^2\,b^8\,c^2\,d^2+4\,a\,b^9\,c^3\,d-b^{10}\,c^4}\right)\,\left(-4\,d\,a^2+c\,a\,b+3\,d\,b^2\right)}{a^{10}\,d^4-4\,a^9\,b\,c\,d^3+6\,a^8\,b^2\,c^2\,d^2-3\,a^8\,b^2\,d^4-4\,a^7\,b^3\,c^3\,d+12\,a^7\,b^3\,c\,d^3+a^6\,b^4\,c^4-18\,a^6\,b^4\,c^2\,d^2+3\,a^6\,b^4\,d^4+12\,a^5\,b^5\,c^3\,d-12\,a^5\,b^5\,c\,d^3-3\,a^4\,b^6\,c^4+18\,a^4\,b^6\,c^2\,d^2-a^4\,b^6\,d^4-12\,a^3\,b^7\,c^3\,d+4\,a^3\,b^7\,c\,d^3+3\,a^2\,b^8\,c^4-6\,a^2\,b^8\,c^2\,d^2+4\,a\,b^9\,c^3\,d-b^{10}\,c^4}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-4\,d\,a^2+c\,a\,b+3\,d\,b^2\right)\,2{}\mathrm{i}}{f\,\left(a^{10}\,d^4-4\,a^9\,b\,c\,d^3+6\,a^8\,b^2\,c^2\,d^2-3\,a^8\,b^2\,d^4-4\,a^7\,b^3\,c^3\,d+12\,a^7\,b^3\,c\,d^3+a^6\,b^4\,c^4-18\,a^6\,b^4\,c^2\,d^2+3\,a^6\,b^4\,d^4+12\,a^5\,b^5\,c^3\,d-12\,a^5\,b^5\,c\,d^3-3\,a^4\,b^6\,c^4+18\,a^4\,b^6\,c^2\,d^2-a^4\,b^6\,d^4-12\,a^3\,b^7\,c^3\,d+4\,a^3\,b^7\,c\,d^3+3\,a^2\,b^8\,c^4-6\,a^2\,b^8\,c^2\,d^2+4\,a\,b^9\,c^3\,d-b^{10}\,c^4\right)}","Not used",1,"(d^2*atan(((d^2*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (d^2*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(4*a^3*b^13*c^19 - 4*a^5*b^11*c^19 + 2*a^16*c^2*d^17 - 6*a^16*c^6*d^13 + 4*a^16*c^8*d^11 + 12*a*b^15*c^9*d^10 - 54*a*b^15*c^11*d^8 + 96*a*b^15*c^13*d^6 - 78*a*b^15*c^15*d^4 + 24*a*b^15*c^17*d^2 + 12*a^2*b^14*c^18*d - 56*a^4*b^12*c^18*d + 44*a^6*b^10*c^18*d + 12*a^9*b^7*c*d^18 - 28*a^11*b^5*c*d^18 + 16*a^13*b^3*c*d^18 - 10*a^15*b*c^3*d^16 - 24*a^15*b*c^5*d^14 + 78*a^15*b*c^7*d^12 - 44*a^15*b*c^9*d^10 - 96*a^2*b^14*c^8*d^11 + 442*a^2*b^14*c^10*d^9 - 816*a^2*b^14*c^12*d^7 + 702*a^2*b^14*c^14*d^5 - 244*a^2*b^14*c^16*d^3 + 336*a^3*b^13*c^7*d^12 - 1620*a^3*b^13*c^9*d^10 + 3206*a^3*b^13*c^11*d^8 - 3064*a^3*b^13*c^13*d^6 + 1314*a^3*b^13*c^15*d^4 - 176*a^3*b^13*c^17*d^2 - 672*a^4*b^12*c^6*d^13 + 3528*a^4*b^12*c^8*d^11 - 7810*a^4*b^12*c^10*d^9 + 8696*a^4*b^12*c^12*d^7 - 4770*a^4*b^12*c^14*d^5 + 1084*a^4*b^12*c^16*d^3 + 840*a^5*b^11*c^5*d^14 - 5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 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204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(4*a^16*c*d^18 + 8*a^2*b^14*c^19 - 8*a^4*b^12*c^19 - 12*a^16*c^5*d^14 + 8*a^16*c^7*d^12 + 12*a*b^15*c^10*d^9 - 48*a*b^15*c^12*d^7 + 84*a*b^15*c^14*d^5 - 72*a*b^15*c^16*d^3 - 112*a^3*b^13*c^18*d + 88*a^5*b^11*c^18*d + 12*a^10*b^6*c*d^18 - 28*a^12*b^4*c*d^18 + 12*a^14*b^2*c*d^18 - 20*a^15*b*c^2*d^17 - 48*a^15*b*c^4*d^15 + 156*a^15*b*c^6*d^13 - 88*a^15*b*c^8*d^11 - 84*a^2*b^14*c^9*d^10 + 328*a^2*b^14*c^11*d^8 - 596*a^2*b^14*c^13*d^6 + 552*a^2*b^14*c^15*d^4 - 208*a^2*b^14*c^17*d^2 + 240*a^3*b^13*c^8*d^11 - 908*a^3*b^13*c^10*d^9 + 1792*a^3*b^13*c^12*d^7 - 1932*a^3*b^13*c^14*d^5 + 920*a^3*b^13*c^16*d^3 - 336*a^4*b^12*c^7*d^12 + 1188*a^4*b^12*c^9*d^10 - 2808*a^4*b^12*c^11*d^8 + 3980*a^4*b^12*c^13*d^6 - 2616*a^4*b^12*c^15*d^4 + 600*a^4*b^12*c^17*d^2 + 168*a^5*b^11*c^6*d^13 - 336*a^5*b^11*c^8*d^11 + 1740*a^5*b^11*c^10*d^9 - 4720*a^5*b^11*c^12*d^7 + 4812*a^5*b^11*c^14*d^5 - 1752*a^5*b^11*c^16*d^3 + 168*a^6*b^10*c^5*d^14 - 1344*a^6*b^10*c^7*d^12 + 2292*a^6*b^10*c^9*d^10 + 1088*a^6*b^10*c^11*d^8 - 4908*a^6*b^10*c^13*d^6 + 3096*a^6*b^10*c^15*d^4 - 392*a^6*b^10*c^17*d^2 - 336*a^7*b^9*c^4*d^15 + 2520*a^7*b^9*c^6*d^13 - 7488*a^7*b^9*c^8*d^11 + 7556*a^7*b^9*c^10*d^9 - 144*a^7*b^9*c^12*d^7 - 3012*a^7*b^9*c^14*d^5 + 904*a^7*b^9*c^16*d^3 + 240*a^8*b^8*c^3*d^16 - 2472*a^8*b^8*c^5*d^14 + 10416*a^8*b^8*c^7*d^12 - 16596*a^8*b^8*c^9*d^10 + 9600*a^8*b^8*c^11*d^8 - 156*a^8*b^8*c^13*d^6 - 1032*a^8*b^8*c^15*d^4 - 84*a^9*b^7*c^2*d^17 + 1632*a^9*b^7*c^4*d^15 - 9204*a^9*b^7*c^6*d^13 + 19800*a^9*b^7*c^8*d^11 - 18048*a^9*b^7*c^10*d^9 + 5856*a^9*b^7*c^12*d^7 + 48*a^9*b^7*c^14*d^5 - 744*a^10*b^6*c^3*d^16 + 5460*a^10*b^6*c^5*d^14 - 15960*a^10*b^6*c^7*d^12 + 20136*a^10*b^6*c^9*d^10 - 10584*a^10*b^6*c^11*d^8 + 1680*a^10*b^6*c^13*d^6 + 212*a^11*b^5*c^2*d^17 - 2176*a^11*b^5*c^4*d^15 + 9180*a^11*b^5*c^6*d^13 - 15416*a^11*b^5*c^8*d^11 + 10936*a^11*b^5*c^10*d^9 - 2736*a^11*b^5*c^12*d^7 + 584*a^12*b^4*c^3*d^16 - 3708*a^12*b^4*c^5*d^14 + 8152*a^12*b^4*c^7*d^12 - 7376*a^12*b^4*c^9*d^10 + 2376*a^12*b^4*c^11*d^8 - 108*a^13*b^3*c^2*d^17 + 928*a^13*b^3*c^4*d^15 - 2820*a^13*b^3*c^6*d^13 + 3288*a^13*b^3*c^8*d^11 - 1288*a^13*b^3*c^10*d^9 - 80*a^14*b^2*c^3*d^16 + 564*a^14*b^2*c^5*d^14 - 936*a^14*b^2*c^7*d^12 + 440*a^14*b^2*c^9*d^10 + 24*a*b^15*c^18*d))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (d^2*((8*(4*a^2*b^16*c^22 - 8*a^4*b^14*c^22 + 4*a^6*b^12*c^22 - 4*a^18*c^2*d^20 + 16*a^18*c^4*d^18 - 24*a^18*c^6*d^16 + 16*a^18*c^8*d^14 - 4*a^18*c^10*d^12 - 4*a*b^17*c^13*d^9 + 16*a*b^17*c^15*d^7 - 24*a*b^17*c^17*d^5 + 16*a*b^17*c^19*d^3 - 32*a^3*b^15*c^21*d + 76*a^5*b^13*c^21*d - 40*a^7*b^11*c^21*d + 4*a^13*b^5*c*d^21 - 8*a^15*b^3*c*d^21 + 24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 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852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 1320*a^10*b^8*c^19*d^3 - 176*a^11*b^7*c^2*d^20 + 8096*a^11*b^7*c^4*d^18 - 54384*a^11*b^7*c^6*d^16 + 156992*a^11*b^7*c^8*d^14 - 242528*a^11*b^7*c^10*d^12 + 214368*a^11*b^7*c^12*d^10 - 107184*a^11*b^7*c^14*d^8 + 27456*a^11*b^7*c^16*d^6 - 2640*a^11*b^7*c^18*d^4 - 2496*a^12*b^6*c^3*d^19 + 24784*a^12*b^6*c^5*d^17 - 89280*a^12*b^6*c^7*d^15 + 162336*a^12*b^6*c^9*d^13 - 165760*a^12*b^6*c^11*d^11 + 96272*a^12*b^6*c^13*d^9 - 29568*a^12*b^6*c^15*d^7 + 3696*a^12*b^6*c^17*d^5 + 484*a^13*b^5*c^2*d^20 - 8888*a^13*b^5*c^4*d^18 + 40876*a^13*b^5*c^6*d^16 - 88000*a^13*b^5*c^8*d^14 + 104060*a^13*b^5*c^10*d^12 - 69784*a^13*b^5*c^12*d^10 + 24948*a^13*b^5*c^14*d^8 - 3696*a^13*b^5*c^16*d^6 + 2408*a^14*b^4*c^3*d^19 - 14692*a^14*b^4*c^5*d^17 + 38208*a^14*b^4*c^7*d^15 - 52532*a^14*b^4*c^9*d^13 + 40072*a^14*b^4*c^11*d^11 - 16060*a^14*b^4*c^13*d^9 + 2640*a^14*b^4*c^15*d^7 - 440*a^15*b^3*c^2*d^20 + 4048*a^15*b^3*c^4*d^18 - 13112*a^15*b^3*c^6*d^16 + 20768*a^15*b^3*c^8*d^14 - 17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 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204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d)*1i)/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)) - (d^2*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 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1932*a^3*b^13*c^14*d^5 + 920*a^3*b^13*c^16*d^3 - 336*a^4*b^12*c^7*d^12 + 1188*a^4*b^12*c^9*d^10 - 2808*a^4*b^12*c^11*d^8 + 3980*a^4*b^12*c^13*d^6 - 2616*a^4*b^12*c^15*d^4 + 600*a^4*b^12*c^17*d^2 + 168*a^5*b^11*c^6*d^13 - 336*a^5*b^11*c^8*d^11 + 1740*a^5*b^11*c^10*d^9 - 4720*a^5*b^11*c^12*d^7 + 4812*a^5*b^11*c^14*d^5 - 1752*a^5*b^11*c^16*d^3 + 168*a^6*b^10*c^5*d^14 - 1344*a^6*b^10*c^7*d^12 + 2292*a^6*b^10*c^9*d^10 + 1088*a^6*b^10*c^11*d^8 - 4908*a^6*b^10*c^13*d^6 + 3096*a^6*b^10*c^15*d^4 - 392*a^6*b^10*c^17*d^2 - 336*a^7*b^9*c^4*d^15 + 2520*a^7*b^9*c^6*d^13 - 7488*a^7*b^9*c^8*d^11 + 7556*a^7*b^9*c^10*d^9 - 144*a^7*b^9*c^12*d^7 - 3012*a^7*b^9*c^14*d^5 + 904*a^7*b^9*c^16*d^3 + 240*a^8*b^8*c^3*d^16 - 2472*a^8*b^8*c^5*d^14 + 10416*a^8*b^8*c^7*d^12 - 16596*a^8*b^8*c^9*d^10 + 9600*a^8*b^8*c^11*d^8 - 156*a^8*b^8*c^13*d^6 - 1032*a^8*b^8*c^15*d^4 - 84*a^9*b^7*c^2*d^17 + 1632*a^9*b^7*c^4*d^15 - 9204*a^9*b^7*c^6*d^13 + 19800*a^9*b^7*c^8*d^11 - 18048*a^9*b^7*c^10*d^9 + 5856*a^9*b^7*c^12*d^7 + 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18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (d^2*((8*(4*a^2*b^16*c^22 - 8*a^4*b^14*c^22 + 4*a^6*b^12*c^22 - 4*a^18*c^2*d^20 + 16*a^18*c^4*d^18 - 24*a^18*c^6*d^16 + 16*a^18*c^8*d^14 - 4*a^18*c^10*d^12 - 4*a*b^17*c^13*d^9 + 16*a*b^17*c^15*d^7 - 24*a*b^17*c^17*d^5 + 16*a*b^17*c^19*d^3 - 32*a^3*b^15*c^21*d + 76*a^5*b^13*c^21*d - 40*a^7*b^11*c^21*d + 4*a^13*b^5*c*d^21 - 8*a^15*b^3*c*d^21 + 24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 40*a^12*b^6*c^2*d^20 + 864*a^12*b^6*c^4*d^18 - 2264*a^12*b^6*c^6*d^16 + 1216*a^12*b^6*c^8*d^14 + 1896*a^12*b^6*c^10*d^12 - 2464*a^12*b^6*c^12*d^10 + 792*a^12*b^6*c^14*d^8 - 328*a^13*b^5*c^3*d^19 + 1052*a^13*b^5*c^5*d^17 - 480*a^13*b^5*c^7*d^15 - 2180*a^13*b^5*c^9*d^13 + 3736*a^13*b^5*c^11*d^11 - 2332*a^13*b^5*c^13*d^9 + 528*a^13*b^5*c^15*d^7 + 76*a^14*b^4*c^2*d^20 - 392*a^14*b^4*c^4*d^18 + 148*a^14*b^4*c^6*d^16 + 1808*a^14*b^4*c^8*d^14 - 3532*a^14*b^4*c^10*d^12 + 2552*a^14*b^4*c^12*d^10 - 660*a^14*b^4*c^14*d^8 + 128*a^15*b^3*c^3*d^19 + 8*a^15*b^3*c^5*d^17 - 1152*a^15*b^3*c^7*d^15 + 2248*a^15*b^3*c^9*d^13 - 1664*a^15*b^3*c^11*d^11 + 440*a^15*b^3*c^13*d^9 - 32*a^16*b^2*c^2*d^20 - 48*a^16*b^2*c^4*d^18 + 512*a^16*b^2*c^6*d^16 - 928*a^16*b^2*c^8*d^14 + 672*a^16*b^2*c^10*d^12 - 176*a^16*b^2*c^12*d^10 - 4*a*b^17*c^21*d + 4*a^17*b*c*d^21))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 1320*a^10*b^8*c^19*d^3 - 176*a^11*b^7*c^2*d^20 + 8096*a^11*b^7*c^4*d^18 - 54384*a^11*b^7*c^6*d^16 + 156992*a^11*b^7*c^8*d^14 - 242528*a^11*b^7*c^10*d^12 + 214368*a^11*b^7*c^12*d^10 - 107184*a^11*b^7*c^14*d^8 + 27456*a^11*b^7*c^16*d^6 - 2640*a^11*b^7*c^18*d^4 - 2496*a^12*b^6*c^3*d^19 + 24784*a^12*b^6*c^5*d^17 - 89280*a^12*b^6*c^7*d^15 + 162336*a^12*b^6*c^9*d^13 - 165760*a^12*b^6*c^11*d^11 + 96272*a^12*b^6*c^13*d^9 - 29568*a^12*b^6*c^15*d^7 + 3696*a^12*b^6*c^17*d^5 + 484*a^13*b^5*c^2*d^20 - 8888*a^13*b^5*c^4*d^18 + 40876*a^13*b^5*c^6*d^16 - 88000*a^13*b^5*c^8*d^14 + 104060*a^13*b^5*c^10*d^12 - 69784*a^13*b^5*c^12*d^10 + 24948*a^13*b^5*c^14*d^8 - 3696*a^13*b^5*c^16*d^6 + 2408*a^14*b^4*c^3*d^19 - 14692*a^14*b^4*c^5*d^17 + 38208*a^14*b^4*c^7*d^15 - 52532*a^14*b^4*c^9*d^13 + 40072*a^14*b^4*c^11*d^11 - 16060*a^14*b^4*c^13*d^9 + 2640*a^14*b^4*c^15*d^7 - 440*a^15*b^3*c^2*d^20 + 4048*a^15*b^3*c^4*d^18 - 13112*a^15*b^3*c^6*d^16 + 20768*a^15*b^3*c^8*d^14 - 17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d)*1i)/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))/((16*(864*a*b^11*c^5*d^8 - 486*a*b^11*c^3*d^10 - 702*a*b^11*c^7*d^6 + 216*a*b^11*c^9*d^4 - 216*a^3*b^9*c*d^12 + 63*a^5*b^7*c*d^12 + 41*a^7*b^5*c*d^12 + 4*a^9*b^3*c*d^12 + 162*a^2*b^10*c^2*d^11 - 783*a^2*b^10*c^4*d^9 + 1278*a^2*b^10*c^6*d^7 - 828*a^2*b^10*c^8*d^5 + 144*a^2*b^10*c^10*d^3 + 1197*a^3*b^9*c^3*d^10 - 2511*a^3*b^9*c^5*d^8 + 2328*a^3*b^9*c^7*d^6 - 750*a^3*b^9*c^9*d^4 + 24*a^3*b^9*c^11*d^2 - 261*a^4*b^8*c^2*d^11 + 1444*a^4*b^8*c^4*d^9 - 2508*a^4*b^8*c^6*d^7 + 1518*a^4*b^8*c^8*d^5 - 184*a^4*b^8*c^10*d^3 - 696*a^5*b^7*c^3*d^10 + 1913*a^5*b^7*c^5*d^8 - 1936*a^5*b^7*c^7*d^6 + 476*a^5*b^7*c^9*d^4 + 66*a^6*b^6*c^2*d^11 - 583*a^6*b^6*c^4*d^9 + 1232*a^6*b^6*c^6*d^7 - 580*a^6*b^6*c^8*d^5 - 21*a^7*b^5*c^3*d^10 - 312*a^7*b^5*c^5*d^8 + 364*a^7*b^5*c^7*d^6 + 19*a^8*b^4*c^2*d^11 - 20*a^8*b^4*c^4*d^9 - 116*a^8*b^4*c^6*d^7 + 16*a^9*b^3*c^3*d^10 + 16*a^9*b^3*c^5*d^8 + 108*a*b^11*c*d^12))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (16*tan(e/2 + (f*x)/2)*(108*a*b^11*c^2*d^11 - 486*a*b^11*c^4*d^9 + 756*a*b^11*c^6*d^7 - 432*a*b^11*c^8*d^5 + 108*a^2*b^10*c*d^12 - 162*a^4*b^8*c*d^12 + 18*a^6*b^6*c*d^12 + 8*a^8*b^4*c*d^12 - 270*a^2*b^10*c^3*d^10 + 90*a^2*b^10*c^5*d^8 + 216*a^2*b^10*c^7*d^6 - 162*a^3*b^9*c^2*d^11 + 864*a^3*b^9*c^4*d^9 - 1632*a^3*b^9*c^6*d^7 + 900*a^3*b^9*c^8*d^5 + 48*a^3*b^9*c^10*d^3 + 396*a^4*b^8*c^3*d^10 + 82*a^4*b^8*c^5*d^8 - 596*a^4*b^8*c^7*d^6 - 80*a^4*b^8*c^9*d^4 + 36*a^5*b^7*c^2*d^11 - 398*a^5*b^7*c^4*d^9 + 1216*a^5*b^7*c^6*d^7 - 584*a^5*b^7*c^8*d^5 - 42*a^6*b^6*c^3*d^10 - 432*a^6*b^6*c^5*d^8 + 600*a^6*b^6*c^7*d^6 + 38*a^7*b^5*c^2*d^11 - 40*a^7*b^5*c^4*d^9 - 232*a^7*b^5*c^6*d^7 + 32*a^8*b^4*c^3*d^10 + 32*a^8*b^4*c^5*d^8))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (d^2*(-(c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 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3528*a^4*b^12*c^8*d^11 - 7810*a^4*b^12*c^10*d^9 + 8696*a^4*b^12*c^12*d^7 - 4770*a^4*b^12*c^14*d^5 + 1084*a^4*b^12*c^16*d^3 + 840*a^5*b^11*c^5*d^14 - 5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(4*a^16*c*d^18 + 8*a^2*b^14*c^19 - 8*a^4*b^12*c^19 - 12*a^16*c^5*d^14 + 8*a^16*c^7*d^12 + 12*a*b^15*c^10*d^9 - 48*a*b^15*c^12*d^7 + 84*a*b^15*c^14*d^5 - 72*a*b^15*c^16*d^3 - 112*a^3*b^13*c^18*d + 88*a^5*b^11*c^18*d + 12*a^10*b^6*c*d^18 - 28*a^12*b^4*c*d^18 + 12*a^14*b^2*c*d^18 - 20*a^15*b*c^2*d^17 - 48*a^15*b*c^4*d^15 + 156*a^15*b*c^6*d^13 - 88*a^15*b*c^8*d^11 - 84*a^2*b^14*c^9*d^10 + 328*a^2*b^14*c^11*d^8 - 596*a^2*b^14*c^13*d^6 + 552*a^2*b^14*c^15*d^4 - 208*a^2*b^14*c^17*d^2 + 240*a^3*b^13*c^8*d^11 - 908*a^3*b^13*c^10*d^9 + 1792*a^3*b^13*c^12*d^7 - 1932*a^3*b^13*c^14*d^5 + 920*a^3*b^13*c^16*d^3 - 336*a^4*b^12*c^7*d^12 + 1188*a^4*b^12*c^9*d^10 - 2808*a^4*b^12*c^11*d^8 + 3980*a^4*b^12*c^13*d^6 - 2616*a^4*b^12*c^15*d^4 + 600*a^4*b^12*c^17*d^2 + 168*a^5*b^11*c^6*d^13 - 336*a^5*b^11*c^8*d^11 + 1740*a^5*b^11*c^10*d^9 - 4720*a^5*b^11*c^12*d^7 + 4812*a^5*b^11*c^14*d^5 - 1752*a^5*b^11*c^16*d^3 + 168*a^6*b^10*c^5*d^14 - 1344*a^6*b^10*c^7*d^12 + 2292*a^6*b^10*c^9*d^10 + 1088*a^6*b^10*c^11*d^8 - 4908*a^6*b^10*c^13*d^6 + 3096*a^6*b^10*c^15*d^4 - 392*a^6*b^10*c^17*d^2 - 336*a^7*b^9*c^4*d^15 + 2520*a^7*b^9*c^6*d^13 - 7488*a^7*b^9*c^8*d^11 + 7556*a^7*b^9*c^10*d^9 - 144*a^7*b^9*c^12*d^7 - 3012*a^7*b^9*c^14*d^5 + 904*a^7*b^9*c^16*d^3 + 240*a^8*b^8*c^3*d^16 - 2472*a^8*b^8*c^5*d^14 + 10416*a^8*b^8*c^7*d^12 - 16596*a^8*b^8*c^9*d^10 + 9600*a^8*b^8*c^11*d^8 - 156*a^8*b^8*c^13*d^6 - 1032*a^8*b^8*c^15*d^4 - 84*a^9*b^7*c^2*d^17 + 1632*a^9*b^7*c^4*d^15 - 9204*a^9*b^7*c^6*d^13 + 19800*a^9*b^7*c^8*d^11 - 18048*a^9*b^7*c^10*d^9 + 5856*a^9*b^7*c^12*d^7 + 48*a^9*b^7*c^14*d^5 - 744*a^10*b^6*c^3*d^16 + 5460*a^10*b^6*c^5*d^14 - 15960*a^10*b^6*c^7*d^12 + 20136*a^10*b^6*c^9*d^10 - 10584*a^10*b^6*c^11*d^8 + 1680*a^10*b^6*c^13*d^6 + 212*a^11*b^5*c^2*d^17 - 2176*a^11*b^5*c^4*d^15 + 9180*a^11*b^5*c^6*d^13 - 15416*a^11*b^5*c^8*d^11 + 10936*a^11*b^5*c^10*d^9 - 2736*a^11*b^5*c^12*d^7 + 584*a^12*b^4*c^3*d^16 - 3708*a^12*b^4*c^5*d^14 + 8152*a^12*b^4*c^7*d^12 - 7376*a^12*b^4*c^9*d^10 + 2376*a^12*b^4*c^11*d^8 - 108*a^13*b^3*c^2*d^17 + 928*a^13*b^3*c^4*d^15 - 2820*a^13*b^3*c^6*d^13 + 3288*a^13*b^3*c^8*d^11 - 1288*a^13*b^3*c^10*d^9 - 80*a^14*b^2*c^3*d^16 + 564*a^14*b^2*c^5*d^14 - 936*a^14*b^2*c^7*d^12 + 440*a^14*b^2*c^9*d^10 + 24*a*b^15*c^18*d))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (d^2*((8*(4*a^2*b^16*c^22 - 8*a^4*b^14*c^22 + 4*a^6*b^12*c^22 - 4*a^18*c^2*d^20 + 16*a^18*c^4*d^18 - 24*a^18*c^6*d^16 + 16*a^18*c^8*d^14 - 4*a^18*c^10*d^12 - 4*a*b^17*c^13*d^9 + 16*a*b^17*c^15*d^7 - 24*a*b^17*c^17*d^5 + 16*a*b^17*c^19*d^3 - 32*a^3*b^15*c^21*d + 76*a^5*b^13*c^21*d - 40*a^7*b^11*c^21*d + 4*a^13*b^5*c*d^21 - 8*a^15*b^3*c*d^21 + 24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 40*a^12*b^6*c^2*d^20 + 864*a^12*b^6*c^4*d^18 - 2264*a^12*b^6*c^6*d^16 + 1216*a^12*b^6*c^8*d^14 + 1896*a^12*b^6*c^10*d^12 - 2464*a^12*b^6*c^12*d^10 + 792*a^12*b^6*c^14*d^8 - 328*a^13*b^5*c^3*d^19 + 1052*a^13*b^5*c^5*d^17 - 480*a^13*b^5*c^7*d^15 - 2180*a^13*b^5*c^9*d^13 + 3736*a^13*b^5*c^11*d^11 - 2332*a^13*b^5*c^13*d^9 + 528*a^13*b^5*c^15*d^7 + 76*a^14*b^4*c^2*d^20 - 392*a^14*b^4*c^4*d^18 + 148*a^14*b^4*c^6*d^16 + 1808*a^14*b^4*c^8*d^14 - 3532*a^14*b^4*c^10*d^12 + 2552*a^14*b^4*c^12*d^10 - 660*a^14*b^4*c^14*d^8 + 128*a^15*b^3*c^3*d^19 + 8*a^15*b^3*c^5*d^17 - 1152*a^15*b^3*c^7*d^15 + 2248*a^15*b^3*c^9*d^13 - 1664*a^15*b^3*c^11*d^11 + 440*a^15*b^3*c^13*d^9 - 32*a^16*b^2*c^2*d^20 - 48*a^16*b^2*c^4*d^18 + 512*a^16*b^2*c^6*d^16 - 928*a^16*b^2*c^8*d^14 + 672*a^16*b^2*c^10*d^12 - 176*a^16*b^2*c^12*d^10 - 4*a*b^17*c^21*d + 4*a^17*b*c*d^21))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 1320*a^10*b^8*c^19*d^3 - 176*a^11*b^7*c^2*d^20 + 8096*a^11*b^7*c^4*d^18 - 54384*a^11*b^7*c^6*d^16 + 156992*a^11*b^7*c^8*d^14 - 242528*a^11*b^7*c^10*d^12 + 214368*a^11*b^7*c^12*d^10 - 107184*a^11*b^7*c^14*d^8 + 27456*a^11*b^7*c^16*d^6 - 2640*a^11*b^7*c^18*d^4 - 2496*a^12*b^6*c^3*d^19 + 24784*a^12*b^6*c^5*d^17 - 89280*a^12*b^6*c^7*d^15 + 162336*a^12*b^6*c^9*d^13 - 165760*a^12*b^6*c^11*d^11 + 96272*a^12*b^6*c^13*d^9 - 29568*a^12*b^6*c^15*d^7 + 3696*a^12*b^6*c^17*d^5 + 484*a^13*b^5*c^2*d^20 - 8888*a^13*b^5*c^4*d^18 + 40876*a^13*b^5*c^6*d^16 - 88000*a^13*b^5*c^8*d^14 + 104060*a^13*b^5*c^10*d^12 - 69784*a^13*b^5*c^12*d^10 + 24948*a^13*b^5*c^14*d^8 - 3696*a^13*b^5*c^16*d^6 + 2408*a^14*b^4*c^3*d^19 - 14692*a^14*b^4*c^5*d^17 + 38208*a^14*b^4*c^7*d^15 - 52532*a^14*b^4*c^9*d^13 + 40072*a^14*b^4*c^11*d^11 - 16060*a^14*b^4*c^13*d^9 + 2640*a^14*b^4*c^15*d^7 - 440*a^15*b^3*c^2*d^20 + 4048*a^15*b^3*c^4*d^18 - 13112*a^15*b^3*c^6*d^16 + 20768*a^15*b^3*c^8*d^14 - 17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)) - (d^2*(-(c + d)^5*(c - d)^5)^(1/2)*((8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 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5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 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1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(4*a^16*c*d^18 + 8*a^2*b^14*c^19 - 8*a^4*b^12*c^19 - 12*a^16*c^5*d^14 + 8*a^16*c^7*d^12 + 12*a*b^15*c^10*d^9 - 48*a*b^15*c^12*d^7 + 84*a*b^15*c^14*d^5 - 72*a*b^15*c^16*d^3 - 112*a^3*b^13*c^18*d + 88*a^5*b^11*c^18*d + 12*a^10*b^6*c*d^18 - 28*a^12*b^4*c*d^18 + 12*a^14*b^2*c*d^18 - 20*a^15*b*c^2*d^17 - 48*a^15*b*c^4*d^15 + 156*a^15*b*c^6*d^13 - 88*a^15*b*c^8*d^11 - 84*a^2*b^14*c^9*d^10 + 328*a^2*b^14*c^11*d^8 - 596*a^2*b^14*c^13*d^6 + 552*a^2*b^14*c^15*d^4 - 208*a^2*b^14*c^17*d^2 + 240*a^3*b^13*c^8*d^11 - 908*a^3*b^13*c^10*d^9 + 1792*a^3*b^13*c^12*d^7 - 1932*a^3*b^13*c^14*d^5 + 920*a^3*b^13*c^16*d^3 - 336*a^4*b^12*c^7*d^12 + 1188*a^4*b^12*c^9*d^10 - 2808*a^4*b^12*c^11*d^8 + 3980*a^4*b^12*c^13*d^6 - 2616*a^4*b^12*c^15*d^4 + 600*a^4*b^12*c^17*d^2 + 168*a^5*b^11*c^6*d^13 - 336*a^5*b^11*c^8*d^11 + 1740*a^5*b^11*c^10*d^9 - 4720*a^5*b^11*c^12*d^7 + 4812*a^5*b^11*c^14*d^5 - 1752*a^5*b^11*c^16*d^3 + 168*a^6*b^10*c^5*d^14 - 1344*a^6*b^10*c^7*d^12 + 2292*a^6*b^10*c^9*d^10 + 1088*a^6*b^10*c^11*d^8 - 4908*a^6*b^10*c^13*d^6 + 3096*a^6*b^10*c^15*d^4 - 392*a^6*b^10*c^17*d^2 - 336*a^7*b^9*c^4*d^15 + 2520*a^7*b^9*c^6*d^13 - 7488*a^7*b^9*c^8*d^11 + 7556*a^7*b^9*c^10*d^9 - 144*a^7*b^9*c^12*d^7 - 3012*a^7*b^9*c^14*d^5 + 904*a^7*b^9*c^16*d^3 + 240*a^8*b^8*c^3*d^16 - 2472*a^8*b^8*c^5*d^14 + 10416*a^8*b^8*c^7*d^12 - 16596*a^8*b^8*c^9*d^10 + 9600*a^8*b^8*c^11*d^8 - 156*a^8*b^8*c^13*d^6 - 1032*a^8*b^8*c^15*d^4 - 84*a^9*b^7*c^2*d^17 + 1632*a^9*b^7*c^4*d^15 - 9204*a^9*b^7*c^6*d^13 + 19800*a^9*b^7*c^8*d^11 - 18048*a^9*b^7*c^10*d^9 + 5856*a^9*b^7*c^12*d^7 + 48*a^9*b^7*c^14*d^5 - 744*a^10*b^6*c^3*d^16 + 5460*a^10*b^6*c^5*d^14 - 15960*a^10*b^6*c^7*d^12 + 20136*a^10*b^6*c^9*d^10 - 10584*a^10*b^6*c^11*d^8 + 1680*a^10*b^6*c^13*d^6 + 212*a^11*b^5*c^2*d^17 - 2176*a^11*b^5*c^4*d^15 + 9180*a^11*b^5*c^6*d^13 - 15416*a^11*b^5*c^8*d^11 + 10936*a^11*b^5*c^10*d^9 - 2736*a^11*b^5*c^12*d^7 + 584*a^12*b^4*c^3*d^16 - 3708*a^12*b^4*c^5*d^14 + 8152*a^12*b^4*c^7*d^12 - 7376*a^12*b^4*c^9*d^10 + 2376*a^12*b^4*c^11*d^8 - 108*a^13*b^3*c^2*d^17 + 928*a^13*b^3*c^4*d^15 - 2820*a^13*b^3*c^6*d^13 + 3288*a^13*b^3*c^8*d^11 - 1288*a^13*b^3*c^10*d^9 - 80*a^14*b^2*c^3*d^16 + 564*a^14*b^2*c^5*d^14 - 936*a^14*b^2*c^7*d^12 + 440*a^14*b^2*c^9*d^10 + 24*a*b^15*c^18*d))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 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24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 40*a^12*b^6*c^2*d^20 + 864*a^12*b^6*c^4*d^18 - 2264*a^12*b^6*c^6*d^16 + 1216*a^12*b^6*c^8*d^14 + 1896*a^12*b^6*c^10*d^12 - 2464*a^12*b^6*c^12*d^10 + 792*a^12*b^6*c^14*d^8 - 328*a^13*b^5*c^3*d^19 + 1052*a^13*b^5*c^5*d^17 - 480*a^13*b^5*c^7*d^15 - 2180*a^13*b^5*c^9*d^13 + 3736*a^13*b^5*c^11*d^11 - 2332*a^13*b^5*c^13*d^9 + 528*a^13*b^5*c^15*d^7 + 76*a^14*b^4*c^2*d^20 - 392*a^14*b^4*c^4*d^18 + 148*a^14*b^4*c^6*d^16 + 1808*a^14*b^4*c^8*d^14 - 3532*a^14*b^4*c^10*d^12 + 2552*a^14*b^4*c^12*d^10 - 660*a^14*b^4*c^14*d^8 + 128*a^15*b^3*c^3*d^19 + 8*a^15*b^3*c^5*d^17 - 1152*a^15*b^3*c^7*d^15 + 2248*a^15*b^3*c^9*d^13 - 1664*a^15*b^3*c^11*d^11 + 440*a^15*b^3*c^13*d^9 - 32*a^16*b^2*c^2*d^20 - 48*a^16*b^2*c^4*d^18 + 512*a^16*b^2*c^6*d^16 - 928*a^16*b^2*c^8*d^14 + 672*a^16*b^2*c^10*d^12 - 176*a^16*b^2*c^12*d^10 - 4*a*b^17*c^21*d + 4*a^17*b*c*d^21))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 1320*a^10*b^8*c^19*d^3 - 176*a^11*b^7*c^2*d^20 + 8096*a^11*b^7*c^4*d^18 - 54384*a^11*b^7*c^6*d^16 + 156992*a^11*b^7*c^8*d^14 - 242528*a^11*b^7*c^10*d^12 + 214368*a^11*b^7*c^12*d^10 - 107184*a^11*b^7*c^14*d^8 + 27456*a^11*b^7*c^16*d^6 - 2640*a^11*b^7*c^18*d^4 - 2496*a^12*b^6*c^3*d^19 + 24784*a^12*b^6*c^5*d^17 - 89280*a^12*b^6*c^7*d^15 + 162336*a^12*b^6*c^9*d^13 - 165760*a^12*b^6*c^11*d^11 + 96272*a^12*b^6*c^13*d^9 - 29568*a^12*b^6*c^15*d^7 + 3696*a^12*b^6*c^17*d^5 + 484*a^13*b^5*c^2*d^20 - 8888*a^13*b^5*c^4*d^18 + 40876*a^13*b^5*c^6*d^16 - 88000*a^13*b^5*c^8*d^14 + 104060*a^13*b^5*c^10*d^12 - 69784*a^13*b^5*c^12*d^10 + 24948*a^13*b^5*c^14*d^8 - 3696*a^13*b^5*c^16*d^6 + 2408*a^14*b^4*c^3*d^19 - 14692*a^14*b^4*c^5*d^17 + 38208*a^14*b^4*c^7*d^15 - 52532*a^14*b^4*c^9*d^13 + 40072*a^14*b^4*c^11*d^11 - 16060*a^14*b^4*c^13*d^9 + 2640*a^14*b^4*c^15*d^7 - 440*a^15*b^3*c^2*d^20 + 4048*a^15*b^3*c^4*d^18 - 13112*a^15*b^3*c^6*d^16 + 20768*a^15*b^3*c^8*d^14 - 17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)))*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d))/(2*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13))))*(-(c + d)^5*(c - d)^5)^(1/2)*(a^2*d^4 + 12*b^2*c^4 + 6*b^2*d^4 + 2*a^2*c^2*d^2 - 15*b^2*c^2*d^2 + 2*a*b*c*d^3 - 8*a*b*c^3*d)*1i)/(f*(a^4*d^14 - b^4*c^14 - 5*a^4*c^2*d^12 + 10*a^4*c^4*d^10 - 10*a^4*c^6*d^8 + 5*a^4*c^8*d^6 - a^4*c^10*d^4 + b^4*c^4*d^10 - 5*b^4*c^6*d^8 + 10*b^4*c^8*d^6 - 10*b^4*c^10*d^4 + 5*b^4*c^12*d^2 - 4*a*b^3*c^3*d^11 + 20*a*b^3*c^5*d^9 - 40*a*b^3*c^7*d^7 + 40*a*b^3*c^9*d^5 - 20*a*b^3*c^11*d^3 + 20*a^3*b*c^3*d^11 - 40*a^3*b*c^5*d^9 + 40*a^3*b*c^7*d^7 - 20*a^3*b*c^9*d^5 + 4*a^3*b*c^11*d^3 + 6*a^2*b^2*c^2*d^12 - 30*a^2*b^2*c^4*d^10 + 60*a^2*b^2*c^6*d^8 - 60*a^2*b^2*c^8*d^6 + 30*a^2*b^2*c^10*d^4 - 6*a^2*b^2*c^12*d^2 + 4*a*b^3*c^13*d - 4*a^3*b*c*d^13)) - ((a^4*d^6 + 2*b^4*c^6 - a^2*b^2*d^6 - 4*a^4*c^2*d^4 + 2*b^4*c^2*d^4 - 4*b^4*c^4*d^2 - 8*a*b^3*c^3*d^3 + 8*a^3*b*c^3*d^3 + 4*a^2*b^2*c^2*d^4 + 5*a*b^3*c*d^5 - 5*a^3*b*c*d^5)/((a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 - b^2*c^4 - b^2*d^4 - 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)) - (tan(e/2 + (f*x)/2)^4*(2*a^3*b^2*d^8 - 2*a*b^4*c^8 - 8*b^5*c^7*d - 2*a^5*d^8 + 7*a^5*c^2*d^6 + 4*a^5*c^4*d^4 - 8*b^5*c^3*d^5 + 16*b^5*c^5*d^3 - 12*a*b^4*c^2*d^6 + 16*a*b^4*c^4*d^4 + 4*a*b^4*c^6*d^2 - 6*a^2*b^3*c*d^7 - a^4*b*c^3*d^5 - 8*a^4*b*c^5*d^3 + a^2*b^3*c^3*d^5 + 8*a^2*b^3*c^5*d^3 + 5*a^3*b^2*c^2*d^6 - 22*a^3*b^2*c^4*d^4 + 6*a^4*b*c*d^7))/(a*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 - b^2*c^4 - b^2*d^4 - 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)) + (tan(e/2 + (f*x)/2)*(2*a^5*d^7 + 2*b^5*c^7 - 2*a^3*b^2*d^7 - 11*a^5*c^2*d^5 + 2*b^5*c^3*d^4 - 4*b^5*c^5*d^2 + 18*a*b^4*c^2*d^5 - 32*a*b^4*c^4*d^3 + 12*a^2*b^3*c*d^6 + 15*a^4*b*c^3*d^4 - 15*a^2*b^3*c^3*d^4 + a^3*b^2*c^2*d^5 + 16*a^3*b^2*c^4*d^3 + 8*a*b^4*c^6*d - 12*a^4*b*c*d^6))/(a*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 - b^2*c^4 - b^2*d^4 - 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^5*(2*a^5*d^7 + 2*b^5*c^7 - 2*a^3*b^2*d^7 - 5*a^5*c^2*d^5 + 2*b^5*c^3*d^4 - 4*b^5*c^5*d^2 + 6*a^2*b^3*c*d^6 + 9*a^4*b*c^3*d^4 - 9*a^2*b^3*c^3*d^4 + 5*a^3*b^2*c^2*d^5 - 6*a^4*b*c*d^6))/(a*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 - b^2*c^4 - b^2*d^4 - 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)) + (2*tan(e/2 + (f*x)/2)^2*(a^5*d^8 + 2*a*b^4*c^8 + 4*b^5*c^7*d - a^3*b^2*d^8 - 3*a^5*c^2*d^6 - 4*a^5*c^4*d^4 + 4*b^5*c^3*d^5 - 8*b^5*c^5*d^3 + 18*a*b^4*c^2*d^6 - 29*a*b^4*c^4*d^4 + 3*a^2*b^3*c*d^7 - 8*a^4*b*c^3*d^5 + 8*a^4*b*c^5*d^3 + 8*a^2*b^3*c^3*d^5 - 8*a^2*b^3*c^5*d^3 - 11*a^3*b^2*c^2*d^6 + 27*a^3*b^2*c^4*d^4 - 3*a^4*b*c*d^7))/(a*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 - b^2*c^4 - b^2*d^4 - 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)) + (2*tan(e/2 + (f*x)/2)^3*(b*c^2 + 2*b*d^2 + 2*a*c*d)*(a^4*d^6 + 2*b^4*c^6 - a^2*b^2*d^6 - 4*a^4*c^2*d^4 + 2*b^4*c^2*d^4 - 4*b^4*c^4*d^2 - 8*a*b^3*c^3*d^3 + 8*a^3*b*c^3*d^3 + 4*a^2*b^2*c^2*d^4 + 5*a*b^3*c*d^5 - 5*a^3*b*c*d^5))/(a*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^2*c^4 + a^2*d^4 - b^2*c^4 - b^2*d^4 - 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2)))/(f*(a*c^2 + tan(e/2 + (f*x)/2)^2*(3*a*c^2 + 4*a*d^2 + 8*b*c*d) + tan(e/2 + (f*x)/2)^4*(3*a*c^2 + 4*a*d^2 + 8*b*c*d) + tan(e/2 + (f*x)/2)^3*(4*b*c^2 + 8*b*d^2 + 8*a*c*d) + tan(e/2 + (f*x)/2)*(2*b*c^2 + 4*a*c*d) + tan(e/2 + (f*x)/2)^5*(2*b*c^2 + 4*a*c*d) + a*c^2*tan(e/2 + (f*x)/2)^6)) - (b^3*atan(((b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^3*b^13*c^19 - 4*a^5*b^11*c^19 + 2*a^16*c^2*d^17 - 6*a^16*c^6*d^13 + 4*a^16*c^8*d^11 + 12*a*b^15*c^9*d^10 - 54*a*b^15*c^11*d^8 + 96*a*b^15*c^13*d^6 - 78*a*b^15*c^15*d^4 + 24*a*b^15*c^17*d^2 + 12*a^2*b^14*c^18*d - 56*a^4*b^12*c^18*d + 44*a^6*b^10*c^18*d + 12*a^9*b^7*c*d^18 - 28*a^11*b^5*c*d^18 + 16*a^13*b^3*c*d^18 - 10*a^15*b*c^3*d^16 - 24*a^15*b*c^5*d^14 + 78*a^15*b*c^7*d^12 - 44*a^15*b*c^9*d^10 - 96*a^2*b^14*c^8*d^11 + 442*a^2*b^14*c^10*d^9 - 816*a^2*b^14*c^12*d^7 + 702*a^2*b^14*c^14*d^5 - 244*a^2*b^14*c^16*d^3 + 336*a^3*b^13*c^7*d^12 - 1620*a^3*b^13*c^9*d^10 + 3206*a^3*b^13*c^11*d^8 - 3064*a^3*b^13*c^13*d^6 + 1314*a^3*b^13*c^15*d^4 - 176*a^3*b^13*c^17*d^2 - 672*a^4*b^12*c^6*d^13 + 3528*a^4*b^12*c^8*d^11 - 7810*a^4*b^12*c^10*d^9 + 8696*a^4*b^12*c^12*d^7 - 4770*a^4*b^12*c^14*d^5 + 1084*a^4*b^12*c^16*d^3 + 840*a^5*b^11*c^5*d^14 - 5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - 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36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(4*a^16*c*d^18 + 8*a^2*b^14*c^19 - 8*a^4*b^12*c^19 - 12*a^16*c^5*d^14 + 8*a^16*c^7*d^12 + 12*a*b^15*c^10*d^9 - 48*a*b^15*c^12*d^7 + 84*a*b^15*c^14*d^5 - 72*a*b^15*c^16*d^3 - 112*a^3*b^13*c^18*d + 88*a^5*b^11*c^18*d + 12*a^10*b^6*c*d^18 - 28*a^12*b^4*c*d^18 + 12*a^14*b^2*c*d^18 - 20*a^15*b*c^2*d^17 - 48*a^15*b*c^4*d^15 + 156*a^15*b*c^6*d^13 - 88*a^15*b*c^8*d^11 - 84*a^2*b^14*c^9*d^10 + 328*a^2*b^14*c^11*d^8 - 596*a^2*b^14*c^13*d^6 + 552*a^2*b^14*c^15*d^4 - 208*a^2*b^14*c^17*d^2 + 240*a^3*b^13*c^8*d^11 - 908*a^3*b^13*c^10*d^9 + 1792*a^3*b^13*c^12*d^7 - 1932*a^3*b^13*c^14*d^5 + 920*a^3*b^13*c^16*d^3 - 336*a^4*b^12*c^7*d^12 + 1188*a^4*b^12*c^9*d^10 - 2808*a^4*b^12*c^11*d^8 + 3980*a^4*b^12*c^13*d^6 - 2616*a^4*b^12*c^15*d^4 + 600*a^4*b^12*c^17*d^2 + 168*a^5*b^11*c^6*d^13 - 336*a^5*b^11*c^8*d^11 + 1740*a^5*b^11*c^10*d^9 - 4720*a^5*b^11*c^12*d^7 + 4812*a^5*b^11*c^14*d^5 - 1752*a^5*b^11*c^16*d^3 + 168*a^6*b^10*c^5*d^14 - 1344*a^6*b^10*c^7*d^12 + 2292*a^6*b^10*c^9*d^10 + 1088*a^6*b^10*c^11*d^8 - 4908*a^6*b^10*c^13*d^6 + 3096*a^6*b^10*c^15*d^4 - 392*a^6*b^10*c^17*d^2 - 336*a^7*b^9*c^4*d^15 + 2520*a^7*b^9*c^6*d^13 - 7488*a^7*b^9*c^8*d^11 + 7556*a^7*b^9*c^10*d^9 - 144*a^7*b^9*c^12*d^7 - 3012*a^7*b^9*c^14*d^5 + 904*a^7*b^9*c^16*d^3 + 240*a^8*b^8*c^3*d^16 - 2472*a^8*b^8*c^5*d^14 + 10416*a^8*b^8*c^7*d^12 - 16596*a^8*b^8*c^9*d^10 + 9600*a^8*b^8*c^11*d^8 - 156*a^8*b^8*c^13*d^6 - 1032*a^8*b^8*c^15*d^4 - 84*a^9*b^7*c^2*d^17 + 1632*a^9*b^7*c^4*d^15 - 9204*a^9*b^7*c^6*d^13 + 19800*a^9*b^7*c^8*d^11 - 18048*a^9*b^7*c^10*d^9 + 5856*a^9*b^7*c^12*d^7 + 48*a^9*b^7*c^14*d^5 - 744*a^10*b^6*c^3*d^16 + 5460*a^10*b^6*c^5*d^14 - 15960*a^10*b^6*c^7*d^12 + 20136*a^10*b^6*c^9*d^10 - 10584*a^10*b^6*c^11*d^8 + 1680*a^10*b^6*c^13*d^6 + 212*a^11*b^5*c^2*d^17 - 2176*a^11*b^5*c^4*d^15 + 9180*a^11*b^5*c^6*d^13 - 15416*a^11*b^5*c^8*d^11 + 10936*a^11*b^5*c^10*d^9 - 2736*a^11*b^5*c^12*d^7 + 584*a^12*b^4*c^3*d^16 - 3708*a^12*b^4*c^5*d^14 + 8152*a^12*b^4*c^7*d^12 - 7376*a^12*b^4*c^9*d^10 + 2376*a^12*b^4*c^11*d^8 - 108*a^13*b^3*c^2*d^17 + 928*a^13*b^3*c^4*d^15 - 2820*a^13*b^3*c^6*d^13 + 3288*a^13*b^3*c^8*d^11 - 1288*a^13*b^3*c^10*d^9 - 80*a^14*b^2*c^3*d^16 + 564*a^14*b^2*c^5*d^14 - 936*a^14*b^2*c^7*d^12 + 440*a^14*b^2*c^9*d^10 + 24*a*b^15*c^18*d))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 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1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 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36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 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7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))*(3*b^2*d - 4*a^2*d + a*b*c)*1i)/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3) - (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^3*b^13*c^19 - 4*a^5*b^11*c^19 + 2*a^16*c^2*d^17 - 6*a^16*c^6*d^13 + 4*a^16*c^8*d^11 + 12*a*b^15*c^9*d^10 - 54*a*b^15*c^11*d^8 + 96*a*b^15*c^13*d^6 - 78*a*b^15*c^15*d^4 + 24*a*b^15*c^17*d^2 + 12*a^2*b^14*c^18*d - 56*a^4*b^12*c^18*d + 44*a^6*b^10*c^18*d + 12*a^9*b^7*c*d^18 - 28*a^11*b^5*c*d^18 + 16*a^13*b^3*c*d^18 - 10*a^15*b*c^3*d^16 - 24*a^15*b*c^5*d^14 + 78*a^15*b*c^7*d^12 - 44*a^15*b*c^9*d^10 - 96*a^2*b^14*c^8*d^11 + 442*a^2*b^14*c^10*d^9 - 816*a^2*b^14*c^12*d^7 + 702*a^2*b^14*c^14*d^5 - 244*a^2*b^14*c^16*d^3 + 336*a^3*b^13*c^7*d^12 - 1620*a^3*b^13*c^9*d^10 + 3206*a^3*b^13*c^11*d^8 - 3064*a^3*b^13*c^13*d^6 + 1314*a^3*b^13*c^15*d^4 - 176*a^3*b^13*c^17*d^2 - 672*a^4*b^12*c^6*d^13 + 3528*a^4*b^12*c^8*d^11 - 7810*a^4*b^12*c^10*d^9 + 8696*a^4*b^12*c^12*d^7 - 4770*a^4*b^12*c^14*d^5 + 1084*a^4*b^12*c^16*d^3 + 840*a^5*b^11*c^5*d^14 - 5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 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24*a^18*c^6*d^16 + 16*a^18*c^8*d^14 - 4*a^18*c^10*d^12 - 4*a*b^17*c^13*d^9 + 16*a*b^17*c^15*d^7 - 24*a*b^17*c^17*d^5 + 16*a*b^17*c^19*d^3 - 32*a^3*b^15*c^21*d + 76*a^5*b^13*c^21*d - 40*a^7*b^11*c^21*d + 4*a^13*b^5*c*d^21 - 8*a^15*b^3*c*d^21 + 24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 40*a^12*b^6*c^2*d^20 + 864*a^12*b^6*c^4*d^18 - 2264*a^12*b^6*c^6*d^16 + 1216*a^12*b^6*c^8*d^14 + 1896*a^12*b^6*c^10*d^12 - 2464*a^12*b^6*c^12*d^10 + 792*a^12*b^6*c^14*d^8 - 328*a^13*b^5*c^3*d^19 + 1052*a^13*b^5*c^5*d^17 - 480*a^13*b^5*c^7*d^15 - 2180*a^13*b^5*c^9*d^13 + 3736*a^13*b^5*c^11*d^11 - 2332*a^13*b^5*c^13*d^9 + 528*a^13*b^5*c^15*d^7 + 76*a^14*b^4*c^2*d^20 - 392*a^14*b^4*c^4*d^18 + 148*a^14*b^4*c^6*d^16 + 1808*a^14*b^4*c^8*d^14 - 3532*a^14*b^4*c^10*d^12 + 2552*a^14*b^4*c^12*d^10 - 660*a^14*b^4*c^14*d^8 + 128*a^15*b^3*c^3*d^19 + 8*a^15*b^3*c^5*d^17 - 1152*a^15*b^3*c^7*d^15 + 2248*a^15*b^3*c^9*d^13 - 1664*a^15*b^3*c^11*d^11 + 440*a^15*b^3*c^13*d^9 - 32*a^16*b^2*c^2*d^20 - 48*a^16*b^2*c^4*d^18 + 512*a^16*b^2*c^6*d^16 - 928*a^16*b^2*c^8*d^14 + 672*a^16*b^2*c^10*d^12 - 176*a^16*b^2*c^12*d^10 - 4*a*b^17*c^21*d + 4*a^17*b*c*d^21))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 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42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 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17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 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3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))/((16*(864*a*b^11*c^5*d^8 - 486*a*b^11*c^3*d^10 - 702*a*b^11*c^7*d^6 + 216*a*b^11*c^9*d^4 - 216*a^3*b^9*c*d^12 + 63*a^5*b^7*c*d^12 + 41*a^7*b^5*c*d^12 + 4*a^9*b^3*c*d^12 + 162*a^2*b^10*c^2*d^11 - 783*a^2*b^10*c^4*d^9 + 1278*a^2*b^10*c^6*d^7 - 828*a^2*b^10*c^8*d^5 + 144*a^2*b^10*c^10*d^3 + 1197*a^3*b^9*c^3*d^10 - 2511*a^3*b^9*c^5*d^8 + 2328*a^3*b^9*c^7*d^6 - 750*a^3*b^9*c^9*d^4 + 24*a^3*b^9*c^11*d^2 - 261*a^4*b^8*c^2*d^11 + 1444*a^4*b^8*c^4*d^9 - 2508*a^4*b^8*c^6*d^7 + 1518*a^4*b^8*c^8*d^5 - 184*a^4*b^8*c^10*d^3 - 696*a^5*b^7*c^3*d^10 + 1913*a^5*b^7*c^5*d^8 - 1936*a^5*b^7*c^7*d^6 + 476*a^5*b^7*c^9*d^4 + 66*a^6*b^6*c^2*d^11 - 583*a^6*b^6*c^4*d^9 + 1232*a^6*b^6*c^6*d^7 - 580*a^6*b^6*c^8*d^5 - 21*a^7*b^5*c^3*d^10 - 312*a^7*b^5*c^5*d^8 + 364*a^7*b^5*c^7*d^6 + 19*a^8*b^4*c^2*d^11 - 20*a^8*b^4*c^4*d^9 - 116*a^8*b^4*c^6*d^7 + 16*a^9*b^3*c^3*d^10 + 16*a^9*b^3*c^5*d^8 + 108*a*b^11*c*d^12))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (16*tan(e/2 + (f*x)/2)*(108*a*b^11*c^2*d^11 - 486*a*b^11*c^4*d^9 + 756*a*b^11*c^6*d^7 - 432*a*b^11*c^8*d^5 + 108*a^2*b^10*c*d^12 - 162*a^4*b^8*c*d^12 + 18*a^6*b^6*c*d^12 + 8*a^8*b^4*c*d^12 - 270*a^2*b^10*c^3*d^10 + 90*a^2*b^10*c^5*d^8 + 216*a^2*b^10*c^7*d^6 - 162*a^3*b^9*c^2*d^11 + 864*a^3*b^9*c^4*d^9 - 1632*a^3*b^9*c^6*d^7 + 900*a^3*b^9*c^8*d^5 + 48*a^3*b^9*c^10*d^3 + 396*a^4*b^8*c^3*d^10 + 82*a^4*b^8*c^5*d^8 - 596*a^4*b^8*c^7*d^6 - 80*a^4*b^8*c^9*d^4 + 36*a^5*b^7*c^2*d^11 - 398*a^5*b^7*c^4*d^9 + 1216*a^5*b^7*c^6*d^7 - 584*a^5*b^7*c^8*d^5 - 42*a^6*b^6*c^3*d^10 - 432*a^6*b^6*c^5*d^8 + 600*a^6*b^6*c^7*d^6 + 38*a^7*b^5*c^2*d^11 - 40*a^7*b^5*c^4*d^9 - 232*a^7*b^5*c^6*d^7 + 32*a^8*b^4*c^3*d^10 + 32*a^8*b^4*c^5*d^8))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^3*b^13*c^19 - 4*a^5*b^11*c^19 + 2*a^16*c^2*d^17 - 6*a^16*c^6*d^13 + 4*a^16*c^8*d^11 + 12*a*b^15*c^9*d^10 - 54*a*b^15*c^11*d^8 + 96*a*b^15*c^13*d^6 - 78*a*b^15*c^15*d^4 + 24*a*b^15*c^17*d^2 + 12*a^2*b^14*c^18*d - 56*a^4*b^12*c^18*d + 44*a^6*b^10*c^18*d + 12*a^9*b^7*c*d^18 - 28*a^11*b^5*c*d^18 + 16*a^13*b^3*c*d^18 - 10*a^15*b*c^3*d^16 - 24*a^15*b*c^5*d^14 + 78*a^15*b*c^7*d^12 - 44*a^15*b*c^9*d^10 - 96*a^2*b^14*c^8*d^11 + 442*a^2*b^14*c^10*d^9 - 816*a^2*b^14*c^12*d^7 + 702*a^2*b^14*c^14*d^5 - 244*a^2*b^14*c^16*d^3 + 336*a^3*b^13*c^7*d^12 - 1620*a^3*b^13*c^9*d^10 + 3206*a^3*b^13*c^11*d^8 - 3064*a^3*b^13*c^13*d^6 + 1314*a^3*b^13*c^15*d^4 - 176*a^3*b^13*c^17*d^2 - 672*a^4*b^12*c^6*d^13 + 3528*a^4*b^12*c^8*d^11 - 7810*a^4*b^12*c^10*d^9 + 8696*a^4*b^12*c^12*d^7 - 4770*a^4*b^12*c^14*d^5 + 1084*a^4*b^12*c^16*d^3 + 840*a^5*b^11*c^5*d^14 - 5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 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156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (b^3*((8*(4*a^2*b^16*c^22 - 8*a^4*b^14*c^22 + 4*a^6*b^12*c^22 - 4*a^18*c^2*d^20 + 16*a^18*c^4*d^18 - 24*a^18*c^6*d^16 + 16*a^18*c^8*d^14 - 4*a^18*c^10*d^12 - 4*a*b^17*c^13*d^9 + 16*a*b^17*c^15*d^7 - 24*a*b^17*c^17*d^5 + 16*a*b^17*c^19*d^3 - 32*a^3*b^15*c^21*d + 76*a^5*b^13*c^21*d - 40*a^7*b^11*c^21*d + 4*a^13*b^5*c*d^21 - 8*a^15*b^3*c*d^21 + 24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 40*a^12*b^6*c^2*d^20 + 864*a^12*b^6*c^4*d^18 - 2264*a^12*b^6*c^6*d^16 + 1216*a^12*b^6*c^8*d^14 + 1896*a^12*b^6*c^10*d^12 - 2464*a^12*b^6*c^12*d^10 + 792*a^12*b^6*c^14*d^8 - 328*a^13*b^5*c^3*d^19 + 1052*a^13*b^5*c^5*d^17 - 480*a^13*b^5*c^7*d^15 - 2180*a^13*b^5*c^9*d^13 + 3736*a^13*b^5*c^11*d^11 - 2332*a^13*b^5*c^13*d^9 + 528*a^13*b^5*c^15*d^7 + 76*a^14*b^4*c^2*d^20 - 392*a^14*b^4*c^4*d^18 + 148*a^14*b^4*c^6*d^16 + 1808*a^14*b^4*c^8*d^14 - 3532*a^14*b^4*c^10*d^12 + 2552*a^14*b^4*c^12*d^10 - 660*a^14*b^4*c^14*d^8 + 128*a^15*b^3*c^3*d^19 + 8*a^15*b^3*c^5*d^17 - 1152*a^15*b^3*c^7*d^15 + 2248*a^15*b^3*c^9*d^13 - 1664*a^15*b^3*c^11*d^11 + 440*a^15*b^3*c^13*d^9 - 32*a^16*b^2*c^2*d^20 - 48*a^16*b^2*c^4*d^18 + 512*a^16*b^2*c^6*d^16 - 928*a^16*b^2*c^8*d^14 + 672*a^16*b^2*c^10*d^12 - 176*a^16*b^2*c^12*d^10 - 4*a*b^17*c^21*d + 4*a^17*b*c*d^21))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 1320*a^10*b^8*c^19*d^3 - 176*a^11*b^7*c^2*d^20 + 8096*a^11*b^7*c^4*d^18 - 54384*a^11*b^7*c^6*d^16 + 156992*a^11*b^7*c^8*d^14 - 242528*a^11*b^7*c^10*d^12 + 214368*a^11*b^7*c^12*d^10 - 107184*a^11*b^7*c^14*d^8 + 27456*a^11*b^7*c^16*d^6 - 2640*a^11*b^7*c^18*d^4 - 2496*a^12*b^6*c^3*d^19 + 24784*a^12*b^6*c^5*d^17 - 89280*a^12*b^6*c^7*d^15 + 162336*a^12*b^6*c^9*d^13 - 165760*a^12*b^6*c^11*d^11 + 96272*a^12*b^6*c^13*d^9 - 29568*a^12*b^6*c^15*d^7 + 3696*a^12*b^6*c^17*d^5 + 484*a^13*b^5*c^2*d^20 - 8888*a^13*b^5*c^4*d^18 + 40876*a^13*b^5*c^6*d^16 - 88000*a^13*b^5*c^8*d^14 + 104060*a^13*b^5*c^10*d^12 - 69784*a^13*b^5*c^12*d^10 + 24948*a^13*b^5*c^14*d^8 - 3696*a^13*b^5*c^16*d^6 + 2408*a^14*b^4*c^3*d^19 - 14692*a^14*b^4*c^5*d^17 + 38208*a^14*b^4*c^7*d^15 - 52532*a^14*b^4*c^9*d^13 + 40072*a^14*b^4*c^11*d^11 - 16060*a^14*b^4*c^13*d^9 + 2640*a^14*b^4*c^15*d^7 - 440*a^15*b^3*c^2*d^20 + 4048*a^15*b^3*c^4*d^18 - 13112*a^15*b^3*c^6*d^16 + 20768*a^15*b^3*c^8*d^14 - 17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3) - (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^3*b^11*c^16 - a^14*c*d^15 - 4*a^14*c^3*d^13 - 4*a^14*c^5*d^11 - 144*a*b^13*c^4*d^12 + 684*a*b^13*c^6*d^10 - 1314*a*b^13*c^8*d^8 + 1224*a*b^13*c^10*d^6 - 504*a*b^13*c^12*d^4 + 36*a*b^13*c^14*d^2 + 24*a^2*b^12*c^15*d + 144*a^4*b^10*c*d^15 - 44*a^4*b^10*c^15*d - 348*a^6*b^8*c*d^15 + 214*a^8*b^6*c*d^15 + 7*a^10*b^4*c*d^15 - 8*a^12*b^2*c*d^15 - a^13*b*c^2*d^14 + 20*a^13*b*c^4*d^12 + 44*a^13*b*c^6*d^10 + 432*a^2*b^12*c^3*d^13 - 2148*a^2*b^12*c^5*d^11 + 4470*a^2*b^12*c^7*d^9 - 4632*a^2*b^12*c^9*d^7 + 2232*a^2*b^12*c^11*d^5 - 252*a^2*b^12*c^13*d^3 - 432*a^3*b^11*c^2*d^14 + 2688*a^3*b^11*c^4*d^12 - 7294*a^3*b^11*c^6*d^10 + 10105*a^3*b^11*c^8*d^8 - 7104*a^3*b^11*c^10*d^6 + 1892*a^3*b^11*c^12*d^4 - 192*a^3*b^11*c^14*d^2 - 2016*a^4*b^10*c^3*d^13 + 8378*a^4*b^10*c^5*d^11 - 15815*a^4*b^10*c^7*d^9 + 14976*a^4*b^10*c^9*d^7 - 5932*a^4*b^10*c^11*d^5 + 624*a^4*b^10*c^13*d^3 + 1140*a^5*b^9*c^2*d^14 - 6574*a^5*b^9*c^4*d^12 + 16053*a^5*b^9*c^6*d^10 - 19912*a^5*b^9*c^8*d^8 + 11320*a^5*b^9*c^10*d^6 - 1920*a^5*b^9*c^12*d^4 + 172*a^5*b^9*c^14*d^2 + 2938*a^6*b^8*c^3*d^13 - 10619*a^6*b^8*c^5*d^11 + 18608*a^6*b^8*c^7*d^9 - 15576*a^6*b^8*c^9*d^7 + 4344*a^6*b^8*c^11*d^5 - 292*a^6*b^8*c^13*d^3 - 818*a^7*b^7*c^2*d^14 + 5107*a^7*b^7*c^4*d^12 - 12464*a^7*b^7*c^6*d^10 + 14693*a^7*b^7*c^8*d^8 - 6184*a^7*b^7*c^10*d^6 + 368*a^7*b^7*c^12*d^4 - 1485*a^8*b^6*c^3*d^13 + 5064*a^8*b^6*c^5*d^11 - 8939*a^8*b^6*c^7*d^9 + 6104*a^8*b^6*c^9*d^7 - 688*a^8*b^6*c^11*d^5 + 55*a^9*b^5*c^2*d^14 - 1056*a^9*b^5*c^4*d^12 + 3649*a^9*b^5*c^6*d^10 - 4524*a^9*b^5*c^8*d^8 + 1120*a^9*b^5*c^10*d^6 + 152*a^10*b^4*c^3*d^13 - 975*a^10*b^4*c^5*d^11 + 2300*a^10*b^4*c^7*d^9 - 1088*a^10*b^4*c^9*d^7 + 16*a^11*b^3*c^2*d^14 + 59*a^11*b^3*c^4*d^12 - 640*a^11*b^3*c^6*d^10 + 628*a^11*b^3*c^8*d^8 + 27*a^12*b^2*c^3*d^13 + 48*a^12*b^2*c^5*d^11 - 220*a^12*b^2*c^7*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (8*(36*a*b^13*c^5*d^11 - 144*a*b^13*c^7*d^9 + 216*a*b^13*c^9*d^7 - 144*a*b^13*c^11*d^5 + 36*a*b^13*c^13*d^3 + 4*a^3*b^11*c^15*d - 36*a^5*b^9*c*d^15 + 60*a^7*b^7*c*d^15 - 13*a^9*b^5*c*d^15 - 10*a^11*b^3*c*d^15 - 4*a^13*b*c^3*d^13 - 4*a^13*b*c^5*d^11 - 72*a^2*b^12*c^4*d^12 + 276*a^2*b^12*c^6*d^10 - 375*a^2*b^12*c^8*d^8 + 216*a^2*b^12*c^10*d^6 - 60*a^2*b^12*c^12*d^4 + 24*a^2*b^12*c^14*d^2 - 36*a^3*b^11*c^5*d^11 + 61*a^3*b^11*c^7*d^9 - 88*a^3*b^11*c^9*d^7 + 180*a^3*b^11*c^11*d^5 - 184*a^3*b^11*c^13*d^3 + 72*a^4*b^10*c^2*d^14 - 168*a^4*b^10*c^4*d^12 + 233*a^4*b^10*c^6*d^10 - 270*a^4*b^10*c^8*d^8 + 100*a^4*b^10*c^10*d^6 + 248*a^4*b^10*c^12*d^4 - 44*a^4*b^10*c^14*d^2 + 120*a^5*b^9*c^3*d^13 - 535*a^5*b^9*c^5*d^11 + 1386*a^5*b^9*c^7*d^9 - 1544*a^5*b^9*c^9*d^7 + 248*a^5*b^9*c^11*d^5 + 172*a^5*b^9*c^13*d^3 - 108*a^6*b^8*c^2*d^14 + 699*a^6*b^8*c^4*d^12 - 2046*a^6*b^8*c^6*d^10 + 2885*a^6*b^8*c^8*d^8 - 1336*a^6*b^8*c^10*d^6 - 148*a^6*b^8*c^12*d^4 - 305*a^7*b^7*c^3*d^13 + 1354*a^7*b^7*c^5*d^11 - 2979*a^7*b^7*c^7*d^9 + 2648*a^7*b^7*c^9*d^7 - 400*a^7*b^7*c^11*d^5 + 19*a^8*b^6*c^2*d^14 - 602*a^8*b^6*c^4*d^12 + 2161*a^8*b^6*c^6*d^10 - 3012*a^8*b^6*c^8*d^8 + 1056*a^8*b^6*c^10*d^6 + 190*a^9*b^5*c^3*d^13 - 895*a^9*b^5*c^5*d^11 + 1860*a^9*b^5*c^7*d^9 - 1088*a^9*b^5*c^9*d^7 + 14*a^10*b^4*c^2*d^14 + 99*a^10*b^4*c^4*d^12 - 552*a^10*b^4*c^6*d^10 + 628*a^10*b^4*c^8*d^8 + 19*a^11*b^3*c^3*d^13 + 40*a^11*b^3*c^5*d^11 - 220*a^11*b^3*c^7*d^9 - a^12*b^2*c^2*d^14 + 20*a^12*b^2*c^4*d^12 + 44*a^12*b^2*c^6*d^10 - a^13*b*c*d^15))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (b^3*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*a^3*b^13*c^19 - 4*a^5*b^11*c^19 + 2*a^16*c^2*d^17 - 6*a^16*c^6*d^13 + 4*a^16*c^8*d^11 + 12*a*b^15*c^9*d^10 - 54*a*b^15*c^11*d^8 + 96*a*b^15*c^13*d^6 - 78*a*b^15*c^15*d^4 + 24*a*b^15*c^17*d^2 + 12*a^2*b^14*c^18*d - 56*a^4*b^12*c^18*d + 44*a^6*b^10*c^18*d + 12*a^9*b^7*c*d^18 - 28*a^11*b^5*c*d^18 + 16*a^13*b^3*c*d^18 - 10*a^15*b*c^3*d^16 - 24*a^15*b*c^5*d^14 + 78*a^15*b*c^7*d^12 - 44*a^15*b*c^9*d^10 - 96*a^2*b^14*c^8*d^11 + 442*a^2*b^14*c^10*d^9 - 816*a^2*b^14*c^12*d^7 + 702*a^2*b^14*c^14*d^5 - 244*a^2*b^14*c^16*d^3 + 336*a^3*b^13*c^7*d^12 - 1620*a^3*b^13*c^9*d^10 + 3206*a^3*b^13*c^11*d^8 - 3064*a^3*b^13*c^13*d^6 + 1314*a^3*b^13*c^15*d^4 - 176*a^3*b^13*c^17*d^2 - 672*a^4*b^12*c^6*d^13 + 3528*a^4*b^12*c^8*d^11 - 7810*a^4*b^12*c^10*d^9 + 8696*a^4*b^12*c^12*d^7 - 4770*a^4*b^12*c^14*d^5 + 1084*a^4*b^12*c^16*d^3 + 840*a^5*b^11*c^5*d^14 - 5124*a^5*b^11*c^7*d^12 + 13320*a^5*b^11*c^9*d^10 - 17850*a^5*b^11*c^11*d^8 + 12400*a^5*b^11*c^13*d^6 - 3954*a^5*b^11*c^15*d^4 + 372*a^5*b^11*c^17*d^2 - 672*a^6*b^10*c^4*d^15 + 5292*a^6*b^10*c^6*d^13 - 16872*a^6*b^10*c^8*d^11 + 27546*a^6*b^10*c^10*d^9 - 23696*a^6*b^10*c^12*d^7 + 9858*a^6*b^10*c^14*d^5 - 1500*a^6*b^10*c^16*d^3 + 336*a^7*b^9*c^3*d^16 - 4032*a^7*b^9*c^5*d^14 + 16212*a^7*b^9*c^7*d^12 - 32304*a^7*b^9*c^9*d^10 + 34018*a^7*b^9*c^11*d^8 - 18048*a^7*b^9*c^13*d^6 + 4038*a^7*b^9*c^15*d^4 - 220*a^7*b^9*c^17*d^2 - 96*a^8*b^8*c^2*d^17 + 2280*a^8*b^8*c^4*d^15 - 11772*a^8*b^8*c^6*d^13 + 28848*a^8*b^8*c^8*d^11 - 37338*a^8*b^8*c^10*d^9 + 25056*a^8*b^8*c^12*d^7 - 7638*a^8*b^8*c^14*d^5 + 660*a^8*b^8*c^16*d^3 - 918*a^9*b^7*c^3*d^16 + 6360*a^9*b^7*c^5*d^14 - 19602*a^9*b^7*c^7*d^12 + 31560*a^9*b^7*c^9*d^10 - 26556*a^9*b^7*c^11*d^8 + 10464*a^9*b^7*c^13*d^6 - 1320*a^9*b^7*c^15*d^4 + 234*a^10*b^6*c^2*d^17 - 2520*a^10*b^6*c^4*d^15 + 10050*a^10*b^6*c^6*d^13 - 20340*a^10*b^6*c^8*d^11 + 21288*a^10*b^6*c^10*d^9 - 10560*a^10*b^6*c^12*d^7 + 1848*a^10*b^6*c^14*d^5 + 726*a^11*b^5*c^3*d^16 - 3768*a^11*b^5*c^5*d^14 + 9670*a^11*b^5*c^7*d^12 - 12648*a^11*b^5*c^9*d^10 + 7896*a^11*b^5*c^11*d^8 - 1848*a^11*b^5*c^13*d^6 - 146*a^12*b^4*c^2*d^17 + 952*a^12*b^4*c^4*d^15 - 3174*a^12*b^4*c^6*d^13 + 5396*a^12*b^4*c^8*d^11 - 4348*a^12*b^4*c^10*d^9 + 1320*a^12*b^4*c^12*d^7 - 134*a^13*b^3*c^3*d^16 + 624*a^13*b^3*c^5*d^14 - 1570*a^13*b^3*c^7*d^12 + 1724*a^13*b^3*c^9*d^10 - 660*a^13*b^3*c^11*d^8 + 6*a^14*b^2*c^2*d^17 - 40*a^14*b^2*c^4*d^15 + 282*a^14*b^2*c^6*d^13 - 468*a^14*b^2*c^8*d^11 + 220*a^14*b^2*c^10*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(4*a^16*c*d^18 + 8*a^2*b^14*c^19 - 8*a^4*b^12*c^19 - 12*a^16*c^5*d^14 + 8*a^16*c^7*d^12 + 12*a*b^15*c^10*d^9 - 48*a*b^15*c^12*d^7 + 84*a*b^15*c^14*d^5 - 72*a*b^15*c^16*d^3 - 112*a^3*b^13*c^18*d + 88*a^5*b^11*c^18*d + 12*a^10*b^6*c*d^18 - 28*a^12*b^4*c*d^18 + 12*a^14*b^2*c*d^18 - 20*a^15*b*c^2*d^17 - 48*a^15*b*c^4*d^15 + 156*a^15*b*c^6*d^13 - 88*a^15*b*c^8*d^11 - 84*a^2*b^14*c^9*d^10 + 328*a^2*b^14*c^11*d^8 - 596*a^2*b^14*c^13*d^6 + 552*a^2*b^14*c^15*d^4 - 208*a^2*b^14*c^17*d^2 + 240*a^3*b^13*c^8*d^11 - 908*a^3*b^13*c^10*d^9 + 1792*a^3*b^13*c^12*d^7 - 1932*a^3*b^13*c^14*d^5 + 920*a^3*b^13*c^16*d^3 - 336*a^4*b^12*c^7*d^12 + 1188*a^4*b^12*c^9*d^10 - 2808*a^4*b^12*c^11*d^8 + 3980*a^4*b^12*c^13*d^6 - 2616*a^4*b^12*c^15*d^4 + 600*a^4*b^12*c^17*d^2 + 168*a^5*b^11*c^6*d^13 - 336*a^5*b^11*c^8*d^11 + 1740*a^5*b^11*c^10*d^9 - 4720*a^5*b^11*c^12*d^7 + 4812*a^5*b^11*c^14*d^5 - 1752*a^5*b^11*c^16*d^3 + 168*a^6*b^10*c^5*d^14 - 1344*a^6*b^10*c^7*d^12 + 2292*a^6*b^10*c^9*d^10 + 1088*a^6*b^10*c^11*d^8 - 4908*a^6*b^10*c^13*d^6 + 3096*a^6*b^10*c^15*d^4 - 392*a^6*b^10*c^17*d^2 - 336*a^7*b^9*c^4*d^15 + 2520*a^7*b^9*c^6*d^13 - 7488*a^7*b^9*c^8*d^11 + 7556*a^7*b^9*c^10*d^9 - 144*a^7*b^9*c^12*d^7 - 3012*a^7*b^9*c^14*d^5 + 904*a^7*b^9*c^16*d^3 + 240*a^8*b^8*c^3*d^16 - 2472*a^8*b^8*c^5*d^14 + 10416*a^8*b^8*c^7*d^12 - 16596*a^8*b^8*c^9*d^10 + 9600*a^8*b^8*c^11*d^8 - 156*a^8*b^8*c^13*d^6 - 1032*a^8*b^8*c^15*d^4 - 84*a^9*b^7*c^2*d^17 + 1632*a^9*b^7*c^4*d^15 - 9204*a^9*b^7*c^6*d^13 + 19800*a^9*b^7*c^8*d^11 - 18048*a^9*b^7*c^10*d^9 + 5856*a^9*b^7*c^12*d^7 + 48*a^9*b^7*c^14*d^5 - 744*a^10*b^6*c^3*d^16 + 5460*a^10*b^6*c^5*d^14 - 15960*a^10*b^6*c^7*d^12 + 20136*a^10*b^6*c^9*d^10 - 10584*a^10*b^6*c^11*d^8 + 1680*a^10*b^6*c^13*d^6 + 212*a^11*b^5*c^2*d^17 - 2176*a^11*b^5*c^4*d^15 + 9180*a^11*b^5*c^6*d^13 - 15416*a^11*b^5*c^8*d^11 + 10936*a^11*b^5*c^10*d^9 - 2736*a^11*b^5*c^12*d^7 + 584*a^12*b^4*c^3*d^16 - 3708*a^12*b^4*c^5*d^14 + 8152*a^12*b^4*c^7*d^12 - 7376*a^12*b^4*c^9*d^10 + 2376*a^12*b^4*c^11*d^8 - 108*a^13*b^3*c^2*d^17 + 928*a^13*b^3*c^4*d^15 - 2820*a^13*b^3*c^6*d^13 + 3288*a^13*b^3*c^8*d^11 - 1288*a^13*b^3*c^10*d^9 - 80*a^14*b^2*c^3*d^16 + 564*a^14*b^2*c^5*d^14 - 936*a^14*b^2*c^7*d^12 + 440*a^14*b^2*c^9*d^10 + 24*a*b^15*c^18*d))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) - (b^3*((8*(4*a^2*b^16*c^22 - 8*a^4*b^14*c^22 + 4*a^6*b^12*c^22 - 4*a^18*c^2*d^20 + 16*a^18*c^4*d^18 - 24*a^18*c^6*d^16 + 16*a^18*c^8*d^14 - 4*a^18*c^10*d^12 - 4*a*b^17*c^13*d^9 + 16*a*b^17*c^15*d^7 - 24*a*b^17*c^17*d^5 + 16*a*b^17*c^19*d^3 - 32*a^3*b^15*c^21*d + 76*a^5*b^13*c^21*d - 40*a^7*b^11*c^21*d + 4*a^13*b^5*c*d^21 - 8*a^15*b^3*c*d^21 + 24*a^17*b*c^3*d^19 - 136*a^17*b*c^5*d^17 + 224*a^17*b*c^7*d^15 - 156*a^17*b*c^9*d^13 + 40*a^17*b*c^11*d^11 + 40*a^2*b^16*c^12*d^10 - 156*a^2*b^16*c^14*d^8 + 224*a^2*b^16*c^16*d^6 - 136*a^2*b^16*c^18*d^4 + 24*a^2*b^16*c^20*d^2 - 176*a^3*b^15*c^11*d^11 + 672*a^3*b^15*c^13*d^9 - 928*a^3*b^15*c^15*d^7 + 512*a^3*b^15*c^17*d^5 - 48*a^3*b^15*c^19*d^3 + 440*a^4*b^14*c^10*d^12 - 1664*a^4*b^14*c^12*d^10 + 2248*a^4*b^14*c^14*d^8 - 1152*a^4*b^14*c^16*d^6 + 8*a^4*b^14*c^18*d^4 + 128*a^4*b^14*c^20*d^2 - 660*a^5*b^13*c^9*d^13 + 2552*a^5*b^13*c^11*d^11 - 3532*a^5*b^13*c^13*d^9 + 1808*a^5*b^13*c^15*d^7 + 148*a^5*b^13*c^17*d^5 - 392*a^5*b^13*c^19*d^3 + 528*a^6*b^12*c^8*d^14 - 2332*a^6*b^12*c^10*d^12 + 3736*a^6*b^12*c^12*d^10 - 2180*a^6*b^12*c^14*d^8 - 480*a^6*b^12*c^16*d^6 + 1052*a^6*b^12*c^18*d^4 - 328*a^6*b^12*c^20*d^2 + 792*a^7*b^11*c^9*d^13 - 2464*a^7*b^11*c^11*d^11 + 1896*a^7*b^11*c^13*d^9 + 1216*a^7*b^11*c^15*d^7 - 2264*a^7*b^11*c^17*d^5 + 864*a^7*b^11*c^19*d^3 - 528*a^8*b^10*c^6*d^16 + 1056*a^8*b^10*c^8*d^14 + 176*a^8*b^10*c^10*d^12 - 528*a^8*b^10*c^12*d^10 - 2288*a^8*b^10*c^14*d^8 + 3520*a^8*b^10*c^16*d^6 - 1584*a^8*b^10*c^18*d^4 + 176*a^8*b^10*c^20*d^2 + 660*a^9*b^9*c^5*d^17 - 2112*a^9*b^9*c^7*d^15 + 2244*a^9*b^9*c^9*d^13 - 1496*a^9*b^9*c^11*d^11 + 2684*a^9*b^9*c^13*d^9 - 3696*a^9*b^9*c^15*d^7 + 2156*a^9*b^9*c^17*d^5 - 440*a^9*b^9*c^19*d^3 - 440*a^10*b^8*c^4*d^18 + 2156*a^10*b^8*c^6*d^16 - 3696*a^10*b^8*c^8*d^14 + 2684*a^10*b^8*c^10*d^12 - 1496*a^10*b^8*c^12*d^10 + 2244*a^10*b^8*c^14*d^8 - 2112*a^10*b^8*c^16*d^6 + 660*a^10*b^8*c^18*d^4 + 176*a^11*b^7*c^3*d^19 - 1584*a^11*b^7*c^5*d^17 + 3520*a^11*b^7*c^7*d^15 - 2288*a^11*b^7*c^9*d^13 - 528*a^11*b^7*c^11*d^11 + 176*a^11*b^7*c^13*d^9 + 1056*a^11*b^7*c^15*d^7 - 528*a^11*b^7*c^17*d^5 - 40*a^12*b^6*c^2*d^20 + 864*a^12*b^6*c^4*d^18 - 2264*a^12*b^6*c^6*d^16 + 1216*a^12*b^6*c^8*d^14 + 1896*a^12*b^6*c^10*d^12 - 2464*a^12*b^6*c^12*d^10 + 792*a^12*b^6*c^14*d^8 - 328*a^13*b^5*c^3*d^19 + 1052*a^13*b^5*c^5*d^17 - 480*a^13*b^5*c^7*d^15 - 2180*a^13*b^5*c^9*d^13 + 3736*a^13*b^5*c^11*d^11 - 2332*a^13*b^5*c^13*d^9 + 528*a^13*b^5*c^15*d^7 + 76*a^14*b^4*c^2*d^20 - 392*a^14*b^4*c^4*d^18 + 148*a^14*b^4*c^6*d^16 + 1808*a^14*b^4*c^8*d^14 - 3532*a^14*b^4*c^10*d^12 + 2552*a^14*b^4*c^12*d^10 - 660*a^14*b^4*c^14*d^8 + 128*a^15*b^3*c^3*d^19 + 8*a^15*b^3*c^5*d^17 - 1152*a^15*b^3*c^7*d^15 + 2248*a^15*b^3*c^9*d^13 - 1664*a^15*b^3*c^11*d^11 + 440*a^15*b^3*c^13*d^9 - 32*a^16*b^2*c^2*d^20 - 48*a^16*b^2*c^4*d^18 + 512*a^16*b^2*c^6*d^16 - 928*a^16*b^2*c^8*d^14 + 672*a^16*b^2*c^10*d^12 - 176*a^16*b^2*c^12*d^10 - 4*a*b^17*c^21*d + 4*a^17*b*c*d^21))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16) + (8*tan(e/2 + (f*x)/2)*(12*a*b^17*c^22 - 12*a^18*c*d^21 - 32*a^3*b^15*c^22 + 28*a^5*b^13*c^22 - 8*a^7*b^11*c^22 + 56*a^18*c^3*d^19 - 104*a^18*c^5*d^17 + 96*a^18*c^7*d^15 - 44*a^18*c^9*d^13 + 8*a^18*c^11*d^11 - 16*a*b^17*c^12*d^10 + 76*a*b^17*c^14*d^8 - 144*a*b^17*c^16*d^6 + 136*a*b^17*c^18*d^4 - 64*a*b^17*c^20*d^2 - 132*a^2*b^16*c^21*d + 352*a^4*b^14*c^21*d - 308*a^6*b^12*c^21*d + 88*a^8*b^10*c^21*d + 16*a^12*b^6*c*d^21 - 44*a^14*b^4*c*d^21 + 40*a^16*b^2*c*d^21 + 132*a^17*b*c^2*d^20 - 616*a^17*b*c^4*d^18 + 1144*a^17*b*c^6*d^16 - 1056*a^17*b*c^8*d^14 + 484*a^17*b*c^10*d^12 - 88*a^17*b*c^12*d^10 + 176*a^2*b^16*c^11*d^11 - 836*a^2*b^16*c^13*d^9 + 1584*a^2*b^16*c^15*d^7 - 1496*a^2*b^16*c^17*d^5 + 704*a^2*b^16*c^19*d^3 - 880*a^3*b^15*c^10*d^12 + 4224*a^3*b^15*c^12*d^10 - 8128*a^3*b^15*c^14*d^8 + 7872*a^3*b^15*c^16*d^6 - 3888*a^3*b^15*c^18*d^4 + 832*a^3*b^15*c^20*d^2 + 2640*a^4*b^14*c^9*d^13 - 13024*a^4*b^14*c^11*d^11 + 26048*a^4*b^14*c^13*d^9 - 26752*a^4*b^14*c^15*d^7 + 14608*a^4*b^14*c^17*d^5 - 3872*a^4*b^14*c^19*d^3 - 5280*a^5*b^13*c^8*d^14 + 27500*a^5*b^13*c^10*d^12 - 59000*a^5*b^13*c^12*d^10 + 66628*a^5*b^13*c^14*d^8 - 41712*a^5*b^13*c^16*d^6 + 13748*a^5*b^13*c^18*d^4 - 1912*a^5*b^13*c^20*d^2 + 7392*a^6*b^12*c^7*d^15 - 42372*a^6*b^12*c^9*d^13 + 101288*a^6*b^12*c^11*d^11 - 129580*a^6*b^12*c^13*d^9 + 94160*a^6*b^12*c^15*d^7 - 37532*a^6*b^12*c^17*d^5 + 6952*a^6*b^12*c^19*d^3 - 7392*a^7*b^11*c^6*d^16 + 49632*a^7*b^11*c^8*d^14 - 137368*a^7*b^11*c^10*d^12 + 202544*a^7*b^11*c^12*d^10 - 170424*a^7*b^11*c^14*d^8 + 80448*a^7*b^11*c^16*d^6 - 19016*a^7*b^11*c^18*d^4 + 1584*a^7*b^11*c^20*d^2 + 5280*a^8*b^10*c^5*d^17 - 45408*a^8*b^10*c^7*d^15 + 150216*a^8*b^10*c^9*d^13 - 257136*a^8*b^10*c^11*d^11 + 249832*a^8*b^10*c^13*d^9 - 138688*a^8*b^10*c^15*d^7 + 40920*a^8*b^10*c^17*d^5 - 5104*a^8*b^10*c^19*d^3 - 2640*a^9*b^9*c^4*d^18 + 32868*a^9*b^9*c^6*d^16 - 133056*a^9*b^9*c^8*d^14 + 266244*a^9*b^9*c^10*d^12 - 299816*a^9*b^9*c^12*d^10 + 195404*a^9*b^9*c^14*d^8 - 70224*a^9*b^9*c^16*d^6 + 11660*a^9*b^9*c^18*d^4 - 440*a^9*b^9*c^20*d^2 + 880*a^10*b^8*c^3*d^19 - 18700*a^10*b^8*c^5*d^17 + 95040*a^10*b^8*c^7*d^15 - 225676*a^10*b^8*c^9*d^13 + 296824*a^10*b^8*c^11*d^11 - 226116*a^10*b^8*c^13*d^9 + 96624*a^10*b^8*c^15*d^7 - 20196*a^10*b^8*c^17*d^5 + 1320*a^10*b^8*c^19*d^3 - 176*a^11*b^7*c^2*d^20 + 8096*a^11*b^7*c^4*d^18 - 54384*a^11*b^7*c^6*d^16 + 156992*a^11*b^7*c^8*d^14 - 242528*a^11*b^7*c^10*d^12 + 214368*a^11*b^7*c^12*d^10 - 107184*a^11*b^7*c^14*d^8 + 27456*a^11*b^7*c^16*d^6 - 2640*a^11*b^7*c^18*d^4 - 2496*a^12*b^6*c^3*d^19 + 24784*a^12*b^6*c^5*d^17 - 89280*a^12*b^6*c^7*d^15 + 162336*a^12*b^6*c^9*d^13 - 165760*a^12*b^6*c^11*d^11 + 96272*a^12*b^6*c^13*d^9 - 29568*a^12*b^6*c^15*d^7 + 3696*a^12*b^6*c^17*d^5 + 484*a^13*b^5*c^2*d^20 - 8888*a^13*b^5*c^4*d^18 + 40876*a^13*b^5*c^6*d^16 - 88000*a^13*b^5*c^8*d^14 + 104060*a^13*b^5*c^10*d^12 - 69784*a^13*b^5*c^12*d^10 + 24948*a^13*b^5*c^14*d^8 - 3696*a^13*b^5*c^16*d^6 + 2408*a^14*b^4*c^3*d^19 - 14692*a^14*b^4*c^5*d^17 + 38208*a^14*b^4*c^7*d^15 - 52532*a^14*b^4*c^9*d^13 + 40072*a^14*b^4*c^11*d^11 - 16060*a^14*b^4*c^13*d^9 + 2640*a^14*b^4*c^15*d^7 - 440*a^15*b^3*c^2*d^20 + 4048*a^15*b^3*c^4*d^18 - 13112*a^15*b^3*c^6*d^16 + 20768*a^15*b^3*c^8*d^14 - 17512*a^15*b^3*c^10*d^12 + 7568*a^15*b^3*c^12*d^10 - 1320*a^15*b^3*c^14*d^8 - 848*a^16*b^2*c^3*d^19 + 3432*a^16*b^2*c^5*d^17 - 6048*a^16*b^2*c^7*d^15 + 5432*a^16*b^2*c^9*d^13 - 2448*a^16*b^2*c^11*d^11 + 440*a^16*b^2*c^13*d^9))/(a^13*d^17 - b^13*c^17 + 2*a^2*b^11*c^17 - a^4*b^9*c^17 + a^9*b^4*d^17 - 2*a^11*b^2*d^17 - 4*a^13*c^2*d^15 + 6*a^13*c^4*d^13 - 4*a^13*c^6*d^11 + a^13*c^8*d^9 - b^13*c^9*d^8 + 4*b^13*c^11*d^6 - 6*b^13*c^13*d^4 + 4*b^13*c^15*d^2 + 9*a*b^12*c^8*d^9 - 36*a*b^12*c^10*d^7 + 54*a*b^12*c^12*d^5 - 36*a*b^12*c^14*d^3 - 18*a^3*b^10*c^16*d + 9*a^5*b^8*c^16*d - 9*a^8*b^5*c*d^16 + 18*a^10*b^3*c*d^16 + 36*a^12*b*c^3*d^14 - 54*a^12*b*c^5*d^12 + 36*a^12*b*c^7*d^10 - 9*a^12*b*c^9*d^8 - 36*a^2*b^11*c^7*d^10 + 146*a^2*b^11*c^9*d^8 - 224*a^2*b^11*c^11*d^6 + 156*a^2*b^11*c^13*d^4 - 44*a^2*b^11*c^15*d^2 + 84*a^3*b^10*c^6*d^11 - 354*a^3*b^10*c^8*d^9 + 576*a^3*b^10*c^10*d^7 - 444*a^3*b^10*c^12*d^5 + 156*a^3*b^10*c^14*d^3 - 126*a^4*b^9*c^5*d^12 + 576*a^4*b^9*c^7*d^10 - 1045*a^4*b^9*c^9*d^8 + 940*a^4*b^9*c^11*d^6 - 420*a^4*b^9*c^13*d^4 + 76*a^4*b^9*c^15*d^2 + 126*a^5*b^8*c^4*d^13 - 672*a^5*b^8*c^6*d^11 + 1437*a^5*b^8*c^8*d^9 - 1548*a^5*b^8*c^10*d^7 + 852*a^5*b^8*c^12*d^5 - 204*a^5*b^8*c^14*d^3 - 84*a^6*b^7*c^3*d^14 + 588*a^6*b^7*c^5*d^12 - 1548*a^6*b^7*c^7*d^10 + 1992*a^6*b^7*c^9*d^8 - 1308*a^6*b^7*c^11*d^6 + 396*a^6*b^7*c^13*d^4 - 36*a^6*b^7*c^15*d^2 + 36*a^7*b^6*c^2*d^15 - 396*a^7*b^6*c^4*d^13 + 1308*a^7*b^6*c^6*d^11 - 1992*a^7*b^6*c^8*d^9 + 1548*a^7*b^6*c^10*d^7 - 588*a^7*b^6*c^12*d^5 + 84*a^7*b^6*c^14*d^3 + 204*a^8*b^5*c^3*d^14 - 852*a^8*b^5*c^5*d^12 + 1548*a^8*b^5*c^7*d^10 - 1437*a^8*b^5*c^9*d^8 + 672*a^8*b^5*c^11*d^6 - 126*a^8*b^5*c^13*d^4 - 76*a^9*b^4*c^2*d^15 + 420*a^9*b^4*c^4*d^13 - 940*a^9*b^4*c^6*d^11 + 1045*a^9*b^4*c^8*d^9 - 576*a^9*b^4*c^10*d^7 + 126*a^9*b^4*c^12*d^5 - 156*a^10*b^3*c^3*d^14 + 444*a^10*b^3*c^5*d^12 - 576*a^10*b^3*c^7*d^10 + 354*a^10*b^3*c^9*d^8 - 84*a^10*b^3*c^11*d^6 + 44*a^11*b^2*c^2*d^15 - 156*a^11*b^2*c^4*d^13 + 224*a^11*b^2*c^6*d^11 - 146*a^11*b^2*c^8*d^9 + 36*a^11*b^2*c^10*d^7 + 9*a*b^12*c^16*d - 9*a^12*b*c*d^16))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))*(3*b^2*d - 4*a^2*d + a*b*c))/(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*b^2*d - 4*a^2*d + a*b*c)*2i)/(f*(a^10*d^4 - b^10*c^4 + 3*a^2*b^8*c^4 - 3*a^4*b^6*c^4 + a^6*b^4*c^4 - a^4*b^6*d^4 + 3*a^6*b^4*d^4 - 3*a^8*b^2*d^4 + 4*a^3*b^7*c*d^3 - 12*a^3*b^7*c^3*d - 12*a^5*b^5*c*d^3 + 12*a^5*b^5*c^3*d + 12*a^7*b^3*c*d^3 - 4*a^7*b^3*c^3*d - 6*a^2*b^8*c^2*d^2 + 18*a^4*b^6*c^2*d^2 - 18*a^6*b^4*c^2*d^2 + 6*a^8*b^2*c^2*d^2 + 4*a*b^9*c^3*d - 4*a^9*b*c*d^3))","B"
714,1,23910,534,25.759652,"\text{Not used}","int((c + d*sin(e + f*x))^5/(a + b*sin(e + f*x))^3,x)","-\frac{\frac{-12\,a^7\,d^5+30\,a^6\,b\,c\,d^4-20\,a^5\,b^2\,c^2\,d^3+21\,a^5\,b^2\,d^5-55\,a^4\,b^3\,c\,d^4+10\,a^3\,b^4\,c^4\,d+50\,a^3\,b^4\,c^2\,d^3-6\,a^3\,b^4\,d^5-4\,a^2\,b^5\,c^5-30\,a^2\,b^5\,c^3\,d^2+10\,a^2\,b^5\,c\,d^4+5\,a\,b^6\,c^4\,d+b^7\,c^5}{b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(12\,a^9\,d^5-30\,a^8\,b\,c\,d^4+20\,a^7\,b^2\,c^2\,d^3-5\,a^7\,b^2\,d^5+15\,a^6\,b^3\,c\,d^4-10\,a^5\,b^4\,c^4\,d-10\,a^5\,b^4\,c^2\,d^3-20\,a^5\,b^4\,d^5+4\,a^4\,b^5\,c^5+30\,a^4\,b^5\,c^3\,d^2+60\,a^4\,b^5\,c\,d^4-25\,a^3\,b^6\,c^4\,d-100\,a^3\,b^6\,c^2\,d^3+4\,a^3\,b^6\,d^5+7\,a^2\,b^7\,c^5+60\,a^2\,b^7\,c^3\,d^2-10\,a\,b^8\,c^4\,d-2\,b^9\,c^5\right)}{a^2\,b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-36\,a^9\,d^5+90\,a^8\,b\,c\,d^4-60\,a^7\,b^2\,c^2\,d^3+31\,a^7\,b^2\,d^5-85\,a^6\,b^3\,c\,d^4+30\,a^5\,b^4\,c^4\,d+110\,a^5\,b^4\,c^2\,d^3+40\,a^5\,b^4\,d^5-12\,a^4\,b^5\,c^5-90\,a^4\,b^5\,c^3\,d^2-120\,a^4\,b^5\,c\,d^4+35\,a^3\,b^6\,c^4\,d+100\,a^3\,b^6\,c^2\,d^3-20\,a^3\,b^6\,d^5-5\,a^2\,b^7\,c^5-60\,a^2\,b^7\,c^3\,d^2+40\,a^2\,b^7\,c\,d^4+10\,a\,b^8\,c^4\,d+2\,b^9\,c^5\right)}{a^2\,b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(54\,a^7\,d^5-135\,a^6\,b\,c\,d^4+90\,a^5\,b^2\,c^2\,d^3-90\,a^5\,b^2\,d^5+10\,a^4\,b^3\,c^3\,d^2+250\,a^4\,b^3\,c\,d^4-55\,a^3\,b^4\,c^4\,d-240\,a^3\,b^4\,c^2\,d^3+17\,a^3\,b^4\,d^5+21\,a^2\,b^5\,c^5+140\,a^2\,b^5\,c^3\,d^2-40\,a^2\,b^5\,c\,d^4-20\,a\,b^6\,c^4\,d+4\,a\,b^6\,d^5-6\,b^7\,c^5\right)}{a\,b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-90\,a^7\,d^5+225\,a^6\,b\,c\,d^4-150\,a^5\,b^2\,c^2\,d^3+162\,a^5\,b^2\,d^5+10\,a^4\,b^3\,c^3\,d^2-410\,a^4\,b^3\,c\,d^4+65\,a^3\,b^4\,c^4\,d+360\,a^3\,b^4\,c^2\,d^3-55\,a^3\,b^4\,d^5-27\,a^2\,b^5\,c^5-220\,a^2\,b^5\,c^3\,d^2+80\,a^2\,b^5\,c\,d^4+40\,a\,b^6\,c^4\,d+4\,a\,b^6\,d^5+6\,b^7\,c^5\right)}{a\,b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(6\,a^7\,d^5-15\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^5\,b^2\,d^5+10\,a^4\,b^3\,c^3\,d^2+30\,a^4\,b^3\,c\,d^4-15\,a^3\,b^4\,c^4\,d-40\,a^3\,b^4\,c^2\,d^3+a^3\,b^4\,d^5+5\,a^2\,b^5\,c^5+20\,a^2\,b^5\,c^3\,d^2-2\,b^7\,c^5\right)}{a\,b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-42\,a^7\,d^5+105\,a^6\,b\,c\,d^4-70\,a^5\,b^2\,c^2\,d^3+74\,a^5\,b^2\,d^5+10\,a^4\,b^3\,c^3\,d^2-190\,a^4\,b^3\,c\,d^4+25\,a^3\,b^4\,c^4\,d+160\,a^3\,b^4\,c^2\,d^3-23\,a^3\,b^4\,d^5-11\,a^2\,b^5\,c^5-100\,a^2\,b^5\,c^3\,d^2+40\,a^2\,b^5\,c\,d^4+20\,a\,b^6\,c^4\,d+2\,b^7\,c^5\right)}{a\,b^3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a^2+4\,b^2\right)\,\left(-12\,a^7\,d^5+30\,a^6\,b\,c\,d^4-20\,a^5\,b^2\,c^2\,d^3+21\,a^5\,b^2\,d^5-55\,a^4\,b^3\,c\,d^4+10\,a^3\,b^4\,c^4\,d+50\,a^3\,b^4\,c^2\,d^3-6\,a^3\,b^4\,d^5-4\,a^2\,b^5\,c^5-30\,a^2\,b^5\,c^3\,d^2+10\,a^2\,b^5\,c\,d^4+5\,a\,b^6\,c^4\,d+b^7\,c^5\right)}{a^2\,b^4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a^2+8\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+a^2+12\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+12\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)}{b^5}\right)}{b^5}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}+\frac{\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)}{b^5}\right)}{b^5}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}}{\frac{8\,\left(-864\,a^{15}\,d^{15}+6480\,a^{14}\,b\,c\,d^{14}-20520\,a^{13}\,b^2\,c^2\,d^{13}+3456\,a^{13}\,b^2\,d^{15}-288\,a^{12}\,b^3\,c^5\,d^{10}+33660\,a^{12}\,b^3\,c^3\,d^{12}-27000\,a^{12}\,b^3\,c\,d^{14}+1440\,a^{11}\,b^4\,c^6\,d^9-24840\,a^{11}\,b^4\,c^4\,d^{11}+91080\,a^{11}\,b^4\,c^2\,d^{13}-4770\,a^{11}\,b^4\,d^{15}-2760\,a^{10}\,b^5\,c^7\,d^8-5928\,a^{10}\,b^5\,c^5\,d^{10}-167550\,a^{10}\,b^5\,c^3\,d^{12}+38835\,a^{10}\,b^5\,c\,d^{14}+2400\,a^9\,b^6\,c^8\,d^7+25220\,a^9\,b^6\,c^6\,d^9+167580\,a^9\,b^6\,c^4\,d^{11}-139125\,a^9\,b^6\,c^2\,d^{13}+2326\,a^9\,b^6\,d^{15}-800\,a^8\,b^7\,c^9\,d^6-15180\,a^8\,b^7\,c^7\,d^8-60342\,a^8\,b^7\,c^5\,d^{10}+281510\,a^8\,b^7\,c^3\,d^{12}-19860\,a^8\,b^7\,c\,d^{14}+48\,a^7\,b^8\,c^{10}\,d^5+480\,a^7\,b^8\,c^8\,d^7-44620\,a^7\,b^8\,c^6\,d^9-335925\,a^7\,b^8\,c^4\,d^{11}+76440\,a^7\,b^8\,c^2\,d^{13}-11\,a^7\,b^8\,d^{15}-120\,a^6\,b^9\,c^{11}\,d^4+80\,a^6\,b^9\,c^9\,d^6+46620\,a^6\,b^9\,c^7\,d^8+206889\,a^6\,b^9\,c^5\,d^{10}-174080\,a^6\,b^9\,c^3\,d^{12}+45\,a^6\,b^9\,c\,d^{14}+80\,a^5\,b^{10}\,c^{12}\,d^3+2652\,a^5\,b^{10}\,c^{10}\,d^5+2940\,a^5\,b^{10}\,c^8\,d^7-2490\,a^5\,b^{10}\,c^6\,d^9+255870\,a^5\,b^{10}\,c^4\,d^{11}+330\,a^5\,b^{10}\,c^2\,d^{13}-20\,a^5\,b^{10}\,d^{15}-1320\,a^4\,b^{11}\,c^{11}\,d^4-18970\,a^4\,b^{11}\,c^9\,d^6-92100\,a^4\,b^{11}\,c^7\,d^8-246516\,a^4\,b^{11}\,c^5\,d^{10}-1550\,a^4\,b^{11}\,c^3\,d^{12}+60\,a^4\,b^{11}\,c\,d^{14}+80\,a^3\,b^{12}\,c^{12}\,d^3+7416\,a^3\,b^{12}\,c^{10}\,d^5+61605\,a^3\,b^{12}\,c^8\,d^7+150460\,a^3\,b^{12}\,c^6\,d^9+2385\,a^3\,b^{12}\,c^4\,d^{11}-60\,a^3\,b^{12}\,c^2\,d^{13}-630\,a^2\,b^{13}\,c^{11}\,d^4-15230\,a^2\,b^{13}\,c^9\,d^6-52680\,a^2\,b^{13}\,c^7\,d^8-1599\,a^2\,b^{13}\,c^5\,d^{10}+20\,a^2\,b^{13}\,c^3\,d^{12}+20\,a\,b^{14}\,c^{12}\,d^3+801\,a\,b^{14}\,c^{10}\,d^5+8040\,a\,b^{14}\,c^8\,d^7+400\,a\,b^{14}\,c^6\,d^9\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-1728\,a^{16}\,d^{15}+12960\,a^{15}\,b\,c\,d^{14}-41040\,a^{14}\,b^2\,c^2\,d^{13}+7344\,a^{14}\,b^2\,d^{15}+70200\,a^{13}\,b^3\,c^3\,d^{12}-56160\,a^{13}\,b^3\,c\,d^{14}-68400\,a^{12}\,b^4\,c^4\,d^{11}+180540\,a^{12}\,b^4\,c^2\,d^{13}-11700\,a^{12}\,b^4\,d^{15}+36288\,a^{11}\,b^5\,c^5\,d^{10}-310860\,a^{11}\,b^5\,c^3\,d^{12}+92970\,a^{11}\,b^5\,c\,d^{14}-9440\,a^{10}\,b^6\,c^6\,d^9+297240\,a^{10}\,b^6\,c^4\,d^{11}-310560\,a^{10}\,b^6\,c^2\,d^{13}+7829\,a^{10}\,b^6\,d^{15}+2760\,a^9\,b^7\,c^7\,d^8-137784\,a^9\,b^7\,c^5\,d^{10}+558240\,a^9\,b^7\,c^3\,d^{12}-66735\,a^9\,b^7\,c\,d^{14}-2400\,a^8\,b^8\,c^8\,d^7+5340\,a^8\,b^8\,c^6\,d^9-565440\,a^8\,b^8\,c^4\,d^{11}+237870\,a^8\,b^8\,c^2\,d^{13}-1314\,a^8\,b^8\,d^{15}+800\,a^7\,b^9\,c^9\,d^6+17940\,a^7\,b^9\,c^7\,d^8+291630\,a^7\,b^9\,c^5\,d^{10}-458210\,a^7\,b^9\,c^3\,d^{12}+14460\,a^7\,b^9\,c\,d^{14}-2400\,a^6\,b^{10}\,c^8\,d^7-31020\,a^6\,b^{10}\,c^6\,d^9+509145\,a^6\,b^{10}\,c^4\,d^{11}-61080\,a^6\,b^{10}\,c^2\,d^{13}-411\,a^6\,b^{10}\,d^{15}-1200\,a^5\,b^{11}\,c^9\,d^6-36120\,a^5\,b^{11}\,c^7\,d^8-314259\,a^5\,b^{11}\,c^5\,d^{10}+134160\,a^5\,b^{11}\,c^3\,d^{12}+2445\,a^5\,b^{11}\,c\,d^{14}+12000\,a^4\,b^{12}\,c^8\,d^7+83780\,a^4\,b^{12}\,c^6\,d^9-168930\,a^4\,b^{12}\,c^4\,d^{11}-5670\,a^4\,b^{12}\,c^2\,d^{13}-20\,a^4\,b^{12}\,d^{15}+7380\,a^3\,b^{13}\,c^7\,d^8+123324\,a^3\,b^{13}\,c^5\,d^{10}+6450\,a^3\,b^{13}\,c^3\,d^{12}+60\,a^3\,b^{13}\,c\,d^{14}-7200\,a^2\,b^{14}\,c^8\,d^7-48660\,a^2\,b^{14}\,c^6\,d^9-3615\,a^2\,b^{14}\,c^4\,d^{11}-60\,a^2\,b^{14}\,c^2\,d^{13}+400\,a\,b^{15}\,c^9\,d^6+8040\,a\,b^{15}\,c^7\,d^8+801\,a\,b^{15}\,c^5\,d^{10}+20\,a\,b^{15}\,c^3\,d^{12}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)}{b^5}\right)}{b^5}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)}{b^5}-\frac{\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)}{b^5}\right)}{b^5}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)}{b^5}}\right)\,\left(a^2\,d^5\,6{}\mathrm{i}+\frac{b^2\,d^3\,\left(20\,c^2+d^2\right)\,1{}\mathrm{i}}{2}-a\,b\,c\,d^4\,15{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^5\,f}-\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}{\frac{8\,\left(-864\,a^{15}\,d^{15}+6480\,a^{14}\,b\,c\,d^{14}-20520\,a^{13}\,b^2\,c^2\,d^{13}+3456\,a^{13}\,b^2\,d^{15}-288\,a^{12}\,b^3\,c^5\,d^{10}+33660\,a^{12}\,b^3\,c^3\,d^{12}-27000\,a^{12}\,b^3\,c\,d^{14}+1440\,a^{11}\,b^4\,c^6\,d^9-24840\,a^{11}\,b^4\,c^4\,d^{11}+91080\,a^{11}\,b^4\,c^2\,d^{13}-4770\,a^{11}\,b^4\,d^{15}-2760\,a^{10}\,b^5\,c^7\,d^8-5928\,a^{10}\,b^5\,c^5\,d^{10}-167550\,a^{10}\,b^5\,c^3\,d^{12}+38835\,a^{10}\,b^5\,c\,d^{14}+2400\,a^9\,b^6\,c^8\,d^7+25220\,a^9\,b^6\,c^6\,d^9+167580\,a^9\,b^6\,c^4\,d^{11}-139125\,a^9\,b^6\,c^2\,d^{13}+2326\,a^9\,b^6\,d^{15}-800\,a^8\,b^7\,c^9\,d^6-15180\,a^8\,b^7\,c^7\,d^8-60342\,a^8\,b^7\,c^5\,d^{10}+281510\,a^8\,b^7\,c^3\,d^{12}-19860\,a^8\,b^7\,c\,d^{14}+48\,a^7\,b^8\,c^{10}\,d^5+480\,a^7\,b^8\,c^8\,d^7-44620\,a^7\,b^8\,c^6\,d^9-335925\,a^7\,b^8\,c^4\,d^{11}+76440\,a^7\,b^8\,c^2\,d^{13}-11\,a^7\,b^8\,d^{15}-120\,a^6\,b^9\,c^{11}\,d^4+80\,a^6\,b^9\,c^9\,d^6+46620\,a^6\,b^9\,c^7\,d^8+206889\,a^6\,b^9\,c^5\,d^{10}-174080\,a^6\,b^9\,c^3\,d^{12}+45\,a^6\,b^9\,c\,d^{14}+80\,a^5\,b^{10}\,c^{12}\,d^3+2652\,a^5\,b^{10}\,c^{10}\,d^5+2940\,a^5\,b^{10}\,c^8\,d^7-2490\,a^5\,b^{10}\,c^6\,d^9+255870\,a^5\,b^{10}\,c^4\,d^{11}+330\,a^5\,b^{10}\,c^2\,d^{13}-20\,a^5\,b^{10}\,d^{15}-1320\,a^4\,b^{11}\,c^{11}\,d^4-18970\,a^4\,b^{11}\,c^9\,d^6-92100\,a^4\,b^{11}\,c^7\,d^8-246516\,a^4\,b^{11}\,c^5\,d^{10}-1550\,a^4\,b^{11}\,c^3\,d^{12}+60\,a^4\,b^{11}\,c\,d^{14}+80\,a^3\,b^{12}\,c^{12}\,d^3+7416\,a^3\,b^{12}\,c^{10}\,d^5+61605\,a^3\,b^{12}\,c^8\,d^7+150460\,a^3\,b^{12}\,c^6\,d^9+2385\,a^3\,b^{12}\,c^4\,d^{11}-60\,a^3\,b^{12}\,c^2\,d^{13}-630\,a^2\,b^{13}\,c^{11}\,d^4-15230\,a^2\,b^{13}\,c^9\,d^6-52680\,a^2\,b^{13}\,c^7\,d^8-1599\,a^2\,b^{13}\,c^5\,d^{10}+20\,a^2\,b^{13}\,c^3\,d^{12}+20\,a\,b^{14}\,c^{12}\,d^3+801\,a\,b^{14}\,c^{10}\,d^5+8040\,a\,b^{14}\,c^8\,d^7+400\,a\,b^{14}\,c^6\,d^9\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-1728\,a^{16}\,d^{15}+12960\,a^{15}\,b\,c\,d^{14}-41040\,a^{14}\,b^2\,c^2\,d^{13}+7344\,a^{14}\,b^2\,d^{15}+70200\,a^{13}\,b^3\,c^3\,d^{12}-56160\,a^{13}\,b^3\,c\,d^{14}-68400\,a^{12}\,b^4\,c^4\,d^{11}+180540\,a^{12}\,b^4\,c^2\,d^{13}-11700\,a^{12}\,b^4\,d^{15}+36288\,a^{11}\,b^5\,c^5\,d^{10}-310860\,a^{11}\,b^5\,c^3\,d^{12}+92970\,a^{11}\,b^5\,c\,d^{14}-9440\,a^{10}\,b^6\,c^6\,d^9+297240\,a^{10}\,b^6\,c^4\,d^{11}-310560\,a^{10}\,b^6\,c^2\,d^{13}+7829\,a^{10}\,b^6\,d^{15}+2760\,a^9\,b^7\,c^7\,d^8-137784\,a^9\,b^7\,c^5\,d^{10}+558240\,a^9\,b^7\,c^3\,d^{12}-66735\,a^9\,b^7\,c\,d^{14}-2400\,a^8\,b^8\,c^8\,d^7+5340\,a^8\,b^8\,c^6\,d^9-565440\,a^8\,b^8\,c^4\,d^{11}+237870\,a^8\,b^8\,c^2\,d^{13}-1314\,a^8\,b^8\,d^{15}+800\,a^7\,b^9\,c^9\,d^6+17940\,a^7\,b^9\,c^7\,d^8+291630\,a^7\,b^9\,c^5\,d^{10}-458210\,a^7\,b^9\,c^3\,d^{12}+14460\,a^7\,b^9\,c\,d^{14}-2400\,a^6\,b^{10}\,c^8\,d^7-31020\,a^6\,b^{10}\,c^6\,d^9+509145\,a^6\,b^{10}\,c^4\,d^{11}-61080\,a^6\,b^{10}\,c^2\,d^{13}-411\,a^6\,b^{10}\,d^{15}-1200\,a^5\,b^{11}\,c^9\,d^6-36120\,a^5\,b^{11}\,c^7\,d^8-314259\,a^5\,b^{11}\,c^5\,d^{10}+134160\,a^5\,b^{11}\,c^3\,d^{12}+2445\,a^5\,b^{11}\,c\,d^{14}+12000\,a^4\,b^{12}\,c^8\,d^7+83780\,a^4\,b^{12}\,c^6\,d^9-168930\,a^4\,b^{12}\,c^4\,d^{11}-5670\,a^4\,b^{12}\,c^2\,d^{13}-20\,a^4\,b^{12}\,d^{15}+7380\,a^3\,b^{13}\,c^7\,d^8+123324\,a^3\,b^{13}\,c^5\,d^{10}+6450\,a^3\,b^{13}\,c^3\,d^{12}+60\,a^3\,b^{13}\,c\,d^{14}-7200\,a^2\,b^{14}\,c^8\,d^7-48660\,a^2\,b^{14}\,c^6\,d^9-3615\,a^2\,b^{14}\,c^4\,d^{11}-60\,a^2\,b^{14}\,c^2\,d^{13}+400\,a\,b^{15}\,c^9\,d^6+8040\,a\,b^{15}\,c^7\,d^8+801\,a\,b^{15}\,c^5\,d^{10}+20\,a\,b^{15}\,c^3\,d^{12}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}-\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}-\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(288\,a^{14}\,b^4\,d^{10}-1440\,a^{13}\,b^5\,c\,d^9+2760\,a^{12}\,b^6\,c^2\,d^8-1104\,a^{12}\,b^6\,d^{10}-2400\,a^{11}\,b^7\,c^3\,d^7+5640\,a^{11}\,b^7\,c\,d^9+800\,a^{10}\,b^8\,c^4\,d^6-10960\,a^{10}\,b^8\,c^2\,d^8+1538\,a^{10}\,b^8\,d^{10}+9600\,a^9\,b^9\,c^3\,d^7-8160\,a^9\,b^9\,c\,d^9-3200\,a^8\,b^{10}\,c^4\,d^6+16240\,a^8\,b^{10}\,c^2\,d^8-872\,a^8\,b^{10}\,d^{10}-14400\,a^7\,b^{11}\,c^3\,d^7+5040\,a^7\,b^{11}\,c\,d^9+4800\,a^6\,b^{12}\,c^4\,d^6-10560\,a^6\,b^{12}\,c^2\,d^8+108\,a^6\,b^{12}\,d^{10}+9600\,a^5\,b^{13}\,c^3\,d^7-960\,a^5\,b^{13}\,c\,d^9-3200\,a^4\,b^{14}\,c^4\,d^6+2440\,a^4\,b^{14}\,c^2\,d^8+40\,a^4\,b^{14}\,d^{10}-2400\,a^3\,b^{15}\,c^3\,d^7-120\,a^3\,b^{15}\,c\,d^9+800\,a^2\,b^{16}\,c^4\,d^6+80\,a^2\,b^{16}\,c^2\,d^8+2\,a^2\,b^{16}\,d^{10}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(288\,a^{15}\,b^4\,d^{10}-1440\,a^{14}\,b^5\,c\,d^9+2760\,a^{13}\,b^6\,c^2\,d^8-1536\,a^{13}\,b^6\,d^{10}-2400\,a^{12}\,b^7\,c^3\,d^7+7800\,a^{12}\,b^7\,c\,d^9+800\,a^{11}\,b^8\,c^4\,d^6-15100\,a^{11}\,b^8\,c^2\,d^8+3194\,a^{11}\,b^8\,d^{10}-48\,a^{10}\,b^9\,c^5\,d^5+12960\,a^{10}\,b^9\,c^3\,d^7-16710\,a^{10}\,b^9\,c\,d^9+120\,a^9\,b^{10}\,c^6\,d^4-3440\,a^9\,b^{10}\,c^4\,d^6+33445\,a^9\,b^{10}\,c^2\,d^8-3134\,a^9\,b^{10}\,d^{10}-80\,a^8\,b^{11}\,c^7\,d^3-1208\,a^8\,b^{11}\,c^5\,d^5-30200\,a^8\,b^{11}\,c^3\,d^7+17160\,a^8\,b^{11}\,c\,d^9+360\,a^7\,b^{12}\,c^6\,d^4+9330\,a^7\,b^{12}\,c^4\,d^6-36000\,a^7\,b^{12}\,c^2\,d^8+1326\,a^7\,b^{12}\,d^{10}+160\,a^6\,b^{13}\,c^7\,d^3+2428\,a^6\,b^{13}\,c^5\,d^5+34960\,a^6\,b^{13}\,c^3\,d^7-7920\,a^6\,b^{13}\,c\,d^9+4\,a^5\,b^{14}\,c^{10}+40\,a^5\,b^{14}\,c^8\,d^2-1310\,a^5\,b^{14}\,c^6\,d^4-13600\,a^5\,b^{14}\,c^4\,d^6+17780\,a^5\,b^{14}\,c^2\,d^8-88\,a^5\,b^{14}\,d^{10}-60\,a^4\,b^{15}\,c^9\,d-440\,a^4\,b^{15}\,c^7\,d^3-1040\,a^4\,b^{15}\,c^5\,d^5-18800\,a^4\,b^{15}\,c^3\,d^7+900\,a^4\,b^{15}\,c\,d^9+4\,a^3\,b^{16}\,c^{10}+325\,a^3\,b^{16}\,c^8\,d^2+2320\,a^3\,b^{16}\,c^6\,d^4+9600\,a^3\,b^{16}\,c^4\,d^6-2400\,a^3\,b^{16}\,c^2\,d^8-39\,a^3\,b^{16}\,d^{10}-30\,a^2\,b^{17}\,c^9\,d-720\,a^2\,b^{17}\,c^7\,d^3-2400\,a^2\,b^{17}\,c^5\,d^5+2400\,a^2\,b^{17}\,c^3\,d^7+120\,a^2\,b^{17}\,c\,d^9+a\,b^{18}\,c^{10}+40\,a\,b^{18}\,c^8\,d^2+400\,a\,b^{18}\,c^6\,d^4-800\,a\,b^{18}\,c^4\,d^6-80\,a\,b^{18}\,c^2\,d^8-2\,a\,b^{18}\,d^{10}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(24\,a^{11}\,b^{10}\,d^5-60\,a^{10}\,b^{11}\,c\,d^4+40\,a^9\,b^{12}\,c^2\,d^3-100\,a^9\,b^{12}\,d^5-8\,a^8\,b^{13}\,c^5-40\,a^8\,b^{13}\,c^3\,d^2+240\,a^8\,b^{13}\,c\,d^4+60\,a^7\,b^{14}\,c^4\,d-80\,a^7\,b^{14}\,c^2\,d^3+164\,a^7\,b^{14}\,d^5+12\,a^6\,b^{15}\,c^5-420\,a^6\,b^{15}\,c\,d^4-120\,a^5\,b^{16}\,c^4\,d+120\,a^5\,b^{16}\,c^2\,d^3-120\,a^5\,b^{16}\,d^5+120\,a^4\,b^{17}\,c^3\,d^2+360\,a^4\,b^{17}\,c\,d^4+60\,a^3\,b^{18}\,c^4\,d-160\,a^3\,b^{18}\,c^2\,d^3+28\,a^3\,b^{18}\,d^5-4\,a^2\,b^{19}\,c^5-80\,a^2\,b^{19}\,c^3\,d^2-120\,a^2\,b^{19}\,c\,d^4+80\,a\,b^{20}\,c^2\,d^3+4\,a\,b^{20}\,d^5\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^{12}\,b^{10}\,d^5+120\,a^{11}\,b^{11}\,c\,d^4-80\,a^{10}\,b^{12}\,c^2\,d^3+212\,a^{10}\,b^{12}\,d^5-540\,a^9\,b^{13}\,c\,d^4+360\,a^8\,b^{14}\,c^2\,d^3-360\,a^8\,b^{14}\,d^5+8\,a^7\,b^{15}\,c^5+40\,a^7\,b^{15}\,c^3\,d^2+960\,a^7\,b^{15}\,c\,d^4-60\,a^6\,b^{16}\,c^4\,d-720\,a^6\,b^{16}\,c^2\,d^3+276\,a^6\,b^{16}\,d^5-12\,a^5\,b^{17}\,c^5-780\,a^5\,b^{17}\,c\,d^4+120\,a^4\,b^{18}\,c^4\,d+680\,a^4\,b^{18}\,c^2\,d^3-80\,a^4\,b^{18}\,d^5-120\,a^3\,b^{19}\,c^3\,d^2+240\,a^3\,b^{19}\,c\,d^4-60\,a^2\,b^{20}\,c^4\,d-240\,a^2\,b^{20}\,c^2\,d^3+4\,a\,b^{21}\,c^5+80\,a\,b^{21}\,c^3\,d^2\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}+\frac{\left(\frac{4\,\left(8\,a^{10}\,b^{14}-32\,a^8\,b^{16}+48\,a^6\,b^{18}-32\,a^4\,b^{20}+8\,a^2\,b^{22}\right)}{a^8\,b^{11}-4\,a^6\,b^{13}+6\,a^4\,b^{15}-4\,a^2\,b^{17}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{14}+44\,a^9\,b^{16}-96\,a^7\,b^{18}+104\,a^5\,b^{20}-56\,a^3\,b^{22}+12\,a\,b^{24}\right)}{a^8\,b^{12}-4\,a^6\,b^{14}+6\,a^4\,b^{16}-4\,a^2\,b^{18}+b^{20}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,{\left(a\,d-b\,c\right)}^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2+6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-29\,a^2\,b^2\,d^2-12\,a\,b^3\,c\,d+b^4\,c^2+20\,b^4\,d^2\right)\,1{}\mathrm{i}}{f\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}","Not used",1,"- ((b^7*c^5 - 12*a^7*d^5 - 4*a^2*b^5*c^5 - 6*a^3*b^4*d^5 + 21*a^5*b^2*d^5 + 10*a^2*b^5*c*d^4 + 10*a^3*b^4*c^4*d - 55*a^4*b^3*c*d^4 - 30*a^2*b^5*c^3*d^2 + 50*a^3*b^4*c^2*d^3 - 20*a^5*b^2*c^2*d^3 + 5*a*b^6*c^4*d + 30*a^6*b*c*d^4)/(b^4*(a^4 + b^4 - 2*a^2*b^2)) - (tan(e/2 + (f*x)/2)^6*(12*a^9*d^5 - 2*b^9*c^5 + 7*a^2*b^7*c^5 + 4*a^4*b^5*c^5 + 4*a^3*b^6*d^5 - 20*a^5*b^4*d^5 - 5*a^7*b^2*d^5 - 25*a^3*b^6*c^4*d + 60*a^4*b^5*c*d^4 - 10*a^5*b^4*c^4*d + 15*a^6*b^3*c*d^4 + 60*a^2*b^7*c^3*d^2 - 100*a^3*b^6*c^2*d^3 + 30*a^4*b^5*c^3*d^2 - 10*a^5*b^4*c^2*d^3 + 20*a^7*b^2*c^2*d^3 - 10*a*b^8*c^4*d - 30*a^8*b*c*d^4))/(a^2*b^4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^2*(2*b^9*c^5 - 36*a^9*d^5 - 5*a^2*b^7*c^5 - 12*a^4*b^5*c^5 - 20*a^3*b^6*d^5 + 40*a^5*b^4*d^5 + 31*a^7*b^2*d^5 + 40*a^2*b^7*c*d^4 + 35*a^3*b^6*c^4*d - 120*a^4*b^5*c*d^4 + 30*a^5*b^4*c^4*d - 85*a^6*b^3*c*d^4 - 60*a^2*b^7*c^3*d^2 + 100*a^3*b^6*c^2*d^3 - 90*a^4*b^5*c^3*d^2 + 110*a^5*b^4*c^2*d^3 - 60*a^7*b^2*c^2*d^3 + 10*a*b^8*c^4*d + 90*a^8*b*c*d^4))/(a^2*b^4*(a^4 + b^4 - 2*a^2*b^2)) - (tan(e/2 + (f*x)/2)^5*(54*a^7*d^5 - 6*b^7*c^5 + 4*a*b^6*d^5 + 21*a^2*b^5*c^5 + 17*a^3*b^4*d^5 - 90*a^5*b^2*d^5 - 40*a^2*b^5*c*d^4 - 55*a^3*b^4*c^4*d + 250*a^4*b^3*c*d^4 + 140*a^2*b^5*c^3*d^2 - 240*a^3*b^4*c^2*d^3 + 10*a^4*b^3*c^3*d^2 + 90*a^5*b^2*c^2*d^3 - 20*a*b^6*c^4*d - 135*a^6*b*c*d^4))/(a*b^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^3*(6*b^7*c^5 - 90*a^7*d^5 + 4*a*b^6*d^5 - 27*a^2*b^5*c^5 - 55*a^3*b^4*d^5 + 162*a^5*b^2*d^5 + 80*a^2*b^5*c*d^4 + 65*a^3*b^4*c^4*d - 410*a^4*b^3*c*d^4 - 220*a^2*b^5*c^3*d^2 + 360*a^3*b^4*c^2*d^3 + 10*a^4*b^3*c^3*d^2 - 150*a^5*b^2*c^2*d^3 + 40*a*b^6*c^4*d + 225*a^6*b*c*d^4))/(a*b^3*(a^4 + b^4 - 2*a^2*b^2)) - (tan(e/2 + (f*x)/2)^7*(6*a^7*d^5 - 2*b^7*c^5 + 5*a^2*b^5*c^5 + a^3*b^4*d^5 - 10*a^5*b^2*d^5 - 15*a^3*b^4*c^4*d + 30*a^4*b^3*c*d^4 + 20*a^2*b^5*c^3*d^2 - 40*a^3*b^4*c^2*d^3 + 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 15*a^6*b*c*d^4))/(a*b^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)*(2*b^7*c^5 - 42*a^7*d^5 - 11*a^2*b^5*c^5 - 23*a^3*b^4*d^5 + 74*a^5*b^2*d^5 + 40*a^2*b^5*c*d^4 + 25*a^3*b^4*c^4*d - 190*a^4*b^3*c*d^4 - 100*a^2*b^5*c^3*d^2 + 160*a^3*b^4*c^2*d^3 + 10*a^4*b^3*c^3*d^2 - 70*a^5*b^2*c^2*d^3 + 20*a*b^6*c^4*d + 105*a^6*b*c*d^4))/(a*b^3*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^4*(3*a^2 + 4*b^2)*(b^7*c^5 - 12*a^7*d^5 - 4*a^2*b^5*c^5 - 6*a^3*b^4*d^5 + 21*a^5*b^2*d^5 + 10*a^2*b^5*c*d^4 + 10*a^3*b^4*c^4*d - 55*a^4*b^3*c*d^4 - 30*a^2*b^5*c^3*d^2 + 50*a^3*b^4*c^2*d^3 - 20*a^5*b^2*c^2*d^3 + 5*a*b^6*c^4*d + 30*a^6*b*c*d^4))/(a^2*b^4*(a^4 + b^4 - 2*a^2*b^2)))/(f*(tan(e/2 + (f*x)/2)^2*(4*a^2 + 4*b^2) + tan(e/2 + (f*x)/2)^6*(4*a^2 + 4*b^2) + tan(e/2 + (f*x)/2)^4*(6*a^2 + 8*b^2) + a^2*tan(e/2 + (f*x)/2)^8 + a^2 + 12*a*b*tan(e/2 + (f*x)/2)^3 + 12*a*b*tan(e/2 + (f*x)/2)^5 + 4*a*b*tan(e/2 + (f*x)/2)^7 + 4*a*b*tan(e/2 + (f*x)/2))) - (atan(((((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*((8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i))/b^5))/b^5)*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*1i)/b^5 + (((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*((4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i))/b^5))/b^5)*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*1i)/b^5)/((8*(2326*a^9*b^6*d^15 - 20*a^5*b^10*d^15 - 11*a^7*b^8*d^15 - 864*a^15*d^15 - 4770*a^11*b^4*d^15 + 3456*a^13*b^2*d^15 + 400*a*b^14*c^6*d^9 + 8040*a*b^14*c^8*d^7 + 801*a*b^14*c^10*d^5 + 20*a*b^14*c^12*d^3 + 60*a^4*b^11*c*d^14 + 45*a^6*b^9*c*d^14 - 19860*a^8*b^7*c*d^14 + 38835*a^10*b^5*c*d^14 - 27000*a^12*b^3*c*d^14 + 20*a^2*b^13*c^3*d^12 - 1599*a^2*b^13*c^5*d^10 - 52680*a^2*b^13*c^7*d^8 - 15230*a^2*b^13*c^9*d^6 - 630*a^2*b^13*c^11*d^4 - 60*a^3*b^12*c^2*d^13 + 2385*a^3*b^12*c^4*d^11 + 150460*a^3*b^12*c^6*d^9 + 61605*a^3*b^12*c^8*d^7 + 7416*a^3*b^12*c^10*d^5 + 80*a^3*b^12*c^12*d^3 - 1550*a^4*b^11*c^3*d^12 - 246516*a^4*b^11*c^5*d^10 - 92100*a^4*b^11*c^7*d^8 - 18970*a^4*b^11*c^9*d^6 - 1320*a^4*b^11*c^11*d^4 + 330*a^5*b^10*c^2*d^13 + 255870*a^5*b^10*c^4*d^11 - 2490*a^5*b^10*c^6*d^9 + 2940*a^5*b^10*c^8*d^7 + 2652*a^5*b^10*c^10*d^5 + 80*a^5*b^10*c^12*d^3 - 174080*a^6*b^9*c^3*d^12 + 206889*a^6*b^9*c^5*d^10 + 46620*a^6*b^9*c^7*d^8 + 80*a^6*b^9*c^9*d^6 - 120*a^6*b^9*c^11*d^4 + 76440*a^7*b^8*c^2*d^13 - 335925*a^7*b^8*c^4*d^11 - 44620*a^7*b^8*c^6*d^9 + 480*a^7*b^8*c^8*d^7 + 48*a^7*b^8*c^10*d^5 + 281510*a^8*b^7*c^3*d^12 - 60342*a^8*b^7*c^5*d^10 - 15180*a^8*b^7*c^7*d^8 - 800*a^8*b^7*c^9*d^6 - 139125*a^9*b^6*c^2*d^13 + 167580*a^9*b^6*c^4*d^11 + 25220*a^9*b^6*c^6*d^9 + 2400*a^9*b^6*c^8*d^7 - 167550*a^10*b^5*c^3*d^12 - 5928*a^10*b^5*c^5*d^10 - 2760*a^10*b^5*c^7*d^8 + 91080*a^11*b^4*c^2*d^13 - 24840*a^11*b^4*c^4*d^11 + 1440*a^11*b^4*c^6*d^9 + 33660*a^12*b^3*c^3*d^12 - 288*a^12*b^3*c^5*d^10 - 20520*a^13*b^2*c^2*d^13 + 6480*a^14*b*c*d^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (16*tan(e/2 + (f*x)/2)*(7829*a^10*b^6*d^15 - 20*a^4*b^12*d^15 - 411*a^6*b^10*d^15 - 1314*a^8*b^8*d^15 - 1728*a^16*d^15 - 11700*a^12*b^4*d^15 + 7344*a^14*b^2*d^15 + 20*a*b^15*c^3*d^12 + 801*a*b^15*c^5*d^10 + 8040*a*b^15*c^7*d^8 + 400*a*b^15*c^9*d^6 + 60*a^3*b^13*c*d^14 + 2445*a^5*b^11*c*d^14 + 14460*a^7*b^9*c*d^14 - 66735*a^9*b^7*c*d^14 + 92970*a^11*b^5*c*d^14 - 56160*a^13*b^3*c*d^14 - 60*a^2*b^14*c^2*d^13 - 3615*a^2*b^14*c^4*d^11 - 48660*a^2*b^14*c^6*d^9 - 7200*a^2*b^14*c^8*d^7 + 6450*a^3*b^13*c^3*d^12 + 123324*a^3*b^13*c^5*d^10 + 7380*a^3*b^13*c^7*d^8 - 5670*a^4*b^12*c^2*d^13 - 168930*a^4*b^12*c^4*d^11 + 83780*a^4*b^12*c^6*d^9 + 12000*a^4*b^12*c^8*d^7 + 134160*a^5*b^11*c^3*d^12 - 314259*a^5*b^11*c^5*d^10 - 36120*a^5*b^11*c^7*d^8 - 1200*a^5*b^11*c^9*d^6 - 61080*a^6*b^10*c^2*d^13 + 509145*a^6*b^10*c^4*d^11 - 31020*a^6*b^10*c^6*d^9 - 2400*a^6*b^10*c^8*d^7 - 458210*a^7*b^9*c^3*d^12 + 291630*a^7*b^9*c^5*d^10 + 17940*a^7*b^9*c^7*d^8 + 800*a^7*b^9*c^9*d^6 + 237870*a^8*b^8*c^2*d^13 - 565440*a^8*b^8*c^4*d^11 + 5340*a^8*b^8*c^6*d^9 - 2400*a^8*b^8*c^8*d^7 + 558240*a^9*b^7*c^3*d^12 - 137784*a^9*b^7*c^5*d^10 + 2760*a^9*b^7*c^7*d^8 - 310560*a^10*b^6*c^2*d^13 + 297240*a^10*b^6*c^4*d^11 - 9440*a^10*b^6*c^6*d^9 - 310860*a^11*b^5*c^3*d^12 + 36288*a^11*b^5*c^5*d^10 + 180540*a^12*b^4*c^2*d^13 - 68400*a^12*b^4*c^4*d^11 + 70200*a^13*b^3*c^3*d^12 - 41040*a^14*b^2*c^2*d^13 + 12960*a^15*b*c*d^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*((8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i))/b^5))/b^5)*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i))/b^5 - (((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*((4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i))/b^5))/b^5)*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i))/b^5))*(a^2*d^5*6i + (b^2*d^3*(20*c^2 + d^2)*1i)/2 - a*b*c*d^4*15i)*2i)/(b^5*f) - (atan((((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(2326*a^9*b^6*d^15 - 20*a^5*b^10*d^15 - 11*a^7*b^8*d^15 - 864*a^15*d^15 - 4770*a^11*b^4*d^15 + 3456*a^13*b^2*d^15 + 400*a*b^14*c^6*d^9 + 8040*a*b^14*c^8*d^7 + 801*a*b^14*c^10*d^5 + 20*a*b^14*c^12*d^3 + 60*a^4*b^11*c*d^14 + 45*a^6*b^9*c*d^14 - 19860*a^8*b^7*c*d^14 + 38835*a^10*b^5*c*d^14 - 27000*a^12*b^3*c*d^14 + 20*a^2*b^13*c^3*d^12 - 1599*a^2*b^13*c^5*d^10 - 52680*a^2*b^13*c^7*d^8 - 15230*a^2*b^13*c^9*d^6 - 630*a^2*b^13*c^11*d^4 - 60*a^3*b^12*c^2*d^13 + 2385*a^3*b^12*c^4*d^11 + 150460*a^3*b^12*c^6*d^9 + 61605*a^3*b^12*c^8*d^7 + 7416*a^3*b^12*c^10*d^5 + 80*a^3*b^12*c^12*d^3 - 1550*a^4*b^11*c^3*d^12 - 246516*a^4*b^11*c^5*d^10 - 92100*a^4*b^11*c^7*d^8 - 18970*a^4*b^11*c^9*d^6 - 1320*a^4*b^11*c^11*d^4 + 330*a^5*b^10*c^2*d^13 + 255870*a^5*b^10*c^4*d^11 - 2490*a^5*b^10*c^6*d^9 + 2940*a^5*b^10*c^8*d^7 + 2652*a^5*b^10*c^10*d^5 + 80*a^5*b^10*c^12*d^3 - 174080*a^6*b^9*c^3*d^12 + 206889*a^6*b^9*c^5*d^10 + 46620*a^6*b^9*c^7*d^8 + 80*a^6*b^9*c^9*d^6 - 120*a^6*b^9*c^11*d^4 + 76440*a^7*b^8*c^2*d^13 - 335925*a^7*b^8*c^4*d^11 - 44620*a^7*b^8*c^6*d^9 + 480*a^7*b^8*c^8*d^7 + 48*a^7*b^8*c^10*d^5 + 281510*a^8*b^7*c^3*d^12 - 60342*a^8*b^7*c^5*d^10 - 15180*a^8*b^7*c^7*d^8 - 800*a^8*b^7*c^9*d^6 - 139125*a^9*b^6*c^2*d^13 + 167580*a^9*b^6*c^4*d^11 + 25220*a^9*b^6*c^6*d^9 + 2400*a^9*b^6*c^8*d^7 - 167550*a^10*b^5*c^3*d^12 - 5928*a^10*b^5*c^5*d^10 - 2760*a^10*b^5*c^7*d^8 + 91080*a^11*b^4*c^2*d^13 - 24840*a^11*b^4*c^4*d^11 + 1440*a^11*b^4*c^6*d^9 + 33660*a^12*b^3*c^3*d^12 - 288*a^12*b^3*c^5*d^10 - 20520*a^13*b^2*c^2*d^13 + 6480*a^14*b*c*d^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (16*tan(e/2 + (f*x)/2)*(7829*a^10*b^6*d^15 - 20*a^4*b^12*d^15 - 411*a^6*b^10*d^15 - 1314*a^8*b^8*d^15 - 1728*a^16*d^15 - 11700*a^12*b^4*d^15 + 7344*a^14*b^2*d^15 + 20*a*b^15*c^3*d^12 + 801*a*b^15*c^5*d^10 + 8040*a*b^15*c^7*d^8 + 400*a*b^15*c^9*d^6 + 60*a^3*b^13*c*d^14 + 2445*a^5*b^11*c*d^14 + 14460*a^7*b^9*c*d^14 - 66735*a^9*b^7*c*d^14 + 92970*a^11*b^5*c*d^14 - 56160*a^13*b^3*c*d^14 - 60*a^2*b^14*c^2*d^13 - 3615*a^2*b^14*c^4*d^11 - 48660*a^2*b^14*c^6*d^9 - 7200*a^2*b^14*c^8*d^7 + 6450*a^3*b^13*c^3*d^12 + 123324*a^3*b^13*c^5*d^10 + 7380*a^3*b^13*c^7*d^8 - 5670*a^4*b^12*c^2*d^13 - 168930*a^4*b^12*c^4*d^11 + 83780*a^4*b^12*c^6*d^9 + 12000*a^4*b^12*c^8*d^7 + 134160*a^5*b^11*c^3*d^12 - 314259*a^5*b^11*c^5*d^10 - 36120*a^5*b^11*c^7*d^8 - 1200*a^5*b^11*c^9*d^6 - 61080*a^6*b^10*c^2*d^13 + 509145*a^6*b^10*c^4*d^11 - 31020*a^6*b^10*c^6*d^9 - 2400*a^6*b^10*c^8*d^7 - 458210*a^7*b^9*c^3*d^12 + 291630*a^7*b^9*c^5*d^10 + 17940*a^7*b^9*c^7*d^8 + 800*a^7*b^9*c^9*d^6 + 237870*a^8*b^8*c^2*d^13 - 565440*a^8*b^8*c^4*d^11 + 5340*a^8*b^8*c^6*d^9 - 2400*a^8*b^8*c^8*d^7 + 558240*a^9*b^7*c^3*d^12 - 137784*a^9*b^7*c^5*d^10 + 2760*a^9*b^7*c^7*d^8 - 310560*a^10*b^6*c^2*d^13 + 297240*a^10*b^6*c^4*d^11 - 9440*a^10*b^6*c^6*d^9 - 310860*a^11*b^5*c^3*d^12 + 36288*a^11*b^5*c^5*d^10 + 180540*a^12*b^4*c^2*d^13 - 68400*a^12*b^4*c^4*d^11 + 70200*a^13*b^3*c^3*d^12 - 41040*a^14*b^2*c^2*d^13 + 12960*a^15*b*c*d^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) - (4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) - ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(2*a^2*b^16*d^10 + 40*a^4*b^14*d^10 + 108*a^6*b^12*d^10 - 872*a^8*b^10*d^10 + 1538*a^10*b^8*d^10 - 1104*a^12*b^6*d^10 + 288*a^14*b^4*d^10 - 120*a^3*b^15*c*d^9 - 960*a^5*b^13*c*d^9 + 5040*a^7*b^11*c*d^9 - 8160*a^9*b^9*c*d^9 + 5640*a^11*b^7*c*d^9 - 1440*a^13*b^5*c*d^9 + 80*a^2*b^16*c^2*d^8 + 800*a^2*b^16*c^4*d^6 - 2400*a^3*b^15*c^3*d^7 + 2440*a^4*b^14*c^2*d^8 - 3200*a^4*b^14*c^4*d^6 + 9600*a^5*b^13*c^3*d^7 - 10560*a^6*b^12*c^2*d^8 + 4800*a^6*b^12*c^4*d^6 - 14400*a^7*b^11*c^3*d^7 + 16240*a^8*b^10*c^2*d^8 - 3200*a^8*b^10*c^4*d^6 + 9600*a^9*b^9*c^3*d^7 - 10960*a^10*b^8*c^2*d^8 + 800*a^10*b^8*c^4*d^6 - 2400*a^11*b^7*c^3*d^7 + 2760*a^12*b^6*c^2*d^8))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^10 - 2*a*b^18*d^10 + 4*a^3*b^16*c^10 + 4*a^5*b^14*c^10 - 39*a^3*b^16*d^10 - 88*a^5*b^14*d^10 + 1326*a^7*b^12*d^10 - 3134*a^9*b^10*d^10 + 3194*a^11*b^8*d^10 - 1536*a^13*b^6*d^10 + 288*a^15*b^4*d^10 - 80*a*b^18*c^2*d^8 - 800*a*b^18*c^4*d^6 + 400*a*b^18*c^6*d^4 + 40*a*b^18*c^8*d^2 + 120*a^2*b^17*c*d^9 - 30*a^2*b^17*c^9*d + 900*a^4*b^15*c*d^9 - 60*a^4*b^15*c^9*d - 7920*a^6*b^13*c*d^9 + 17160*a^8*b^11*c*d^9 - 16710*a^10*b^9*c*d^9 + 7800*a^12*b^7*c*d^9 - 1440*a^14*b^5*c*d^9 + 2400*a^2*b^17*c^3*d^7 - 2400*a^2*b^17*c^5*d^5 - 720*a^2*b^17*c^7*d^3 - 2400*a^3*b^16*c^2*d^8 + 9600*a^3*b^16*c^4*d^6 + 2320*a^3*b^16*c^6*d^4 + 325*a^3*b^16*c^8*d^2 - 18800*a^4*b^15*c^3*d^7 - 1040*a^4*b^15*c^5*d^5 - 440*a^4*b^15*c^7*d^3 + 17780*a^5*b^14*c^2*d^8 - 13600*a^5*b^14*c^4*d^6 - 1310*a^5*b^14*c^6*d^4 + 40*a^5*b^14*c^8*d^2 + 34960*a^6*b^13*c^3*d^7 + 2428*a^6*b^13*c^5*d^5 + 160*a^6*b^13*c^7*d^3 - 36000*a^7*b^12*c^2*d^8 + 9330*a^7*b^12*c^4*d^6 + 360*a^7*b^12*c^6*d^4 - 30200*a^8*b^11*c^3*d^7 - 1208*a^8*b^11*c^5*d^5 - 80*a^8*b^11*c^7*d^3 + 33445*a^9*b^10*c^2*d^8 - 3440*a^9*b^10*c^4*d^6 + 120*a^9*b^10*c^6*d^4 + 12960*a^10*b^9*c^3*d^7 - 48*a^10*b^9*c^5*d^5 - 15100*a^11*b^8*c^2*d^8 + 800*a^11*b^8*c^4*d^6 - 2400*a^12*b^7*c^3*d^7 + 2760*a^13*b^6*c^2*d^8))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + ((a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*a*b^20*d^5 - 4*a^2*b^19*c^5 + 12*a^6*b^15*c^5 - 8*a^8*b^13*c^5 + 28*a^3*b^18*d^5 - 120*a^5*b^16*d^5 + 164*a^7*b^14*d^5 - 100*a^9*b^12*d^5 + 24*a^11*b^10*d^5 + 80*a*b^20*c^2*d^3 - 120*a^2*b^19*c*d^4 + 60*a^3*b^18*c^4*d + 360*a^4*b^17*c*d^4 - 120*a^5*b^16*c^4*d - 420*a^6*b^15*c*d^4 + 60*a^7*b^14*c^4*d + 240*a^8*b^13*c*d^4 - 60*a^10*b^11*c*d^4 - 80*a^2*b^19*c^3*d^2 - 160*a^3*b^18*c^2*d^3 + 120*a^4*b^17*c^3*d^2 + 120*a^5*b^16*c^2*d^3 - 80*a^7*b^14*c^2*d^3 - 40*a^8*b^13*c^3*d^2 + 40*a^9*b^12*c^2*d^3))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) - (8*tan(e/2 + (f*x)/2)*(4*a*b^21*c^5 - 12*a^5*b^17*c^5 + 8*a^7*b^15*c^5 - 80*a^4*b^18*d^5 + 276*a^6*b^16*d^5 - 360*a^8*b^14*d^5 + 212*a^10*b^12*d^5 - 48*a^12*b^10*d^5 + 80*a*b^21*c^3*d^2 - 60*a^2*b^20*c^4*d + 240*a^3*b^19*c*d^4 + 120*a^4*b^18*c^4*d - 780*a^5*b^17*c*d^4 - 60*a^6*b^16*c^4*d + 960*a^7*b^15*c*d^4 - 540*a^9*b^13*c*d^4 + 120*a^11*b^11*c*d^4 - 240*a^2*b^20*c^2*d^3 - 120*a^3*b^19*c^3*d^2 + 680*a^4*b^18*c^2*d^3 - 720*a^6*b^16*c^2*d^3 + 40*a^7*b^15*c^3*d^2 + 360*a^8*b^14*c^2*d^3 - 80*a^10*b^12*c^2*d^3))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12) + (((4*(8*a^2*b^22 - 32*a^4*b^20 + 48*a^6*b^18 - 32*a^8*b^16 + 8*a^10*b^14))/(b^19 - 4*a^2*b^17 + 6*a^4*b^15 - 4*a^6*b^13 + a^8*b^11) + (8*tan(e/2 + (f*x)/2)*(12*a*b^24 - 56*a^3*b^22 + 104*a^5*b^20 - 96*a^7*b^18 + 44*a^9*b^16 - 8*a^11*b^14))/(b^20 - 4*a^2*b^18 + 6*a^4*b^16 - 4*a^6*b^14 + a^8*b^12))*(a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*(a*d - b*c)^3*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 20*b^4*d^2 + 2*a^2*b^2*c^2 - 29*a^2*b^2*d^2 - 12*a*b^3*c*d + 6*a^3*b*c*d)*1i)/(f*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))","B"
715,1,16958,318,21.743437,"\text{Not used}","int((c + d*sin(e + f*x))^4/(a + b*sin(e + f*x))^3,x)","-\frac{\frac{6\,a^6\,d^4-8\,a^5\,b\,c\,d^3-11\,a^4\,b^2\,d^4+8\,a^3\,b^3\,c^3\,d+20\,a^3\,b^3\,c\,d^3-4\,a^2\,b^4\,c^4-18\,a^2\,b^4\,c^2\,d^2+2\,a^2\,b^4\,d^4+4\,a\,b^5\,c^3\,d+b^6\,c^4}{b^3\,{\left(a^2-b^2\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,a^8\,d^4-8\,a^7\,b\,c\,d^3-3\,a^6\,b^2\,d^4+8\,a^5\,b^3\,c^3\,d+12\,a^5\,b^3\,c\,d^3-4\,a^4\,b^4\,c^4-18\,a^4\,b^4\,c^2\,d^2-13\,a^4\,b^4\,d^4+12\,a^3\,b^5\,c^3\,d+20\,a^3\,b^5\,c\,d^3-3\,a^2\,b^6\,c^4-18\,a^2\,b^6\,c^2\,d^2+4\,a^2\,b^6\,d^4+4\,a\,b^7\,c^3\,d+b^8\,c^4\right)}{a^2\,b^3\,{\left(a^2-b^2\right)}^2}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(6\,a^6\,d^4-8\,a^5\,b\,c\,d^3-11\,a^4\,b^2\,d^4+8\,a^3\,b^3\,c^3\,d+20\,a^3\,b^3\,c\,d^3-4\,a^2\,b^4\,c^4-18\,a^2\,b^4\,c^2\,d^2+2\,a^2\,b^4\,d^4+4\,a\,b^5\,c^3\,d+b^6\,c^4\right)}{a\,b^2\,{\left(a^2-b^2\right)}^2}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(21\,a^6\,d^4-28\,a^5\,b\,c\,d^3+6\,a^4\,b^2\,c^2\,d^2-38\,a^4\,b^2\,d^4+20\,a^3\,b^3\,c^3\,d+64\,a^3\,b^3\,c\,d^3-11\,a^2\,b^4\,c^4-60\,a^2\,b^4\,c^2\,d^2+8\,a^2\,b^4\,d^4+16\,a\,b^5\,c^3\,d+2\,b^6\,c^4\right)}{a\,b^2\,{\left(a^2-b^2\right)}^2}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-3\,a^6\,d^4+4\,a^5\,b\,c\,d^3+6\,a^4\,b^2\,c^2\,d^2+6\,a^4\,b^2\,d^4-12\,a^3\,b^3\,c^3\,d-16\,a^3\,b^3\,c\,d^3+5\,a^2\,b^4\,c^4+12\,a^2\,b^4\,c^2\,d^2-2\,b^6\,c^4\right)}{a\,b^2\,{\left(a^2-b^2\right)}^2}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a^8\,d^4-8\,a^7\,b\,c\,d^3-3\,a^6\,b^2\,d^4+8\,a^5\,b^3\,c^3\,d+4\,a^5\,b^3\,c\,d^3-4\,a^4\,b^4\,c^4-18\,a^4\,b^4\,c^2\,d^2-12\,a^4\,b^4\,d^4+20\,a^3\,b^5\,c^3\,d+40\,a^3\,b^5\,c\,d^3-7\,a^2\,b^6\,c^4-36\,a^2\,b^6\,c^2\,d^2+8\,a\,b^7\,c^3\,d+2\,b^8\,c^4\right)}{a^2\,b^3\,{\left(a^2-b^2\right)}^2}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+a^2+8\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}+\frac{2\,d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}-\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{16\,\left(54\,a^{12}\,d^{12}-216\,a^{11}\,b\,c\,d^{11}-36\,a^{10}\,b^2\,c^4\,d^8+180\,a^{10}\,b^2\,c^2\,d^{10}-243\,a^{10}\,b^2\,d^{12}+96\,a^9\,b^3\,c^5\,d^7+376\,a^9\,b^3\,c^3\,d^9+1116\,a^9\,b^3\,c\,d^{11}-64\,a^8\,b^4\,c^6\,d^6-678\,a^8\,b^4\,c^4\,d^8-1572\,a^8\,b^4\,c^2\,d^{10}+378\,a^8\,b^4\,d^{12}+144\,a^7\,b^5\,c^5\,d^7-104\,a^7\,b^5\,c^3\,d^9-1944\,a^7\,b^5\,c\,d^{11}-12\,a^6\,b^6\,c^8\,d^4+88\,a^6\,b^6\,c^6\,d^6+1758\,a^6\,b^6\,c^4\,d^8+3492\,a^6\,b^6\,c^2\,d^{10}-216\,a^6\,b^6\,d^{12}+16\,a^5\,b^7\,c^9\,d^3+240\,a^5\,b^7\,c^7\,d^5-336\,a^5\,b^7\,c^5\,d^7-1592\,a^5\,b^7\,c^3\,d^9+1296\,a^5\,b^7\,c\,d^{11}-204\,a^4\,b^8\,c^8\,d^4-1412\,a^4\,b^8\,c^6\,d^6-2598\,a^4\,b^8\,c^4\,d^8-3144\,a^4\,b^8\,c^2\,d^{10}+16\,a^3\,b^9\,c^9\,d^3+888\,a^3\,b^9\,c^7\,d^5+3552\,a^3\,b^9\,c^5\,d^7+3840\,a^3\,b^9\,c^3\,d^9-99\,a^2\,b^{10}\,c^8\,d^4-1384\,a^2\,b^{10}\,c^6\,d^6-2352\,a^2\,b^{10}\,c^4\,d^8+4\,a\,b^{11}\,c^9\,d^3+96\,a\,b^{11}\,c^7\,d^5+576\,a\,b^{11}\,c^5\,d^7\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(216\,a^{13}\,d^{12}-864\,a^{12}\,b\,c\,d^{11}+1152\,a^{11}\,b^2\,c^2\,d^{10}-972\,a^{11}\,b^2\,d^{12}-512\,a^{10}\,b^3\,c^3\,d^9+3888\,a^{10}\,b^3\,c\,d^{11}+72\,a^9\,b^4\,c^4\,d^8-4968\,a^9\,b^4\,c^2\,d^{10}+1728\,a^9\,b^4\,d^{12}-192\,a^8\,b^5\,c^5\,d^7+1296\,a^8\,b^5\,c^3\,d^9-7200\,a^8\,b^5\,c\,d^{11}+128\,a^7\,b^6\,c^6\,d^6+1428\,a^7\,b^6\,c^4\,d^8+9984\,a^7\,b^6\,c^2\,d^{10}-1404\,a^7\,b^6\,d^{12}-480\,a^6\,b^7\,c^5\,d^7-3744\,a^6\,b^7\,c^3\,d^9+6192\,a^6\,b^7\,c\,d^{11}-192\,a^5\,b^8\,c^6\,d^6-2304\,a^5\,b^8\,c^4\,d^8-9672\,a^5\,b^8\,c^2\,d^{10}+432\,a^5\,b^8\,d^{12}+1536\,a^4\,b^9\,c^5\,d^7+5648\,a^4\,b^9\,c^3\,d^9-2016\,a^4\,b^9\,c\,d^{11}+36\,a^3\,b^{10}\,c^4\,d^8+3504\,a^3\,b^{10}\,c^2\,d^{10}-864\,a^2\,b^{11}\,c^5\,d^7-2688\,a^2\,b^{11}\,c^3\,d^9+64\,a\,b^{12}\,c^6\,d^6+768\,a\,b^{12}\,c^4\,d^8\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{d^3\,\left(3\,a\,d-4\,b\,c\right)\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}}\right)\,\left(3\,a\,d-4\,b\,c\right)}{b^4\,f}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(54\,a^{12}\,d^{12}-216\,a^{11}\,b\,c\,d^{11}-36\,a^{10}\,b^2\,c^4\,d^8+180\,a^{10}\,b^2\,c^2\,d^{10}-243\,a^{10}\,b^2\,d^{12}+96\,a^9\,b^3\,c^5\,d^7+376\,a^9\,b^3\,c^3\,d^9+1116\,a^9\,b^3\,c\,d^{11}-64\,a^8\,b^4\,c^6\,d^6-678\,a^8\,b^4\,c^4\,d^8-1572\,a^8\,b^4\,c^2\,d^{10}+378\,a^8\,b^4\,d^{12}+144\,a^7\,b^5\,c^5\,d^7-104\,a^7\,b^5\,c^3\,d^9-1944\,a^7\,b^5\,c\,d^{11}-12\,a^6\,b^6\,c^8\,d^4+88\,a^6\,b^6\,c^6\,d^6+1758\,a^6\,b^6\,c^4\,d^8+3492\,a^6\,b^6\,c^2\,d^{10}-216\,a^6\,b^6\,d^{12}+16\,a^5\,b^7\,c^9\,d^3+240\,a^5\,b^7\,c^7\,d^5-336\,a^5\,b^7\,c^5\,d^7-1592\,a^5\,b^7\,c^3\,d^9+1296\,a^5\,b^7\,c\,d^{11}-204\,a^4\,b^8\,c^8\,d^4-1412\,a^4\,b^8\,c^6\,d^6-2598\,a^4\,b^8\,c^4\,d^8-3144\,a^4\,b^8\,c^2\,d^{10}+16\,a^3\,b^9\,c^9\,d^3+888\,a^3\,b^9\,c^7\,d^5+3552\,a^3\,b^9\,c^5\,d^7+3840\,a^3\,b^9\,c^3\,d^9-99\,a^2\,b^{10}\,c^8\,d^4-1384\,a^2\,b^{10}\,c^6\,d^6-2352\,a^2\,b^{10}\,c^4\,d^8+4\,a\,b^{11}\,c^9\,d^3+96\,a\,b^{11}\,c^7\,d^5+576\,a\,b^{11}\,c^5\,d^7\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(216\,a^{13}\,d^{12}-864\,a^{12}\,b\,c\,d^{11}+1152\,a^{11}\,b^2\,c^2\,d^{10}-972\,a^{11}\,b^2\,d^{12}-512\,a^{10}\,b^3\,c^3\,d^9+3888\,a^{10}\,b^3\,c\,d^{11}+72\,a^9\,b^4\,c^4\,d^8-4968\,a^9\,b^4\,c^2\,d^{10}+1728\,a^9\,b^4\,d^{12}-192\,a^8\,b^5\,c^5\,d^7+1296\,a^8\,b^5\,c^3\,d^9-7200\,a^8\,b^5\,c\,d^{11}+128\,a^7\,b^6\,c^6\,d^6+1428\,a^7\,b^6\,c^4\,d^8+9984\,a^7\,b^6\,c^2\,d^{10}-1404\,a^7\,b^6\,d^{12}-480\,a^6\,b^7\,c^5\,d^7-3744\,a^6\,b^7\,c^3\,d^9+6192\,a^6\,b^7\,c\,d^{11}-192\,a^5\,b^8\,c^6\,d^6-2304\,a^5\,b^8\,c^4\,d^8-9672\,a^5\,b^8\,c^2\,d^{10}+432\,a^5\,b^8\,d^{12}+1536\,a^4\,b^9\,c^5\,d^7+5648\,a^4\,b^9\,c^3\,d^9-2016\,a^4\,b^9\,c\,d^{11}+36\,a^3\,b^{10}\,c^4\,d^8+3504\,a^3\,b^{10}\,c^2\,d^{10}-864\,a^2\,b^{11}\,c^5\,d^7-2688\,a^2\,b^{11}\,c^3\,d^9+64\,a\,b^{12}\,c^6\,d^6+768\,a\,b^{12}\,c^4\,d^8\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}-\frac{\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(36\,a^{12}\,b^3\,d^8-96\,a^{11}\,b^4\,c\,d^7+64\,a^{10}\,b^5\,c^2\,d^6-144\,a^{10}\,b^5\,d^8+384\,a^9\,b^6\,c\,d^7-256\,a^8\,b^7\,c^2\,d^6+216\,a^8\,b^7\,d^8-576\,a^7\,b^8\,c\,d^7+384\,a^6\,b^9\,c^2\,d^6-144\,a^6\,b^9\,d^8+384\,a^5\,b^{10}\,c\,d^7-256\,a^4\,b^{11}\,c^2\,d^6+36\,a^4\,b^{11}\,d^8-96\,a^3\,b^{12}\,c\,d^7+64\,a^2\,b^{13}\,c^2\,d^6\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(72\,a^{13}\,b^3\,d^8-192\,a^{12}\,b^4\,c\,d^7+128\,a^{11}\,b^5\,c^2\,d^6-396\,a^{11}\,b^5\,d^8+1056\,a^{10}\,b^6\,c\,d^7+24\,a^9\,b^7\,c^4\,d^4-632\,a^9\,b^7\,c^2\,d^6+873\,a^9\,b^7\,d^8-32\,a^8\,b^8\,c^5\,d^3-240\,a^8\,b^8\,c^3\,d^5-2424\,a^8\,b^8\,c\,d^7+144\,a^7\,b^9\,c^4\,d^4+1644\,a^7\,b^9\,c^2\,d^6-936\,a^7\,b^9\,d^8+64\,a^6\,b^{10}\,c^5\,d^3+408\,a^6\,b^{10}\,c^3\,d^5+2736\,a^6\,b^{10}\,c\,d^7+4\,a^5\,b^{11}\,c^8+24\,a^5\,b^{11}\,c^6\,d^2-426\,a^5\,b^{11}\,c^4\,d^4-2200\,a^5\,b^{11}\,c^2\,d^6+468\,a^5\,b^{11}\,d^8-48\,a^4\,b^{12}\,c^7\,d-200\,a^4\,b^{12}\,c^5\,d^3-96\,a^4\,b^{12}\,c^3\,d^5-1440\,a^4\,b^{12}\,c\,d^7+4\,a^3\,b^{13}\,c^8+204\,a^3\,b^{13}\,c^6\,d^2+744\,a^3\,b^{13}\,c^4\,d^4+1440\,a^3\,b^{13}\,c^2\,d^6-72\,a^3\,b^{13}\,d^8-24\,a^2\,b^{14}\,c^7\,d-336\,a^2\,b^{14}\,c^5\,d^3-576\,a^2\,b^{14}\,c^3\,d^5+192\,a^2\,b^{14}\,c\,d^7+a\,b^{15}\,c^8+24\,a\,b^{15}\,c^6\,d^2+144\,a\,b^{15}\,c^4\,d^4-128\,a\,b^{15}\,c^2\,d^6\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(6\,a^{10}\,b^8\,d^4-8\,a^9\,b^9\,c\,d^3+4\,a^8\,b^{10}\,c^4+12\,a^8\,b^{10}\,c^2\,d^2-24\,a^8\,b^{10}\,d^4-24\,a^7\,b^{11}\,c^3\,d+16\,a^7\,b^{11}\,c\,d^3-6\,a^6\,b^{12}\,c^4+42\,a^6\,b^{12}\,d^4+48\,a^5\,b^{13}\,c^3\,d-24\,a^5\,b^{13}\,c\,d^3-36\,a^4\,b^{14}\,c^2\,d^2-36\,a^4\,b^{14}\,d^4-24\,a^3\,b^{15}\,c^3\,d+32\,a^3\,b^{15}\,c\,d^3+2\,a^2\,b^{16}\,c^4+24\,a^2\,b^{16}\,c^2\,d^2+12\,a^2\,b^{16}\,d^4-16\,a\,b^{17}\,c\,d^3\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,a^{11}\,b^8\,d^4-32\,a^{10}\,b^9\,c\,d^3-108\,a^9\,b^{10}\,d^4+144\,a^8\,b^{11}\,c\,d^3+8\,a^7\,b^{12}\,c^4+24\,a^7\,b^{12}\,c^2\,d^2+192\,a^7\,b^{12}\,d^4-48\,a^6\,b^{13}\,c^3\,d-288\,a^6\,b^{13}\,c\,d^3-12\,a^5\,b^{14}\,c^4-156\,a^5\,b^{14}\,d^4+96\,a^4\,b^{15}\,c^3\,d+272\,a^4\,b^{15}\,c\,d^3-72\,a^3\,b^{16}\,c^2\,d^2+48\,a^3\,b^{16}\,d^4-48\,a^2\,b^{17}\,c^3\,d-96\,a^2\,b^{17}\,c\,d^3+4\,a\,b^{18}\,c^4+48\,a\,b^{18}\,c^2\,d^2\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^{11}-16\,a^8\,b^{13}+24\,a^6\,b^{15}-16\,a^4\,b^{17}+4\,a^2\,b^{19}\right)}{a^8\,b^8-4\,a^6\,b^{10}+6\,a^4\,b^{12}-4\,a^2\,b^{14}+b^{16}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^{11}+44\,a^9\,b^{13}-96\,a^7\,b^{15}+104\,a^5\,b^{17}-56\,a^3\,b^{19}+12\,a\,b^{21}\right)}{a^8\,b^9-4\,a^6\,b^{11}+6\,a^4\,b^{13}-4\,a^2\,b^{15}+b^{17}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,{\left(a\,d-b\,c\right)}^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2+4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2-10\,a\,b^3\,c\,d+b^4\,c^2+12\,b^4\,d^2\right)\,1{}\mathrm{i}}{f\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"(2*d^3*atan(((d^3*(3*a*d - 4*b*c)*((8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (d^3*(3*a*d - 4*b*c)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (d^3*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(3*a*d - 4*b*c)*1i)/b^4)*1i)/b^4))/b^4 - (d^3*(3*a*d - 4*b*c)*((8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) - (8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (d^3*(3*a*d - 4*b*c)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (d^3*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(3*a*d - 4*b*c)*1i)/b^4)*1i)/b^4))/b^4)/((16*(54*a^12*d^12 - 216*a^6*b^6*d^12 + 378*a^8*b^4*d^12 - 243*a^10*b^2*d^12 + 576*a*b^11*c^5*d^7 + 96*a*b^11*c^7*d^5 + 4*a*b^11*c^9*d^3 + 1296*a^5*b^7*c*d^11 - 1944*a^7*b^5*c*d^11 + 1116*a^9*b^3*c*d^11 - 2352*a^2*b^10*c^4*d^8 - 1384*a^2*b^10*c^6*d^6 - 99*a^2*b^10*c^8*d^4 + 3840*a^3*b^9*c^3*d^9 + 3552*a^3*b^9*c^5*d^7 + 888*a^3*b^9*c^7*d^5 + 16*a^3*b^9*c^9*d^3 - 3144*a^4*b^8*c^2*d^10 - 2598*a^4*b^8*c^4*d^8 - 1412*a^4*b^8*c^6*d^6 - 204*a^4*b^8*c^8*d^4 - 1592*a^5*b^7*c^3*d^9 - 336*a^5*b^7*c^5*d^7 + 240*a^5*b^7*c^7*d^5 + 16*a^5*b^7*c^9*d^3 + 3492*a^6*b^6*c^2*d^10 + 1758*a^6*b^6*c^4*d^8 + 88*a^6*b^6*c^6*d^6 - 12*a^6*b^6*c^8*d^4 - 104*a^7*b^5*c^3*d^9 + 144*a^7*b^5*c^5*d^7 - 1572*a^8*b^4*c^2*d^10 - 678*a^8*b^4*c^4*d^8 - 64*a^8*b^4*c^6*d^6 + 376*a^9*b^3*c^3*d^9 + 96*a^9*b^3*c^5*d^7 + 180*a^10*b^2*c^2*d^10 - 36*a^10*b^2*c^4*d^8 - 216*a^11*b*c*d^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (16*tan(e/2 + (f*x)/2)*(216*a^13*d^12 + 432*a^5*b^8*d^12 - 1404*a^7*b^6*d^12 + 1728*a^9*b^4*d^12 - 972*a^11*b^2*d^12 + 768*a*b^12*c^4*d^8 + 64*a*b^12*c^6*d^6 - 2016*a^4*b^9*c*d^11 + 6192*a^6*b^7*c*d^11 - 7200*a^8*b^5*c*d^11 + 3888*a^10*b^3*c*d^11 - 2688*a^2*b^11*c^3*d^9 - 864*a^2*b^11*c^5*d^7 + 3504*a^3*b^10*c^2*d^10 + 36*a^3*b^10*c^4*d^8 + 5648*a^4*b^9*c^3*d^9 + 1536*a^4*b^9*c^5*d^7 - 9672*a^5*b^8*c^2*d^10 - 2304*a^5*b^8*c^4*d^8 - 192*a^5*b^8*c^6*d^6 - 3744*a^6*b^7*c^3*d^9 - 480*a^6*b^7*c^5*d^7 + 9984*a^7*b^6*c^2*d^10 + 1428*a^7*b^6*c^4*d^8 + 128*a^7*b^6*c^6*d^6 + 1296*a^8*b^5*c^3*d^9 - 192*a^8*b^5*c^5*d^7 - 4968*a^9*b^4*c^2*d^10 + 72*a^9*b^4*c^4*d^8 - 512*a^10*b^3*c^3*d^9 + 1152*a^11*b^2*c^2*d^10 - 864*a^12*b*c*d^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (d^3*(3*a*d - 4*b*c)*((8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (d^3*(3*a*d - 4*b*c)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (d^3*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(3*a*d - 4*b*c)*1i)/b^4)*1i)/b^4)*1i)/b^4 + (d^3*(3*a*d - 4*b*c)*((8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) - (8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (d^3*(3*a*d - 4*b*c)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (d^3*((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(3*a*d - 4*b*c)*1i)/b^4)*1i)/b^4)*1i)/b^4))*(3*a*d - 4*b*c))/(b^4*f) - ((6*a^6*d^4 + b^6*c^4 - 4*a^2*b^4*c^4 + 2*a^2*b^4*d^4 - 11*a^4*b^2*d^4 + 20*a^3*b^3*c*d^3 + 8*a^3*b^3*c^3*d - 18*a^2*b^4*c^2*d^2 + 4*a*b^5*c^3*d - 8*a^5*b*c*d^3)/(b^3*(a^2 - b^2)^2) + (2*tan(e/2 + (f*x)/2)^2*(6*a^8*d^4 + b^8*c^4 - 3*a^2*b^6*c^4 - 4*a^4*b^4*c^4 + 4*a^2*b^6*d^4 - 13*a^4*b^4*d^4 - 3*a^6*b^2*d^4 + 20*a^3*b^5*c*d^3 + 12*a^3*b^5*c^3*d + 12*a^5*b^3*c*d^3 + 8*a^5*b^3*c^3*d - 18*a^2*b^6*c^2*d^2 - 18*a^4*b^4*c^2*d^2 + 4*a*b^7*c^3*d - 8*a^7*b*c*d^3))/(a^2*b^3*(a^2 - b^2)^2) + (4*tan(e/2 + (f*x)/2)^3*(6*a^6*d^4 + b^6*c^4 - 4*a^2*b^4*c^4 + 2*a^2*b^4*d^4 - 11*a^4*b^2*d^4 + 20*a^3*b^3*c*d^3 + 8*a^3*b^3*c^3*d - 18*a^2*b^4*c^2*d^2 + 4*a*b^5*c^3*d - 8*a^5*b*c*d^3))/(a*b^2*(a^2 - b^2)^2) + (tan(e/2 + (f*x)/2)*(21*a^6*d^4 + 2*b^6*c^4 - 11*a^2*b^4*c^4 + 8*a^2*b^4*d^4 - 38*a^4*b^2*d^4 + 64*a^3*b^3*c*d^3 + 20*a^3*b^3*c^3*d - 60*a^2*b^4*c^2*d^2 + 6*a^4*b^2*c^2*d^2 + 16*a*b^5*c^3*d - 28*a^5*b*c*d^3))/(a*b^2*(a^2 - b^2)^2) - (tan(e/2 + (f*x)/2)^5*(5*a^2*b^4*c^4 - 2*b^6*c^4 - 3*a^6*d^4 + 6*a^4*b^2*d^4 - 16*a^3*b^3*c*d^3 - 12*a^3*b^3*c^3*d + 12*a^2*b^4*c^2*d^2 + 6*a^4*b^2*c^2*d^2 + 4*a^5*b*c*d^3))/(a*b^2*(a^2 - b^2)^2) + (tan(e/2 + (f*x)/2)^4*(6*a^8*d^4 + 2*b^8*c^4 - 7*a^2*b^6*c^4 - 4*a^4*b^4*c^4 - 12*a^4*b^4*d^4 - 3*a^6*b^2*d^4 + 40*a^3*b^5*c*d^3 + 20*a^3*b^5*c^3*d + 4*a^5*b^3*c*d^3 + 8*a^5*b^3*c^3*d - 36*a^2*b^6*c^2*d^2 - 18*a^4*b^4*c^2*d^2 + 8*a*b^7*c^3*d - 8*a^7*b*c*d^3))/(a^2*b^3*(a^2 - b^2)^2))/(f*(tan(e/2 + (f*x)/2)^2*(3*a^2 + 4*b^2) + tan(e/2 + (f*x)/2)^4*(3*a^2 + 4*b^2) + a^2*tan(e/2 + (f*x)/2)^6 + a^2 + 8*a*b*tan(e/2 + (f*x)/2)^3 + 4*a*b*tan(e/2 + (f*x)/2)^5 + 4*a*b*tan(e/2 + (f*x)/2))) + (atan((((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) - (8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(54*a^12*d^12 - 216*a^6*b^6*d^12 + 378*a^8*b^4*d^12 - 243*a^10*b^2*d^12 + 576*a*b^11*c^5*d^7 + 96*a*b^11*c^7*d^5 + 4*a*b^11*c^9*d^3 + 1296*a^5*b^7*c*d^11 - 1944*a^7*b^5*c*d^11 + 1116*a^9*b^3*c*d^11 - 2352*a^2*b^10*c^4*d^8 - 1384*a^2*b^10*c^6*d^6 - 99*a^2*b^10*c^8*d^4 + 3840*a^3*b^9*c^3*d^9 + 3552*a^3*b^9*c^5*d^7 + 888*a^3*b^9*c^7*d^5 + 16*a^3*b^9*c^9*d^3 - 3144*a^4*b^8*c^2*d^10 - 2598*a^4*b^8*c^4*d^8 - 1412*a^4*b^8*c^6*d^6 - 204*a^4*b^8*c^8*d^4 - 1592*a^5*b^7*c^3*d^9 - 336*a^5*b^7*c^5*d^7 + 240*a^5*b^7*c^7*d^5 + 16*a^5*b^7*c^9*d^3 + 3492*a^6*b^6*c^2*d^10 + 1758*a^6*b^6*c^4*d^8 + 88*a^6*b^6*c^6*d^6 - 12*a^6*b^6*c^8*d^4 - 104*a^7*b^5*c^3*d^9 + 144*a^7*b^5*c^5*d^7 - 1572*a^8*b^4*c^2*d^10 - 678*a^8*b^4*c^4*d^8 - 64*a^8*b^4*c^6*d^6 + 376*a^9*b^3*c^3*d^9 + 96*a^9*b^3*c^5*d^7 + 180*a^10*b^2*c^2*d^10 - 36*a^10*b^2*c^4*d^8 - 216*a^11*b*c*d^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (16*tan(e/2 + (f*x)/2)*(216*a^13*d^12 + 432*a^5*b^8*d^12 - 1404*a^7*b^6*d^12 + 1728*a^9*b^4*d^12 - 972*a^11*b^2*d^12 + 768*a*b^12*c^4*d^8 + 64*a*b^12*c^6*d^6 - 2016*a^4*b^9*c*d^11 + 6192*a^6*b^7*c*d^11 - 7200*a^8*b^5*c*d^11 + 3888*a^10*b^3*c*d^11 - 2688*a^2*b^11*c^3*d^9 - 864*a^2*b^11*c^5*d^7 + 3504*a^3*b^10*c^2*d^10 + 36*a^3*b^10*c^4*d^8 + 5648*a^4*b^9*c^3*d^9 + 1536*a^4*b^9*c^5*d^7 - 9672*a^5*b^8*c^2*d^10 - 2304*a^5*b^8*c^4*d^8 - 192*a^5*b^8*c^6*d^6 - 3744*a^6*b^7*c^3*d^9 - 480*a^6*b^7*c^5*d^7 + 9984*a^7*b^6*c^2*d^10 + 1428*a^7*b^6*c^4*d^8 + 128*a^7*b^6*c^6*d^6 + 1296*a^8*b^5*c^3*d^9 - 192*a^8*b^5*c^5*d^7 - 4968*a^9*b^4*c^2*d^10 + 72*a^9*b^4*c^4*d^8 - 512*a^10*b^3*c^3*d^9 + 1152*a^11*b^2*c^2*d^10 - 864*a^12*b*c*d^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) - (((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(36*a^4*b^11*d^8 - 144*a^6*b^9*d^8 + 216*a^8*b^7*d^8 - 144*a^10*b^5*d^8 + 36*a^12*b^3*d^8 - 96*a^3*b^12*c*d^7 + 384*a^5*b^10*c*d^7 - 576*a^7*b^8*c*d^7 + 384*a^9*b^6*c*d^7 - 96*a^11*b^4*c*d^7 + 64*a^2*b^13*c^2*d^6 - 256*a^4*b^11*c^2*d^6 + 384*a^6*b^9*c^2*d^6 - 256*a^8*b^7*c^2*d^6 + 64*a^10*b^5*c^2*d^6))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) - (8*tan(e/2 + (f*x)/2)*(a*b^15*c^8 + 4*a^3*b^13*c^8 + 4*a^5*b^11*c^8 - 72*a^3*b^13*d^8 + 468*a^5*b^11*d^8 - 936*a^7*b^9*d^8 + 873*a^9*b^7*d^8 - 396*a^11*b^5*d^8 + 72*a^13*b^3*d^8 - 128*a*b^15*c^2*d^6 + 144*a*b^15*c^4*d^4 + 24*a*b^15*c^6*d^2 + 192*a^2*b^14*c*d^7 - 24*a^2*b^14*c^7*d - 1440*a^4*b^12*c*d^7 - 48*a^4*b^12*c^7*d + 2736*a^6*b^10*c*d^7 - 2424*a^8*b^8*c*d^7 + 1056*a^10*b^6*c*d^7 - 192*a^12*b^4*c*d^7 - 576*a^2*b^14*c^3*d^5 - 336*a^2*b^14*c^5*d^3 + 1440*a^3*b^13*c^2*d^6 + 744*a^3*b^13*c^4*d^4 + 204*a^3*b^13*c^6*d^2 - 96*a^4*b^12*c^3*d^5 - 200*a^4*b^12*c^5*d^3 - 2200*a^5*b^11*c^2*d^6 - 426*a^5*b^11*c^4*d^4 + 24*a^5*b^11*c^6*d^2 + 408*a^6*b^10*c^3*d^5 + 64*a^6*b^10*c^5*d^3 + 1644*a^7*b^9*c^2*d^6 + 144*a^7*b^9*c^4*d^4 - 240*a^8*b^8*c^3*d^5 - 32*a^8*b^8*c^5*d^3 - 632*a^9*b^7*c^2*d^6 + 24*a^9*b^7*c^4*d^4 + 128*a^11*b^5*c^2*d^6))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + ((a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^16*c^4 - 6*a^6*b^12*c^4 + 4*a^8*b^10*c^4 + 12*a^2*b^16*d^4 - 36*a^4*b^14*d^4 + 42*a^6*b^12*d^4 - 24*a^8*b^10*d^4 + 6*a^10*b^8*d^4 + 32*a^3*b^15*c*d^3 - 24*a^3*b^15*c^3*d - 24*a^5*b^13*c*d^3 + 48*a^5*b^13*c^3*d + 16*a^7*b^11*c*d^3 - 24*a^7*b^11*c^3*d - 8*a^9*b^9*c*d^3 + 24*a^2*b^16*c^2*d^2 - 36*a^4*b^14*c^2*d^2 + 12*a^8*b^10*c^2*d^2 - 16*a*b^17*c*d^3))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^4 - 12*a^5*b^14*c^4 + 8*a^7*b^12*c^4 + 48*a^3*b^16*d^4 - 156*a^5*b^14*d^4 + 192*a^7*b^12*d^4 - 108*a^9*b^10*d^4 + 24*a^11*b^8*d^4 + 48*a*b^18*c^2*d^2 - 96*a^2*b^17*c*d^3 - 48*a^2*b^17*c^3*d + 272*a^4*b^15*c*d^3 + 96*a^4*b^15*c^3*d - 288*a^6*b^13*c*d^3 - 48*a^6*b^13*c^3*d + 144*a^8*b^11*c*d^3 - 32*a^10*b^9*c*d^3 - 72*a^3*b^16*c^2*d^2 + 24*a^7*b^12*c^2*d^2))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9) + (((8*(4*a^2*b^19 - 16*a^4*b^17 + 24*a^6*b^15 - 16*a^8*b^13 + 4*a^10*b^11))/(b^16 - 4*a^2*b^14 + 6*a^4*b^12 - 4*a^6*b^10 + a^8*b^8) + (8*tan(e/2 + (f*x)/2)*(12*a*b^21 - 56*a^3*b^19 + 104*a^5*b^17 - 96*a^7*b^15 + 44*a^9*b^13 - 8*a^11*b^11))/(b^17 - 4*a^2*b^15 + 6*a^4*b^13 - 4*a^6*b^11 + a^8*b^9))*(a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(a*d - b*c)^2*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 12*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 - 10*a*b^3*c*d + 4*a^3*b*c*d)*1i)/(f*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
716,1,11848,248,20.931663,"\text{Not used}","int((c + d*sin(e + f*x))^3/(a + b*sin(e + f*x))^3,x)","-\frac{\frac{-2\,a^5\,d^3+6\,a^3\,b^2\,c^2\,d+5\,a^3\,b^2\,d^3-4\,a^2\,b^3\,c^3-9\,a^2\,b^3\,c\,d^2+3\,a\,b^4\,c^2\,d+b^5\,c^3}{b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^5\,d^3+3\,a^4\,b\,c\,d^2-9\,a^3\,b^2\,c^2\,d-4\,a^3\,b^2\,d^3+5\,a^2\,b^3\,c^3+6\,a^2\,b^3\,c\,d^2-2\,b^5\,c^3\right)}{a\,b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-7\,a^5\,d^3+3\,a^4\,b\,c\,d^2+15\,a^3\,b^2\,c^2\,d+16\,a^3\,b^2\,d^3-11\,a^2\,b^3\,c^3-30\,a^2\,b^3\,c\,d^2+12\,a\,b^4\,c^2\,d+2\,b^5\,c^3\right)}{a\,b\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)\,\left(-2\,a^5\,d^3+6\,a^3\,b^2\,c^2\,d+5\,a^3\,b^2\,d^3-4\,a^2\,b^3\,c^3-9\,a^2\,b^3\,c\,d^2+3\,a\,b^4\,c^2\,d+b^5\,c^3\right)}{a^2\,b^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{2\,d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}}{\frac{16\,\left(-2\,a^9\,d^9-4\,a^8\,b\,c^3\,d^6-6\,a^8\,b\,c\,d^8+18\,a^7\,b^2\,c^2\,d^7+13\,a^7\,b^2\,d^9+10\,a^6\,b^3\,c^3\,d^6+6\,a^6\,b^3\,c\,d^8+4\,a^5\,b^4\,c^6\,d^3+12\,a^5\,b^4\,c^4\,d^5-45\,a^5\,b^4\,c^2\,d^7-26\,a^5\,b^4\,d^9-36\,a^4\,b^5\,c^5\,d^4-68\,a^4\,b^5\,c^3\,d^6+6\,a^4\,b^5\,c\,d^8+4\,a^3\,b^6\,c^6\,d^3+111\,a^3\,b^6\,c^4\,d^5+126\,a^3\,b^6\,c^2\,d^7+24\,a^3\,b^6\,d^9-18\,a^2\,b^7\,c^5\,d^4-118\,a^2\,b^7\,c^3\,d^6-60\,a^2\,b^7\,c\,d^8+a\,b^8\,c^6\,d^3+12\,a\,b^8\,c^4\,d^5+36\,a\,b^8\,c^2\,d^7\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,d^9-36\,a^8\,b^2\,d^9-8\,a^7\,b^3\,c^3\,d^6-12\,a^7\,b^3\,c\,d^8+36\,a^6\,b^4\,c^2\,d^7+72\,a^6\,b^4\,d^9+12\,a^5\,b^5\,c^3\,d^6-72\,a^4\,b^6\,c^2\,d^7-68\,a^4\,b^6\,d^9+36\,a^3\,b^7\,c\,d^8+36\,a^2\,b^8\,c^2\,d^7+24\,a^2\,b^8\,d^9-4\,a\,b^9\,c^3\,d^6-24\,a\,b^9\,c\,d^8\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}-\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{d^3\,\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)}{b^3\,f}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(-2\,a^9\,d^9-4\,a^8\,b\,c^3\,d^6-6\,a^8\,b\,c\,d^8+18\,a^7\,b^2\,c^2\,d^7+13\,a^7\,b^2\,d^9+10\,a^6\,b^3\,c^3\,d^6+6\,a^6\,b^3\,c\,d^8+4\,a^5\,b^4\,c^6\,d^3+12\,a^5\,b^4\,c^4\,d^5-45\,a^5\,b^4\,c^2\,d^7-26\,a^5\,b^4\,d^9-36\,a^4\,b^5\,c^5\,d^4-68\,a^4\,b^5\,c^3\,d^6+6\,a^4\,b^5\,c\,d^8+4\,a^3\,b^6\,c^6\,d^3+111\,a^3\,b^6\,c^4\,d^5+126\,a^3\,b^6\,c^2\,d^7+24\,a^3\,b^6\,d^9-18\,a^2\,b^7\,c^5\,d^4-118\,a^2\,b^7\,c^3\,d^6-60\,a^2\,b^7\,c\,d^8+a\,b^8\,c^6\,d^3+12\,a\,b^8\,c^4\,d^5+36\,a\,b^8\,c^2\,d^7\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,d^9-36\,a^8\,b^2\,d^9-8\,a^7\,b^3\,c^3\,d^6-12\,a^7\,b^3\,c\,d^8+36\,a^6\,b^4\,c^2\,d^7+72\,a^6\,b^4\,d^9+12\,a^5\,b^5\,c^3\,d^6-72\,a^4\,b^6\,c^2\,d^7-68\,a^4\,b^6\,d^9+36\,a^3\,b^7\,c\,d^8+36\,a^2\,b^8\,c^2\,d^7+24\,a^2\,b^8\,d^9-4\,a\,b^9\,c^3\,d^6-24\,a\,b^9\,c\,d^8\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}-\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}-\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{10}\,b^2\,d^6-16\,a^8\,b^4\,d^6+24\,a^6\,b^6\,d^6-16\,a^4\,b^8\,d^6+4\,a^2\,b^{10}\,d^6\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{11}\,b^2\,d^6-44\,a^9\,b^4\,d^6-8\,a^8\,b^5\,c^3\,d^3-12\,a^8\,b^5\,c\,d^5+36\,a^7\,b^6\,c^2\,d^4+105\,a^7\,b^6\,d^6+16\,a^6\,b^7\,c^3\,d^3+6\,a^6\,b^7\,c\,d^5+4\,a^5\,b^8\,c^6+12\,a^5\,b^8\,c^4\,d^2-81\,a^5\,b^8\,c^2\,d^4-124\,a^5\,b^8\,d^6-36\,a^4\,b^9\,c^5\,d-68\,a^4\,b^9\,c^3\,d^3+24\,a^4\,b^9\,c\,d^5+4\,a^3\,b^{10}\,c^6+111\,a^3\,b^{10}\,c^4\,d^2+144\,a^3\,b^{10}\,c^2\,d^4+72\,a^3\,b^{10}\,d^6-18\,a^2\,b^{11}\,c^5\,d-120\,a^2\,b^{11}\,c^3\,d^3-72\,a^2\,b^{11}\,c\,d^5+a\,b^{12}\,c^6+12\,a\,b^{12}\,c^4\,d^2+36\,a\,b^{12}\,c^2\,d^4-8\,a\,b^{12}\,d^6\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(2\,a^9\,b^6\,d^3-4\,a^8\,b^7\,c^3-6\,a^8\,b^7\,c\,d^2+18\,a^7\,b^8\,c^2\,d-4\,a^7\,b^8\,d^3+6\,a^6\,b^9\,c^3-36\,a^5\,b^{10}\,c^2\,d+6\,a^5\,b^{10}\,d^3+18\,a^4\,b^{11}\,c\,d^2+18\,a^3\,b^{12}\,c^2\,d-8\,a^3\,b^{12}\,d^3-2\,a^2\,b^{13}\,c^3-12\,a^2\,b^{13}\,c\,d^2+4\,a\,b^{14}\,d^3\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{10}\,b^6\,d^3+36\,a^8\,b^8\,d^3+8\,a^7\,b^9\,c^3+12\,a^7\,b^9\,c\,d^2-36\,a^6\,b^{10}\,c^2\,d-72\,a^6\,b^{10}\,d^3-12\,a^5\,b^{11}\,c^3+72\,a^4\,b^{12}\,c^2\,d+68\,a^4\,b^{12}\,d^3-36\,a^3\,b^{13}\,c\,d^2-36\,a^2\,b^{14}\,c^2\,d-24\,a^2\,b^{14}\,d^3+4\,a\,b^{15}\,c^3+24\,a\,b^{15}\,c\,d^2\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}+\frac{\left(\frac{8\,\left(4\,a^{10}\,b^8-16\,a^8\,b^{10}+24\,a^6\,b^{12}-16\,a^4\,b^{14}+4\,a^2\,b^{16}\right)}{a^8\,b^5-4\,a^6\,b^7+6\,a^4\,b^9-4\,a^2\,b^{11}+b^{13}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,a^{11}\,b^8+44\,a^9\,b^{10}-96\,a^7\,b^{12}+104\,a^5\,b^{14}-56\,a^3\,b^{16}+12\,a\,b^{18}\right)}{a^8\,b^6-4\,a^6\,b^8+6\,a^4\,b^{10}-4\,a^2\,b^{12}+b^{14}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4\,d^2+2\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2-8\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)\,1{}\mathrm{i}}{f\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"- ((b^5*c^3 - 2*a^5*d^3 - 4*a^2*b^3*c^3 + 5*a^3*b^2*d^3 - 9*a^2*b^3*c*d^2 + 6*a^3*b^2*c^2*d + 3*a*b^4*c^2*d)/(b^2*(a^4 + b^4 - 2*a^2*b^2)) - (tan(e/2 + (f*x)/2)^3*(a^5*d^3 - 2*b^5*c^3 + 5*a^2*b^3*c^3 - 4*a^3*b^2*d^3 + 6*a^2*b^3*c*d^2 - 9*a^3*b^2*c^2*d + 3*a^4*b*c*d^2))/(a*b*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)*(2*b^5*c^3 - 7*a^5*d^3 - 11*a^2*b^3*c^3 + 16*a^3*b^2*d^3 - 30*a^2*b^3*c*d^2 + 15*a^3*b^2*c^2*d + 12*a*b^4*c^2*d + 3*a^4*b*c*d^2))/(a*b*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^2*(a^2 + 2*b^2)*(b^5*c^3 - 2*a^5*d^3 - 4*a^2*b^3*c^3 + 5*a^3*b^2*d^3 - 9*a^2*b^3*c*d^2 + 6*a^3*b^2*c^2*d + 3*a*b^4*c^2*d))/(a^2*b^2*(a^4 + b^4 - 2*a^2*b^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(e/2 + (f*x)/2)^4 + a^2 + 4*a*b*tan(e/2 + (f*x)/2)^3 + 4*a*b*tan(e/2 + (f*x)/2))) - (2*d^3*atan(((d^3*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (d^3*((8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (d^3*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3)*1i)/b^3 - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6)))/b^3 + (d^3*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (d^3*((8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (d^3*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3)*1i)/b^3 - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6)))/b^3)/((16*(24*a^3*b^6*d^9 - 2*a^9*d^9 - 26*a^5*b^4*d^9 + 13*a^7*b^2*d^9 + 36*a*b^8*c^2*d^7 + 12*a*b^8*c^4*d^5 + a*b^8*c^6*d^3 - 60*a^2*b^7*c*d^8 + 6*a^4*b^5*c*d^8 + 6*a^6*b^3*c*d^8 - 4*a^8*b*c^3*d^6 - 118*a^2*b^7*c^3*d^6 - 18*a^2*b^7*c^5*d^4 + 126*a^3*b^6*c^2*d^7 + 111*a^3*b^6*c^4*d^5 + 4*a^3*b^6*c^6*d^3 - 68*a^4*b^5*c^3*d^6 - 36*a^4*b^5*c^5*d^4 - 45*a^5*b^4*c^2*d^7 + 12*a^5*b^4*c^4*d^5 + 4*a^5*b^4*c^6*d^3 + 10*a^6*b^3*c^3*d^6 + 18*a^7*b^2*c^2*d^7 - 6*a^8*b*c*d^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (16*tan(e/2 + (f*x)/2)*(8*a^10*d^9 + 24*a^2*b^8*d^9 - 68*a^4*b^6*d^9 + 72*a^6*b^4*d^9 - 36*a^8*b^2*d^9 - 4*a*b^9*c^3*d^6 + 36*a^3*b^7*c*d^8 - 12*a^7*b^3*c*d^8 + 36*a^2*b^8*c^2*d^7 - 72*a^4*b^6*c^2*d^7 + 12*a^5*b^5*c^3*d^6 + 36*a^6*b^4*c^2*d^7 - 8*a^7*b^3*c^3*d^6 - 24*a*b^9*c*d^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (d^3*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (d^3*((8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (d^3*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3)*1i)/b^3 - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3 - (d^3*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (d^3*((8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (d^3*((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3)*1i)/b^3 - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*1i)/b^3)))/(b^3*f) - (atan((((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(24*a^3*b^6*d^9 - 2*a^9*d^9 - 26*a^5*b^4*d^9 + 13*a^7*b^2*d^9 + 36*a*b^8*c^2*d^7 + 12*a*b^8*c^4*d^5 + a*b^8*c^6*d^3 - 60*a^2*b^7*c*d^8 + 6*a^4*b^5*c*d^8 + 6*a^6*b^3*c*d^8 - 4*a^8*b*c^3*d^6 - 118*a^2*b^7*c^3*d^6 - 18*a^2*b^7*c^5*d^4 + 126*a^3*b^6*c^2*d^7 + 111*a^3*b^6*c^4*d^5 + 4*a^3*b^6*c^6*d^3 - 68*a^4*b^5*c^3*d^6 - 36*a^4*b^5*c^5*d^4 - 45*a^5*b^4*c^2*d^7 + 12*a^5*b^4*c^4*d^5 + 4*a^5*b^4*c^6*d^3 + 10*a^6*b^3*c^3*d^6 + 18*a^7*b^2*c^2*d^7 - 6*a^8*b*c*d^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (16*tan(e/2 + (f*x)/2)*(8*a^10*d^9 + 24*a^2*b^8*d^9 - 68*a^4*b^6*d^9 + 72*a^6*b^4*d^9 - 36*a^8*b^2*d^9 - 4*a*b^9*c^3*d^6 + 36*a^3*b^7*c*d^8 - 12*a^7*b^3*c*d^8 + 36*a^2*b^8*c^2*d^7 - 72*a^4*b^6*c^2*d^7 + 12*a^5*b^5*c^3*d^6 + 36*a^6*b^4*c^2*d^7 - 8*a^7*b^3*c^3*d^6 - 24*a*b^9*c*d^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) - (8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) - ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a^2*b^10*d^6 - 16*a^4*b^8*d^6 + 24*a^6*b^6*d^6 - 16*a^8*b^4*d^6 + 4*a^10*b^2*d^6))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^6 - 8*a*b^12*d^6 + 4*a^3*b^10*c^6 + 4*a^5*b^8*c^6 + 72*a^3*b^10*d^6 - 124*a^5*b^8*d^6 + 105*a^7*b^6*d^6 - 44*a^9*b^4*d^6 + 8*a^11*b^2*d^6 + 36*a*b^12*c^2*d^4 + 12*a*b^12*c^4*d^2 - 72*a^2*b^11*c*d^5 - 18*a^2*b^11*c^5*d + 24*a^4*b^9*c*d^5 - 36*a^4*b^9*c^5*d + 6*a^6*b^7*c*d^5 - 12*a^8*b^5*c*d^5 - 120*a^2*b^11*c^3*d^3 + 144*a^3*b^10*c^2*d^4 + 111*a^3*b^10*c^4*d^2 - 68*a^4*b^9*c^3*d^3 - 81*a^5*b^8*c^2*d^4 + 12*a^5*b^8*c^4*d^2 + 16*a^6*b^7*c^3*d^3 + 36*a^7*b^6*c^2*d^4 - 8*a^8*b^5*c^3*d^3))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + ((a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^14*d^3 - 2*a^2*b^13*c^3 + 6*a^6*b^9*c^3 - 4*a^8*b^7*c^3 - 8*a^3*b^12*d^3 + 6*a^5*b^10*d^3 - 4*a^7*b^8*d^3 + 2*a^9*b^6*d^3 - 12*a^2*b^13*c*d^2 + 18*a^3*b^12*c^2*d + 18*a^4*b^11*c*d^2 - 36*a^5*b^10*c^2*d + 18*a^7*b^8*c^2*d - 6*a^8*b^7*c*d^2))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) - (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^3 - 12*a^5*b^11*c^3 + 8*a^7*b^9*c^3 - 24*a^2*b^14*d^3 + 68*a^4*b^12*d^3 - 72*a^6*b^10*d^3 + 36*a^8*b^8*d^3 - 8*a^10*b^6*d^3 - 36*a^2*b^14*c^2*d - 36*a^3*b^13*c*d^2 + 72*a^4*b^12*c^2*d - 36*a^6*b^10*c^2*d + 12*a^7*b^9*c*d^2 + 24*a*b^15*c*d^2))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6) + (((8*(4*a^2*b^16 - 16*a^4*b^14 + 24*a^6*b^12 - 16*a^8*b^10 + 4*a^10*b^8))/(b^13 - 4*a^2*b^11 + 6*a^4*b^9 - 4*a^6*b^7 + a^8*b^5) + (8*tan(e/2 + (f*x)/2)*(12*a*b^18 - 56*a^3*b^16 + 104*a^5*b^14 - 96*a^7*b^12 + 44*a^9*b^10 - 8*a^11*b^8))/(b^14 - 4*a^2*b^12 + 6*a^4*b^10 - 4*a^6*b^8 + a^8*b^6))*(a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*(a*d - b*c)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 8*a*b^3*c*d + 2*a^3*b*c*d)*1i)/(f*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
717,1,641,196,10.442643,"\text{Not used}","int((c + d*sin(e + f*x))^2/(a + b*sin(e + f*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)\,\left(2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2}\right)\,\left(2\,a^2\,c^2+a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2+2\,b^2\,d^2\right)}{f\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{4\,a^3\,c\,d-4\,a^2\,b\,c^2-3\,a^2\,b\,d^2+2\,a\,b^2\,c\,d+b^3\,c^2}{a^4-2\,a^2\,b^2+b^4}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^4\,d^2+10\,a^3\,b\,c\,d-11\,a^2\,b^2\,c^2-10\,a^2\,b^2\,d^2+8\,a\,b^3\,c\,d+2\,b^4\,c^2\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a^4\,d^2-6\,a^3\,b\,c\,d+5\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2-2\,b^4\,c^2\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)\,\left(4\,a^3\,c\,d-4\,a^2\,b\,c^2-3\,a^2\,b\,d^2+2\,a\,b^2\,c\,d+b^3\,c^2\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}","Not used",1,"(atan(((((2*a^4*b + 2*b^5 - 4*a^2*b^3)*(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))/(2*(a + b)^(5/2)*(a - b)^(5/2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(e/2 + (f*x)/2)*(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))/((a + b)^(5/2)*(a - b)^(5/2)))*(a^4 + b^4 - 2*a^2*b^2))/(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))*(2*a^2*c^2 + a^2*d^2 + b^2*c^2 + 2*b^2*d^2 - 6*a*b*c*d))/(f*(a + b)^(5/2)*(a - b)^(5/2)) - ((b^3*c^2 - 4*a^2*b*c^2 - 3*a^2*b*d^2 + 4*a^3*c*d + 2*a*b^2*c*d)/(a^4 + b^4 - 2*a^2*b^2) + (tan(e/2 + (f*x)/2)*(a^4*d^2 + 2*b^4*c^2 - 11*a^2*b^2*c^2 - 10*a^2*b^2*d^2 + 8*a*b^3*c*d + 10*a^3*b*c*d))/(a*(a^4 + b^4 - 2*a^2*b^2)) - (tan(e/2 + (f*x)/2)^3*(a^4*d^2 - 2*b^4*c^2 + 5*a^2*b^2*c^2 + 2*a^2*b^2*d^2 - 6*a^3*b*c*d))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^2*(a^2 + 2*b^2)*(b^3*c^2 - 4*a^2*b*c^2 - 3*a^2*b*d^2 + 4*a^3*c*d + 2*a*b^2*c*d))/(a^2*(a^4 + b^4 - 2*a^2*b^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(e/2 + (f*x)/2)^4 + a^2 + 4*a*b*tan(e/2 + (f*x)/2)^3 + 4*a*b*tan(e/2 + (f*x)/2)))","B"
718,1,477,162,9.792671,"\text{Not used}","int((c + d*sin(e + f*x))/(a + b*sin(e + f*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)\,\left(2\,c\,a^2-3\,d\,a\,b+c\,b^2\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,c\,a^2-3\,d\,a\,b+c\,b^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{2\,c\,a^2-3\,d\,a\,b+c\,b^2}\right)\,\left(2\,c\,a^2-3\,d\,a\,b+c\,b^2\right)}{f\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{2\,d\,a^3-4\,c\,a^2\,b+d\,a\,b^2+c\,b^3}{a^4-2\,a^2\,b^2+b^4}+\frac{b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,d\,a^3-5\,c\,a^2\,b+2\,c\,b^3\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,d\,a^3-11\,c\,a^2\,b+4\,d\,a\,b^2+2\,c\,b^3\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)\,\left(2\,d\,a^3-4\,c\,a^2\,b+d\,a\,b^2+c\,b^3\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}","Not used",1,"(atan(((((2*a^4*b + 2*b^5 - 4*a^2*b^3)*(2*a^2*c + b^2*c - 3*a*b*d))/(2*(a + b)^(5/2)*(a - b)^(5/2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(e/2 + (f*x)/2)*(2*a^2*c + b^2*c - 3*a*b*d))/((a + b)^(5/2)*(a - b)^(5/2)))*(a^4 + b^4 - 2*a^2*b^2))/(2*a^2*c + b^2*c - 3*a*b*d))*(2*a^2*c + b^2*c - 3*a*b*d))/(f*(a + b)^(5/2)*(a - b)^(5/2)) - ((2*a^3*d + b^3*c - 4*a^2*b*c + a*b^2*d)/(a^4 + b^4 - 2*a^2*b^2) + (b*tan(e/2 + (f*x)/2)^3*(3*a^3*d + 2*b^3*c - 5*a^2*b*c))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(e/2 + (f*x)/2)*(5*a^3*d + 2*b^3*c - 11*a^2*b*c + 4*a*b^2*d))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^2*(a^2 + 2*b^2)*(2*a^3*d + b^3*c - 4*a^2*b*c + a*b^2*d))/(a^2*(a^4 + b^4 - 2*a^2*b^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(e/2 + (f*x)/2)^4 + a^2 + 4*a*b*tan(e/2 + (f*x)/2)^3 + 4*a*b*tan(e/2 + (f*x)/2)))","B"
719,1,395,131,10.150265,"\text{Not used}","int(1/(a + b*sin(e + f*x))^3,x)","\frac{\frac{4\,a^2\,b-b^3}{a^4-2\,a^2\,b^2+b^4}+\frac{b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(11\,a^2\,b-2\,b^3\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,a^2\,b-b^3\right)\,\left(a^2+2\,b^2\right)}{a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(5\,a^2\,b-2\,b^3\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}+\frac{\mathrm{atan}\left(\frac{\left(\frac{\left(2\,a^2+b^2\right)\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^2+b^2\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{2\,a^2+b^2}\right)\,\left(2\,a^2+b^2\right)}{f\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((4*a^2*b - b^3)/(a^4 + b^4 - 2*a^2*b^2) + (b*tan(e/2 + (f*x)/2)*(11*a^2*b - 2*b^3))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^2*(4*a^2*b - b^3)*(a^2 + 2*b^2))/(a^2*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(e/2 + (f*x)/2)^3*(5*a^2*b - 2*b^3))/(a*(a^4 + b^4 - 2*a^2*b^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(e/2 + (f*x)/2)^4 + a^2 + 4*a*b*tan(e/2 + (f*x)/2)^3 + 4*a*b*tan(e/2 + (f*x)/2))) + (atan(((((2*a^2 + b^2)*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/(2*(a + b)^(5/2)*(a - b)^(5/2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(e/2 + (f*x)/2)*(2*a^2 + b^2))/((a + b)^(5/2)*(a - b)^(5/2)))*(a^4 + b^4 - 2*a^2*b^2))/(2*a^2 + b^2))*(2*a^2 + b^2))/(f*(a + b)^(5/2)*(a - b)^(5/2))","B"
720,1,62873,285,30.172767,"\text{Not used}","int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))),x)","-\frac{\frac{6\,d\,a^3\,b^2-4\,c\,a^2\,b^3-3\,d\,a\,b^4+c\,b^5}{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(17\,d\,a^3\,b^2-11\,c\,a^2\,b^3-8\,d\,a\,b^4+2\,c\,b^5\right)}{a\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)\,\left(6\,d\,a^3\,b^2-4\,c\,a^2\,b^3-3\,d\,a\,b^4+c\,b^5\right)}{a^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(7\,d\,a^3\,b^2-5\,c\,a^2\,b^3-4\,d\,a\,b^4+2\,c\,b^5\right)}{a\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}+\frac{d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)\,1{}\mathrm{i}}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}-\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)\,1{}\mathrm{i}}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}}{\frac{16\,\left(12\,a^9\,b\,c\,d^7-36\,a^8\,b^2\,c^2\,d^6+40\,a^7\,b^3\,c^3\,d^5-34\,a^7\,b^3\,c\,d^7-20\,a^6\,b^4\,c^4\,d^4+50\,a^6\,b^4\,c^2\,d^6+4\,a^5\,b^5\,c^5\,d^3-16\,a^5\,b^5\,c^3\,d^5+36\,a^5\,b^5\,c\,d^7-8\,a^4\,b^6\,c^4\,d^4-25\,a^4\,b^6\,c^2\,d^6+4\,a^3\,b^7\,c^5\,d^3-a^3\,b^7\,c^3\,d^5-18\,a^3\,b^7\,c\,d^7+a^2\,b^8\,c^4\,d^4+2\,a^2\,b^8\,c^2\,d^6+a\,b^9\,c^5\,d^3+4\,a\,b^9\,c^3\,d^5+4\,a\,b^9\,c\,d^7\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^8\,b^2\,c\,d^7+72\,a^7\,b^3\,c^2\,d^6-40\,a^6\,b^4\,c^3\,d^5+52\,a^6\,b^4\,c\,d^7+8\,a^5\,b^5\,c^4\,d^4-20\,a^5\,b^5\,c^2\,d^6-16\,a^4\,b^6\,c^3\,d^5-26\,a^4\,b^6\,c\,d^7+8\,a^3\,b^7\,c^4\,d^4-2\,a^3\,b^7\,c^2\,d^6+2\,a^2\,b^8\,c^3\,d^5+4\,a^2\,b^8\,c\,d^7+2\,a\,b^9\,c^4\,d^4+4\,a\,b^9\,c^2\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}-\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{d^3\,\sqrt{d^2-c^2}\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}\right)}{-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2}}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{f\,\left(-a^3\,c^2\,d^3+a^3\,d^5+3\,a^2\,b\,c^3\,d^2-3\,a^2\,b\,c\,d^4-3\,a\,b^2\,c^4\,d+3\,a\,b^2\,c^2\,d^3+b^3\,c^5-b^3\,c^3\,d^2\right)}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,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b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{b\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}}{\frac{16\,\left(12\,a^9\,b\,c\,d^7-36\,a^8\,b^2\,c^2\,d^6+40\,a^7\,b^3\,c^3\,d^5-34\,a^7\,b^3\,c\,d^7-20\,a^6\,b^4\,c^4\,d^4+50\,a^6\,b^4\,c^2\,d^6+4\,a^5\,b^5\,c^5\,d^3-16\,a^5\,b^5\,c^3\,d^5+36\,a^5\,b^5\,c\,d^7-8\,a^4\,b^6\,c^4\,d^4-25\,a^4\,b^6\,c^2\,d^6+4\,a^3\,b^7\,c^5\,d^3-a^3\,b^7\,c^3\,d^5-18\,a^3\,b^7\,c\,d^7+a^2\,b^8\,c^4\,d^4+2\,a^2\,b^8\,c^2\,d^6+a\,b^9\,c^5\,d^3+4\,a\,b^9\,c^3\,d^5+4\,a\,b^9\,c\,d^7\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-48\,a^8\,b^2\,c\,d^7+72\,a^7\,b^3\,c^2\,d^6-40\,a^6\,b^4\,c^3\,d^5+52\,a^6\,b^4\,c\,d^7+8\,a^5\,b^5\,c^4\,d^4-20\,a^5\,b^5\,c^2\,d^6-16\,a^4\,b^6\,c^3\,d^5-26\,a^4\,b^6\,c\,d^7+8\,a^3\,b^7\,c^4\,d^4-2\,a^3\,b^7\,c^2\,d^6+2\,a^2\,b^8\,c^3\,d^5+4\,a^2\,b^8\,c\,d^7+2\,a\,b^9\,c^4\,d^4+4\,a\,b^9\,c^2\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{b\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{12}\,b\,c\,d^8+28\,a^{11}\,b^2\,c^2\,d^7-140\,a^{10}\,b^3\,c^3\,d^6-16\,a^{10}\,b^3\,c\,d^8+240\,a^9\,b^4\,c^4\,d^5-28\,a^9\,b^4\,c^2\,d^7-216\,a^8\,b^5\,c^5\,d^4+164\,a^8\,b^5\,c^3\,d^6+24\,a^8\,b^5\,c\,d^8+112\,a^7\,b^6\,c^6\,d^3-188\,a^7\,b^6\,c^4\,d^5+a^7\,b^6\,c^2\,d^7-32\,a^6\,b^7\,c^7\,d^2+64\,a^6\,b^7\,c^5\,d^4-98\,a^6\,b^7\,c^3\,d^6-16\,a^6\,b^7\,c\,d^8+4\,a^5\,b^8\,c^8\,d+20\,a^5\,b^8\,c^6\,d^3+95\,a^5\,b^8\,c^4\,d^5+12\,a^5\,b^8\,c^2\,d^7-20\,a^4\,b^9\,c^7\,d^2-20\,a^4\,b^9\,c^5\,d^4+24\,a^4\,b^9\,c^3\,d^6+4\,a^4\,b^9\,c\,d^8+4\,a^3\,b^{10}\,c^8\,d-a^3\,b^{10}\,c^6\,d^3-16\,a^3\,b^{10}\,c^4\,d^5-4\,a^3\,b^{10}\,c^2\,d^7-2\,a^2\,b^{11}\,c^7\,d^2-8\,a^2\,b^{11}\,c^5\,d^4-4\,a^2\,b^{11}\,c^3\,d^6+a\,b^{12}\,c^8\,d+4\,a\,b^{12}\,c^6\,d^3+4\,a\,b^{12}\,c^4\,d^5\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{13}\,c\,d^8-8\,a^{12}\,b\,c^2\,d^7+40\,a^{11}\,b^2\,c^3\,d^6-96\,a^{11}\,b^2\,c\,d^8-144\,a^{10}\,b^3\,c^4\,d^5+336\,a^{10}\,b^3\,c^2\,d^7+240\,a^9\,b^4\,c^5\,d^4-564\,a^9\,b^4\,c^3\,d^6+176\,a^9\,b^4\,c\,d^8-216\,a^8\,b^5\,c^6\,d^3+612\,a^8\,b^5\,c^4\,d^5-472\,a^8\,b^5\,c^2\,d^7+112\,a^7\,b^6\,c^7\,d^2-412\,a^7\,b^6\,c^5\,d^4+481\,a^7\,b^6\,c^3\,d^6-162\,a^7\,b^6\,c\,d^8-32\,a^6\,b^7\,c^8\,d+128\,a^6\,b^7\,c^6\,d^3-250\,a^6\,b^7\,c^4\,d^5+372\,a^6\,b^7\,c^2\,d^7+4\,a^5\,b^8\,c^9+12\,a^5\,b^8\,c^7\,d^2+55\,a^5\,b^8\,c^5\,d^4-274\,a^5\,b^8\,c^3\,d^6+76\,a^5\,b^8\,c\,d^8-20\,a^4\,b^9\,c^8\,d+20\,a^4\,b^9\,c^6\,d^3+80\,a^4\,b^9\,c^4\,d^5-152\,a^4\,b^9\,c^2\,d^7+4\,a^3\,b^{10}\,c^9-9\,a^3\,b^{10}\,c^7\,d^2-14\,a^3\,b^{10}\,c^5\,d^4+72\,a^3\,b^{10}\,c^3\,d^6-16\,a^3\,b^{10}\,c\,d^8-2\,a^2\,b^{11}\,c^8\,d-4\,a^2\,b^{11}\,c^6\,d^3+8\,a^2\,b^{11}\,c^4\,d^5+32\,a^2\,b^{11}\,c^2\,d^7+a\,b^{12}\,c^9+2\,a\,b^{12}\,c^7\,d^2-4\,a\,b^{12}\,c^5\,d^4-16\,a\,b^{12}\,c^3\,d^6\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{16}\,c^2\,d^8-32\,a^{15}\,b\,c^3\,d^7+12\,a^{15}\,b\,c\,d^9+112\,a^{14}\,b^2\,c^4\,d^6-92\,a^{14}\,b^2\,c^2\,d^8-224\,a^{13}\,b^3\,c^5\,d^5+318\,a^{13}\,b^3\,c^3\,d^7-34\,a^{13}\,b^3\,c\,d^9+280\,a^{12}\,b^4\,c^6\,d^4-654\,a^{12}\,b^4\,c^4\,d^6+234\,a^{12}\,b^4\,c^2\,d^8-224\,a^{11}\,b^5\,c^7\,d^3+886\,a^{11}\,b^5\,c^5\,d^5-702\,a^{11}\,b^5\,c^3\,d^7+36\,a^{11}\,b^5\,c\,d^9+112\,a^{10}\,b^6\,c^8\,d^2-822\,a^{10}\,b^6\,c^6\,d^4+1202\,a^{10}\,b^6\,c^4\,d^6-232\,a^{10}\,b^6\,c^2\,d^8-32\,a^9\,b^7\,c^9\,d+522\,a^9\,b^7\,c^7\,d^3-1290\,a^9\,b^7\,c^5\,d^5+638\,a^9\,b^7\,c^3\,d^7-18\,a^9\,b^7\,c\,d^9+4\,a^8\,b^8\,c^{10}-218\,a^8\,b^8\,c^8\,d^2+894\,a^8\,b^8\,c^6\,d^4-970\,a^8\,b^8\,c^4\,d^6+110\,a^8\,b^8\,c^2\,d^8+54\,a^7\,b^9\,c^9\,d-394\,a^7\,b^9\,c^7\,d^3+878\,a^7\,b^9\,c^5\,d^5-282\,a^7\,b^9\,c^3\,d^7+4\,a^7\,b^9\,c\,d^9-6\,a^6\,b^{10}\,c^{10}+102\,a^6\,b^{10}\,c^8\,d^2-466\,a^6\,b^{10}\,c^6\,d^4+390\,a^6\,b^{10}\,c^4\,d^6-24\,a^6\,b^{10}\,c^2\,d^8-12\,a^5\,b^{11}\,c^9\,d+122\,a^5\,b^{11}\,c^7\,d^3-310\,a^5\,b^{11}\,c^5\,d^5+60\,a^5\,b^{11}\,c^3\,d^7+2\,a^4\,b^{12}\,c^8\,d^2+138\,a^4\,b^{12}\,c^6\,d^4-80\,a^4\,b^{12}\,c^4\,d^6-10\,a^3\,b^{13}\,c^9\,d-30\,a^3\,b^{13}\,c^7\,d^3+60\,a^3\,b^{13}\,c^5\,d^5+2\,a^2\,b^{14}\,c^{10}+2\,a^2\,b^{14}\,c^8\,d^2-24\,a^2\,b^{14}\,c^6\,d^4+4\,a\,b^{15}\,c^7\,d^3\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{16}\,c\,d^9-40\,a^{15}\,b\,c^2\,d^8+56\,a^{14}\,b^2\,c^3\,d^7-16\,a^{14}\,b^2\,c\,d^9+64\,a^{13}\,b^3\,c^4\,d^6+56\,a^{13}\,b^3\,c^2\,d^8-328\,a^{12}\,b^4\,c^5\,d^5+36\,a^{12}\,b^4\,c^3\,d^7+12\,a^{12}\,b^4\,c\,d^9+512\,a^{11}\,b^5\,c^6\,d^4-508\,a^{11}\,b^5\,c^4\,d^6-12\,a^{11}\,b^5\,c^2\,d^8-440\,a^{10}\,b^6\,c^7\,d^3+1172\,a^{10}\,b^6\,c^5\,d^5-204\,a^{10}\,b^6\,c^3\,d^7-8\,a^{10}\,b^6\,c\,d^9+224\,a^9\,b^7\,c^8\,d^2-1404\,a^9\,b^7\,c^6\,d^4+804\,a^9\,b^7\,c^4\,d^6+16\,a^9\,b^7\,c^2\,d^8-64\,a^8\,b^8\,c^9\,d+1004\,a^8\,b^8\,c^7\,d^3-1380\,a^8\,b^8\,c^5\,d^5+76\,a^8\,b^8\,c^3\,d^7+4\,a^8\,b^8\,c\,d^9+8\,a^7\,b^9\,c^{10}-436\,a^7\,b^9\,c^8\,d^2+1308\,a^7\,b^9\,c^6\,d^4-340\,a^7\,b^9\,c^4\,d^6-20\,a^7\,b^9\,c^2\,d^8+108\,a^6\,b^{10}\,c^9\,d-708\,a^6\,b^{10}\,c^7\,d^3+556\,a^6\,b^{10}\,c^5\,d^5+36\,a^6\,b^{10}\,c^3\,d^7-12\,a^5\,b^{11}\,c^{10}+204\,a^5\,b^{11}\,c^8\,d^2-452\,a^5\,b^{11}\,c^6\,d^4-20\,a^5\,b^{11}\,c^4\,d^6-24\,a^4\,b^{12}\,c^9\,d+164\,a^4\,b^{12}\,c^7\,d^3-20\,a^4\,b^{12}\,c^5\,d^5+4\,a^3\,b^{13}\,c^8\,d^2+36\,a^3\,b^{13}\,c^6\,d^4-20\,a^2\,b^{14}\,c^9\,d-20\,a^2\,b^{14}\,c^7\,d^3+4\,a\,b^{15}\,c^{10}+4\,a\,b^{15}\,c^8\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}+\frac{b\,\left(\frac{8\,\left(4\,a^{19}\,c^2\,d^9-28\,a^{18}\,b\,c^3\,d^8-4\,a^{18}\,b\,c\,d^{10}+80\,a^{17}\,b^2\,c^4\,d^7+12\,a^{17}\,b^2\,c^2\,d^9-112\,a^{16}\,b^3\,c^5\,d^6+32\,a^{16}\,b^3\,c^3\,d^8+16\,a^{16}\,b^3\,c\,d^{10}+56\,a^{15}\,b^4\,c^6\,d^5-208\,a^{15}\,b^4\,c^4\,d^7-88\,a^{15}\,b^4\,c^2\,d^9+56\,a^{14}\,b^5\,c^7\,d^4+392\,a^{14}\,b^5\,c^5\,d^6+152\,a^{14}\,b^5\,c^3\,d^8-24\,a^{14}\,b^5\,c\,d^{10}-112\,a^{13}\,b^6\,c^8\,d^3-280\,a^{13}\,b^6\,c^6\,d^5+32\,a^{13}\,b^6\,c^4\,d^7+152\,a^{13}\,b^6\,c^2\,d^9+80\,a^{12}\,b^7\,c^9\,d^2-112\,a^{12}\,b^7\,c^7\,d^4-448\,a^{12}\,b^7\,c^5\,d^6-368\,a^{12}\,b^7\,c^3\,d^8+16\,a^{12}\,b^7\,c\,d^{10}-28\,a^{11}\,b^8\,c^{10}\,d+368\,a^{11}\,b^8\,c^8\,d^3+560\,a^{11}\,b^8\,c^6\,d^5+352\,a^{11}\,b^8\,c^4\,d^7-108\,a^{11}\,b^8\,c^2\,d^9+4\,a^{10}\,b^9\,c^{11}-292\,a^{10}\,b^9\,c^9\,d^2-112\,a^{10}\,b^9\,c^7\,d^4+112\,a^{10}\,b^9\,c^5\,d^6+292\,a^{10}\,b^9\,c^3\,d^8-4\,a^{10}\,b^9\,c\,d^{10}+108\,a^9\,b^{10}\,c^{10}\,d-352\,a^9\,b^{10}\,c^8\,d^3-560\,a^9\,b^{10}\,c^6\,d^5-368\,a^9\,b^{10}\,c^4\,d^7+28\,a^9\,b^{10}\,c^2\,d^9-16\,a^8\,b^{11}\,c^{11}+368\,a^8\,b^{11}\,c^9\,d^2+448\,a^8\,b^{11}\,c^7\,d^4+112\,a^8\,b^{11}\,c^5\,d^6-80\,a^8\,b^{11}\,c^3\,d^8-152\,a^7\,b^{12}\,c^{10}\,d-32\,a^7\,b^{12}\,c^8\,d^3+280\,a^7\,b^{12}\,c^6\,d^5+112\,a^7\,b^{12}\,c^4\,d^7+24\,a^6\,b^{13}\,c^{11}-152\,a^6\,b^{13}\,c^9\,d^2-392\,a^6\,b^{13}\,c^7\,d^4-56\,a^6\,b^{13}\,c^5\,d^6+88\,a^5\,b^{14}\,c^{10}\,d+208\,a^5\,b^{14}\,c^8\,d^3-56\,a^5\,b^{14}\,c^6\,d^5-16\,a^4\,b^{15}\,c^{11}-32\,a^4\,b^{15}\,c^9\,d^2+112\,a^4\,b^{15}\,c^7\,d^4-12\,a^3\,b^{16}\,c^{10}\,d-80\,a^3\,b^{16}\,c^8\,d^3+4\,a^2\,b^{17}\,c^{11}+28\,a^2\,b^{17}\,c^9\,d^2-4\,a\,b^{18}\,c^{10}\,d\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{19}\,c^3\,d^8-12\,a^{19}\,c\,d^{10}-64\,a^{18}\,b\,c^4\,d^7+96\,a^{18}\,b\,c^2\,d^9+224\,a^{17}\,b^2\,c^5\,d^6-380\,a^{17}\,b^2\,c^3\,d^8+64\,a^{17}\,b^2\,c\,d^{10}-448\,a^{16}\,b^3\,c^6\,d^5+1024\,a^{16}\,b^3\,c^4\,d^7-512\,a^{16}\,b^3\,c^2\,d^9+560\,a^{15}\,b^4\,c^7\,d^4-2072\,a^{15}\,b^4\,c^5\,d^6+1888\,a^{15}\,b^4\,c^3\,d^8-136\,a^{15}\,b^4\,c\,d^{10}-448\,a^{14}\,b^5\,c^8\,d^3+3136\,a^{14}\,b^5\,c^6\,d^5-4352\,a^{14}\,b^5\,c^4\,d^7+1088\,a^{14}\,b^5\,c^2\,d^9+224\,a^{13}\,b^6\,c^9\,d^2-3416\,a^{13}\,b^6\,c^7\,d^4+7168\,a^{13}\,b^6\,c^5\,d^6-3912\,a^{13}\,b^6\,c^3\,d^8+144\,a^{13}\,b^6\,c\,d^{10}-64\,a^{12}\,b^7\,c^{10}\,d+2560\,a^{12}\,b^7\,c^8\,d^3-8960\,a^{12}\,b^7\,c^6\,d^5+8448\,a^{12}\,b^7\,c^4\,d^7-1152\,a^{12}\,b^7\,c^2\,d^9+8\,a^{11}\,b^8\,c^{11}-1244\,a^{11}\,b^8\,c^9\,d^2+8512\,a^{11}\,b^8\,c^7\,d^4-12432\,a^{11}\,b^8\,c^5\,d^6+4088\,a^{11}\,b^8\,c^3\,d^8-76\,a^{11}\,b^8\,c\,d^{10}+352\,a^{10}\,b^9\,c^{10}\,d-5888\,a^{10}\,b^9\,c^8\,d^3+13440\,a^{10}\,b^9\,c^6\,d^5-8512\,a^{10}\,b^9\,c^4\,d^7+608\,a^{10}\,b^9\,c^2\,d^9-44\,a^9\,b^{10}\,c^{11}+2752\,a^9\,b^{10}\,c^9\,d^2-11088\,a^9\,b^{10}\,c^7\,d^4+11648\,a^9\,b^{10}\,c^5\,d^6-2140\,a^9\,b^{10}\,c^3\,d^8+16\,a^9\,b^{10}\,c\,d^{10}-768\,a^8\,b^{11}\,c^{10}\,d+6912\,a^8\,b^{11}\,c^8\,d^3-11200\,a^8\,b^{11}\,c^6\,d^5+4352\,a^8\,b^{11}\,c^4\,d^7-128\,a^8\,b^{11}\,c^2\,d^9+96\,a^7\,b^{12}\,c^{11}-3048\,a^7\,b^{12}\,c^9\,d^2+7952\,a^7\,b^{12}\,c^7\,d^4-5656\,a^7\,b^{12}\,c^5\,d^6+448\,a^7\,b^{12}\,c^3\,d^8+832\,a^6\,b^{13}\,c^{10}\,d-4288\,a^6\,b^{13}\,c^8\,d^3+4928\,a^6\,b^{13}\,c^6\,d^5-896\,a^6\,b^{13}\,c^4\,d^7-104\,a^5\,b^{14}\,c^{11}+1712\,a^5\,b^{14}\,c^9\,d^2-2968\,a^5\,b^{14}\,c^7\,d^4+1120\,a^5\,b^{14}\,c^5\,d^6-448\,a^4\,b^{15}\,c^{10}\,d+1280\,a^4\,b^{15}\,c^8\,d^3-896\,a^4\,b^{15}\,c^6\,d^5+56\,a^3\,b^{16}\,c^{11}-412\,a^3\,b^{16}\,c^9\,d^2+448\,a^3\,b^{16}\,c^7\,d^4+96\,a^2\,b^{17}\,c^{10}\,d-128\,a^2\,b^{17}\,c^8\,d^3-12\,a\,b^{18}\,c^{11}+16\,a\,b^{18}\,c^9\,d^2\right)}{a^{14}\,d^6-6\,a^{13}\,b\,c\,d^5+15\,a^{12}\,b^2\,c^2\,d^4-4\,a^{12}\,b^2\,d^6-20\,a^{11}\,b^3\,c^3\,d^3+24\,a^{11}\,b^3\,c\,d^5+15\,a^{10}\,b^4\,c^4\,d^2-60\,a^{10}\,b^4\,c^2\,d^4+6\,a^{10}\,b^4\,d^6-6\,a^9\,b^5\,c^5\,d+80\,a^9\,b^5\,c^3\,d^3-36\,a^9\,b^5\,c\,d^5+a^8\,b^6\,c^6-60\,a^8\,b^6\,c^4\,d^2+90\,a^8\,b^6\,c^2\,d^4-4\,a^8\,b^6\,d^6+24\,a^7\,b^7\,c^5\,d-120\,a^7\,b^7\,c^3\,d^3+24\,a^7\,b^7\,c\,d^5-4\,a^6\,b^8\,c^6+90\,a^6\,b^8\,c^4\,d^2-60\,a^6\,b^8\,c^2\,d^4+a^6\,b^8\,d^6-36\,a^5\,b^9\,c^5\,d+80\,a^5\,b^9\,c^3\,d^3-6\,a^5\,b^9\,c\,d^5+6\,a^4\,b^{10}\,c^6-60\,a^4\,b^{10}\,c^4\,d^2+15\,a^4\,b^{10}\,c^2\,d^4+24\,a^3\,b^{11}\,c^5\,d-20\,a^3\,b^{11}\,c^3\,d^3-4\,a^2\,b^{12}\,c^6+15\,a^2\,b^{12}\,c^4\,d^2-6\,a\,b^{13}\,c^5\,d+b^{14}\,c^6}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}\right)\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)}{2\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4\,d^2-6\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-5\,a^2\,b^2\,d^2+b^4\,c^2+2\,b^4\,d^2\right)\,1{}\mathrm{i}}{f\,\left(a^{13}\,d^3-3\,a^{12}\,b\,c\,d^2+3\,a^{11}\,b^2\,c^2\,d-5\,a^{11}\,b^2\,d^3-a^{10}\,b^3\,c^3+15\,a^{10}\,b^3\,c\,d^2-15\,a^9\,b^4\,c^2\,d+10\,a^9\,b^4\,d^3+5\,a^8\,b^5\,c^3-30\,a^8\,b^5\,c\,d^2+30\,a^7\,b^6\,c^2\,d-10\,a^7\,b^6\,d^3-10\,a^6\,b^7\,c^3+30\,a^6\,b^7\,c\,d^2-30\,a^5\,b^8\,c^2\,d+5\,a^5\,b^8\,d^3+10\,a^4\,b^9\,c^3-15\,a^4\,b^9\,c\,d^2+15\,a^3\,b^{10}\,c^2\,d-a^3\,b^{10}\,d^3-5\,a^2\,b^{11}\,c^3+3\,a^2\,b^{11}\,c\,d^2-3\,a\,b^{12}\,c^2\,d+b^{13}\,c^3\right)}","Not used",1,"(d^3*atan(((d^3*(d^2 - c^2)^(1/2)*((8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (d^3*(d^2 - c^2)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (d^3*(d^2 - c^2)^(1/2)*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4))*1i)/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4) - (d^3*(d^2 - c^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (d^3*(d^2 - c^2)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (d^3*(d^2 - c^2)^(1/2)*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4))*1i)/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4))/((16*(4*a*b^9*c^3*d^5 + a*b^9*c^5*d^3 - 18*a^3*b^7*c*d^7 + 36*a^5*b^5*c*d^7 - 34*a^7*b^3*c*d^7 + 2*a^2*b^8*c^2*d^6 + a^2*b^8*c^4*d^4 - a^3*b^7*c^3*d^5 + 4*a^3*b^7*c^5*d^3 - 25*a^4*b^6*c^2*d^6 - 8*a^4*b^6*c^4*d^4 - 16*a^5*b^5*c^3*d^5 + 4*a^5*b^5*c^5*d^3 + 50*a^6*b^4*c^2*d^6 - 20*a^6*b^4*c^4*d^4 + 40*a^7*b^3*c^3*d^5 - 36*a^8*b^2*c^2*d^6 + 4*a*b^9*c*d^7 + 12*a^9*b*c*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (16*tan(e/2 + (f*x)/2)*(4*a*b^9*c^2*d^6 + 2*a*b^9*c^4*d^4 + 4*a^2*b^8*c*d^7 - 26*a^4*b^6*c*d^7 + 52*a^6*b^4*c*d^7 - 48*a^8*b^2*c*d^7 + 2*a^2*b^8*c^3*d^5 - 2*a^3*b^7*c^2*d^6 + 8*a^3*b^7*c^4*d^4 - 16*a^4*b^6*c^3*d^5 - 20*a^5*b^5*c^2*d^6 + 8*a^5*b^5*c^4*d^4 - 40*a^6*b^4*c^3*d^5 + 72*a^7*b^3*c^2*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (d^3*(d^2 - c^2)^(1/2)*((8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (d^3*(d^2 - c^2)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (d^3*(d^2 - c^2)^(1/2)*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4) - (d^3*(d^2 - c^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (d^3*(d^2 - c^2)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (d^3*(d^2 - c^2)^(1/2)*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))/(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)))*(d^2 - c^2)^(1/2)*2i)/(f*(a^3*d^5 + b^3*c^5 - a^3*c^2*d^3 - b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d - 3*a^2*b*c*d^4)) - ((b^5*c - 4*a^2*b^3*c + 6*a^3*b^2*d - 3*a*b^4*d)/((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(e/2 + (f*x)/2)*(2*b^5*c - 11*a^2*b^3*c + 17*a^3*b^2*d - 8*a*b^4*d))/(a*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^4 + b^4 - 2*a^2*b^2)) + (tan(e/2 + (f*x)/2)^2*(a^2 + 2*b^2)*(b^5*c - 4*a^2*b^3*c + 6*a^3*b^2*d - 3*a*b^4*d))/(a^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(e/2 + (f*x)/2)^3*(2*b^5*c - 5*a^2*b^3*c + 7*a^3*b^2*d - 4*a*b^4*d))/(a*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^4 + b^4 - 2*a^2*b^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(e/2 + (f*x)/2)^4 + a^2 + 4*a*b*tan(e/2 + (f*x)/2)^3 + 4*a*b*tan(e/2 + (f*x)/2))) - (b*atan(((b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (b*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d)*1i)/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (b*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d)*1i)/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))/((16*(4*a*b^9*c^3*d^5 + a*b^9*c^5*d^3 - 18*a^3*b^7*c*d^7 + 36*a^5*b^5*c*d^7 - 34*a^7*b^3*c*d^7 + 2*a^2*b^8*c^2*d^6 + a^2*b^8*c^4*d^4 - a^3*b^7*c^3*d^5 + 4*a^3*b^7*c^5*d^3 - 25*a^4*b^6*c^2*d^6 - 8*a^4*b^6*c^4*d^4 - 16*a^5*b^5*c^3*d^5 + 4*a^5*b^5*c^5*d^3 + 50*a^6*b^4*c^2*d^6 - 20*a^6*b^4*c^4*d^4 + 40*a^7*b^3*c^3*d^5 - 36*a^8*b^2*c^2*d^6 + 4*a*b^9*c*d^7 + 12*a^9*b*c*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (16*tan(e/2 + (f*x)/2)*(4*a*b^9*c^2*d^6 + 2*a*b^9*c^4*d^4 + 4*a^2*b^8*c*d^7 - 26*a^4*b^6*c*d^7 + 52*a^6*b^4*c*d^7 - 48*a^8*b^2*c*d^7 + 2*a^2*b^8*c^3*d^5 - 2*a^3*b^7*c^2*d^6 + 8*a^3*b^7*c^4*d^4 - 16*a^4*b^6*c^3*d^5 - 20*a^5*b^5*c^2*d^6 + 8*a^5*b^5*c^4*d^4 - 40*a^6*b^4*c^3*d^5 + 72*a^7*b^3*c^2*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (b*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*a*b^12*c^4*d^5 + 4*a*b^12*c^6*d^3 + 4*a^3*b^10*c^8*d + 4*a^4*b^9*c*d^8 + 4*a^5*b^8*c^8*d - 16*a^6*b^7*c*d^8 + 24*a^8*b^5*c*d^8 - 16*a^10*b^3*c*d^8 - 4*a^2*b^11*c^3*d^6 - 8*a^2*b^11*c^5*d^4 - 2*a^2*b^11*c^7*d^2 - 4*a^3*b^10*c^2*d^7 - 16*a^3*b^10*c^4*d^5 - a^3*b^10*c^6*d^3 + 24*a^4*b^9*c^3*d^6 - 20*a^4*b^9*c^5*d^4 - 20*a^4*b^9*c^7*d^2 + 12*a^5*b^8*c^2*d^7 + 95*a^5*b^8*c^4*d^5 + 20*a^5*b^8*c^6*d^3 - 98*a^6*b^7*c^3*d^6 + 64*a^6*b^7*c^5*d^4 - 32*a^6*b^7*c^7*d^2 + a^7*b^6*c^2*d^7 - 188*a^7*b^6*c^4*d^5 + 112*a^7*b^6*c^6*d^3 + 164*a^8*b^5*c^3*d^6 - 216*a^8*b^5*c^5*d^4 - 28*a^9*b^4*c^2*d^7 + 240*a^9*b^4*c^4*d^5 - 140*a^10*b^3*c^3*d^6 + 28*a^11*b^2*c^2*d^7 + a*b^12*c^8*d + 4*a^12*b*c*d^8))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(a*b^12*c^9 + 4*a^13*c*d^8 + 4*a^3*b^10*c^9 + 4*a^5*b^8*c^9 - 16*a*b^12*c^3*d^6 - 4*a*b^12*c^5*d^4 + 2*a*b^12*c^7*d^2 - 2*a^2*b^11*c^8*d - 16*a^3*b^10*c*d^8 - 20*a^4*b^9*c^8*d + 76*a^5*b^8*c*d^8 - 32*a^6*b^7*c^8*d - 162*a^7*b^6*c*d^8 + 176*a^9*b^4*c*d^8 - 96*a^11*b^2*c*d^8 - 8*a^12*b*c^2*d^7 + 32*a^2*b^11*c^2*d^7 + 8*a^2*b^11*c^4*d^5 - 4*a^2*b^11*c^6*d^3 + 72*a^3*b^10*c^3*d^6 - 14*a^3*b^10*c^5*d^4 - 9*a^3*b^10*c^7*d^2 - 152*a^4*b^9*c^2*d^7 + 80*a^4*b^9*c^4*d^5 + 20*a^4*b^9*c^6*d^3 - 274*a^5*b^8*c^3*d^6 + 55*a^5*b^8*c^5*d^4 + 12*a^5*b^8*c^7*d^2 + 372*a^6*b^7*c^2*d^7 - 250*a^6*b^7*c^4*d^5 + 128*a^6*b^7*c^6*d^3 + 481*a^7*b^6*c^3*d^6 - 412*a^7*b^6*c^5*d^4 + 112*a^7*b^6*c^7*d^2 - 472*a^8*b^5*c^2*d^7 + 612*a^8*b^5*c^4*d^5 - 216*a^8*b^5*c^6*d^3 - 564*a^9*b^4*c^3*d^6 + 240*a^9*b^4*c^5*d^4 + 336*a^10*b^3*c^2*d^7 - 144*a^10*b^3*c^4*d^5 + 40*a^11*b^2*c^3*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^14*c^10 - 6*a^6*b^10*c^10 + 4*a^8*b^8*c^10 + 4*a^16*c^2*d^8 + 4*a*b^15*c^7*d^3 - 10*a^3*b^13*c^9*d - 12*a^5*b^11*c^9*d + 4*a^7*b^9*c*d^9 + 54*a^7*b^9*c^9*d - 18*a^9*b^7*c*d^9 - 32*a^9*b^7*c^9*d + 36*a^11*b^5*c*d^9 - 34*a^13*b^3*c*d^9 - 32*a^15*b*c^3*d^7 - 24*a^2*b^14*c^6*d^4 + 2*a^2*b^14*c^8*d^2 + 60*a^3*b^13*c^5*d^5 - 30*a^3*b^13*c^7*d^3 - 80*a^4*b^12*c^4*d^6 + 138*a^4*b^12*c^6*d^4 + 2*a^4*b^12*c^8*d^2 + 60*a^5*b^11*c^3*d^7 - 310*a^5*b^11*c^5*d^5 + 122*a^5*b^11*c^7*d^3 - 24*a^6*b^10*c^2*d^8 + 390*a^6*b^10*c^4*d^6 - 466*a^6*b^10*c^6*d^4 + 102*a^6*b^10*c^8*d^2 - 282*a^7*b^9*c^3*d^7 + 878*a^7*b^9*c^5*d^5 - 394*a^7*b^9*c^7*d^3 + 110*a^8*b^8*c^2*d^8 - 970*a^8*b^8*c^4*d^6 + 894*a^8*b^8*c^6*d^4 - 218*a^8*b^8*c^8*d^2 + 638*a^9*b^7*c^3*d^7 - 1290*a^9*b^7*c^5*d^5 + 522*a^9*b^7*c^7*d^3 - 232*a^10*b^6*c^2*d^8 + 1202*a^10*b^6*c^4*d^6 - 822*a^10*b^6*c^6*d^4 + 112*a^10*b^6*c^8*d^2 - 702*a^11*b^5*c^3*d^7 + 886*a^11*b^5*c^5*d^5 - 224*a^11*b^5*c^7*d^3 + 234*a^12*b^4*c^2*d^8 - 654*a^12*b^4*c^4*d^6 + 280*a^12*b^4*c^6*d^4 + 318*a^13*b^3*c^3*d^7 - 224*a^13*b^3*c^5*d^5 - 92*a^14*b^2*c^2*d^8 + 112*a^14*b^2*c^4*d^6 + 12*a^15*b*c*d^9))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (8*tan(e/2 + (f*x)/2)*(4*a*b^15*c^10 + 8*a^16*c*d^9 - 12*a^5*b^11*c^10 + 8*a^7*b^9*c^10 + 4*a*b^15*c^8*d^2 - 20*a^2*b^14*c^9*d - 24*a^4*b^12*c^9*d + 108*a^6*b^10*c^9*d + 4*a^8*b^8*c*d^9 - 64*a^8*b^8*c^9*d - 8*a^10*b^6*c*d^9 + 12*a^12*b^4*c*d^9 - 16*a^14*b^2*c*d^9 - 40*a^15*b*c^2*d^8 - 20*a^2*b^14*c^7*d^3 + 36*a^3*b^13*c^6*d^4 + 4*a^3*b^13*c^8*d^2 - 20*a^4*b^12*c^5*d^5 + 164*a^4*b^12*c^7*d^3 - 20*a^5*b^11*c^4*d^6 - 452*a^5*b^11*c^6*d^4 + 204*a^5*b^11*c^8*d^2 + 36*a^6*b^10*c^3*d^7 + 556*a^6*b^10*c^5*d^5 - 708*a^6*b^10*c^7*d^3 - 20*a^7*b^9*c^2*d^8 - 340*a^7*b^9*c^4*d^6 + 1308*a^7*b^9*c^6*d^4 - 436*a^7*b^9*c^8*d^2 + 76*a^8*b^8*c^3*d^7 - 1380*a^8*b^8*c^5*d^5 + 1004*a^8*b^8*c^7*d^3 + 16*a^9*b^7*c^2*d^8 + 804*a^9*b^7*c^4*d^6 - 1404*a^9*b^7*c^6*d^4 + 224*a^9*b^7*c^8*d^2 - 204*a^10*b^6*c^3*d^7 + 1172*a^10*b^6*c^5*d^5 - 440*a^10*b^6*c^7*d^3 - 12*a^11*b^5*c^2*d^8 - 508*a^11*b^5*c^4*d^6 + 512*a^11*b^5*c^6*d^4 + 36*a^12*b^4*c^3*d^7 - 328*a^12*b^4*c^5*d^5 + 56*a^13*b^3*c^2*d^8 + 64*a^13*b^3*c^4*d^6 + 56*a^14*b^2*c^3*d^7))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) + (b*((8*(4*a^2*b^17*c^11 - 16*a^4*b^15*c^11 + 24*a^6*b^13*c^11 - 16*a^8*b^11*c^11 + 4*a^10*b^9*c^11 + 4*a^19*c^2*d^9 - 12*a^3*b^16*c^10*d + 88*a^5*b^14*c^10*d - 152*a^7*b^12*c^10*d + 108*a^9*b^10*c^10*d - 4*a^10*b^9*c*d^10 - 28*a^11*b^8*c^10*d + 16*a^12*b^7*c*d^10 - 24*a^14*b^5*c*d^10 + 16*a^16*b^3*c*d^10 - 28*a^18*b*c^3*d^8 + 28*a^2*b^17*c^9*d^2 - 80*a^3*b^16*c^8*d^3 + 112*a^4*b^15*c^7*d^4 - 32*a^4*b^15*c^9*d^2 - 56*a^5*b^14*c^6*d^5 + 208*a^5*b^14*c^8*d^3 - 56*a^6*b^13*c^5*d^6 - 392*a^6*b^13*c^7*d^4 - 152*a^6*b^13*c^9*d^2 + 112*a^7*b^12*c^4*d^7 + 280*a^7*b^12*c^6*d^5 - 32*a^7*b^12*c^8*d^3 - 80*a^8*b^11*c^3*d^8 + 112*a^8*b^11*c^5*d^6 + 448*a^8*b^11*c^7*d^4 + 368*a^8*b^11*c^9*d^2 + 28*a^9*b^10*c^2*d^9 - 368*a^9*b^10*c^4*d^7 - 560*a^9*b^10*c^6*d^5 - 352*a^9*b^10*c^8*d^3 + 292*a^10*b^9*c^3*d^8 + 112*a^10*b^9*c^5*d^6 - 112*a^10*b^9*c^7*d^4 - 292*a^10*b^9*c^9*d^2 - 108*a^11*b^8*c^2*d^9 + 352*a^11*b^8*c^4*d^7 + 560*a^11*b^8*c^6*d^5 + 368*a^11*b^8*c^8*d^3 - 368*a^12*b^7*c^3*d^8 - 448*a^12*b^7*c^5*d^6 - 112*a^12*b^7*c^7*d^4 + 80*a^12*b^7*c^9*d^2 + 152*a^13*b^6*c^2*d^9 + 32*a^13*b^6*c^4*d^7 - 280*a^13*b^6*c^6*d^5 - 112*a^13*b^6*c^8*d^3 + 152*a^14*b^5*c^3*d^8 + 392*a^14*b^5*c^5*d^6 + 56*a^14*b^5*c^7*d^4 - 88*a^15*b^4*c^2*d^9 - 208*a^15*b^4*c^4*d^7 + 56*a^15*b^4*c^6*d^5 + 32*a^16*b^3*c^3*d^8 - 112*a^16*b^3*c^5*d^6 + 12*a^17*b^2*c^2*d^9 + 80*a^17*b^2*c^4*d^7 - 4*a*b^18*c^10*d - 4*a^18*b*c*d^10))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^16*c^11 - 12*a^19*c*d^10 - 12*a*b^18*c^11 - 104*a^5*b^14*c^11 + 96*a^7*b^12*c^11 - 44*a^9*b^10*c^11 + 8*a^11*b^8*c^11 + 8*a^19*c^3*d^8 + 16*a*b^18*c^9*d^2 + 96*a^2*b^17*c^10*d - 448*a^4*b^15*c^10*d + 832*a^6*b^13*c^10*d - 768*a^8*b^11*c^10*d + 16*a^9*b^10*c*d^10 + 352*a^10*b^9*c^10*d - 76*a^11*b^8*c*d^10 - 64*a^12*b^7*c^10*d + 144*a^13*b^6*c*d^10 - 136*a^15*b^4*c*d^10 + 64*a^17*b^2*c*d^10 + 96*a^18*b*c^2*d^9 - 64*a^18*b*c^4*d^7 - 128*a^2*b^17*c^8*d^3 + 448*a^3*b^16*c^7*d^4 - 412*a^3*b^16*c^9*d^2 - 896*a^4*b^15*c^6*d^5 + 1280*a^4*b^15*c^8*d^3 + 1120*a^5*b^14*c^5*d^6 - 2968*a^5*b^14*c^7*d^4 + 1712*a^5*b^14*c^9*d^2 - 896*a^6*b^13*c^4*d^7 + 4928*a^6*b^13*c^6*d^5 - 4288*a^6*b^13*c^8*d^3 + 448*a^7*b^12*c^3*d^8 - 5656*a^7*b^12*c^5*d^6 + 7952*a^7*b^12*c^7*d^4 - 3048*a^7*b^12*c^9*d^2 - 128*a^8*b^11*c^2*d^9 + 4352*a^8*b^11*c^4*d^7 - 11200*a^8*b^11*c^6*d^5 + 6912*a^8*b^11*c^8*d^3 - 2140*a^9*b^10*c^3*d^8 + 11648*a^9*b^10*c^5*d^6 - 11088*a^9*b^10*c^7*d^4 + 2752*a^9*b^10*c^9*d^2 + 608*a^10*b^9*c^2*d^9 - 8512*a^10*b^9*c^4*d^7 + 13440*a^10*b^9*c^6*d^5 - 5888*a^10*b^9*c^8*d^3 + 4088*a^11*b^8*c^3*d^8 - 12432*a^11*b^8*c^5*d^6 + 8512*a^11*b^8*c^7*d^4 - 1244*a^11*b^8*c^9*d^2 - 1152*a^12*b^7*c^2*d^9 + 8448*a^12*b^7*c^4*d^7 - 8960*a^12*b^7*c^6*d^5 + 2560*a^12*b^7*c^8*d^3 - 3912*a^13*b^6*c^3*d^8 + 7168*a^13*b^6*c^5*d^6 - 3416*a^13*b^6*c^7*d^4 + 224*a^13*b^6*c^9*d^2 + 1088*a^14*b^5*c^2*d^9 - 4352*a^14*b^5*c^4*d^7 + 3136*a^14*b^5*c^6*d^5 - 448*a^14*b^5*c^8*d^3 + 1888*a^15*b^4*c^3*d^8 - 2072*a^15*b^4*c^5*d^6 + 560*a^15*b^4*c^7*d^4 - 512*a^16*b^3*c^2*d^9 + 1024*a^16*b^3*c^4*d^7 - 448*a^16*b^3*c^6*d^5 - 380*a^17*b^2*c^3*d^8 + 224*a^17*b^2*c^5*d^6))/(a^14*d^6 + b^14*c^6 - 4*a^2*b^12*c^6 + 6*a^4*b^10*c^6 - 4*a^6*b^8*c^6 + a^8*b^6*c^6 + a^6*b^8*d^6 - 4*a^8*b^6*d^6 + 6*a^10*b^4*d^6 - 4*a^12*b^2*d^6 + 24*a^3*b^11*c^5*d - 6*a^5*b^9*c*d^5 - 36*a^5*b^9*c^5*d + 24*a^7*b^7*c*d^5 + 24*a^7*b^7*c^5*d - 36*a^9*b^5*c*d^5 - 6*a^9*b^5*c^5*d + 24*a^11*b^3*c*d^5 + 15*a^2*b^12*c^4*d^2 - 20*a^3*b^11*c^3*d^3 + 15*a^4*b^10*c^2*d^4 - 60*a^4*b^10*c^4*d^2 + 80*a^5*b^9*c^3*d^3 - 60*a^6*b^8*c^2*d^4 + 90*a^6*b^8*c^4*d^2 - 120*a^7*b^7*c^3*d^3 + 90*a^8*b^6*c^2*d^4 - 60*a^8*b^6*c^4*d^2 + 80*a^9*b^5*c^3*d^3 - 60*a^10*b^4*c^2*d^4 + 15*a^10*b^4*c^4*d^2 - 20*a^11*b^3*c^3*d^3 + 15*a^12*b^2*c^2*d^4 - 6*a*b^13*c^5*d - 6*a^13*b*c*d^5))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2)))*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d))/(2*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4*d^2 + b^4*c^2 + 2*b^4*d^2 + 2*a^2*b^2*c^2 - 5*a^2*b^2*d^2 - 6*a^3*b*c*d)*1i)/(f*(a^13*d^3 + b^13*c^3 - 5*a^2*b^11*c^3 + 10*a^4*b^9*c^3 - 10*a^6*b^7*c^3 + 5*a^8*b^5*c^3 - a^10*b^3*c^3 - a^3*b^10*d^3 + 5*a^5*b^8*d^3 - 10*a^7*b^6*d^3 + 10*a^9*b^4*d^3 - 5*a^11*b^2*d^3 + 3*a^2*b^11*c*d^2 + 15*a^3*b^10*c^2*d - 15*a^4*b^9*c*d^2 - 30*a^5*b^8*c^2*d + 30*a^6*b^7*c*d^2 + 30*a^7*b^6*c^2*d - 30*a^8*b^5*c*d^2 - 15*a^9*b^4*c^2*d + 15*a^10*b^3*c*d^2 + 3*a^11*b^2*c^2*d - 3*a*b^12*c^2*d - 3*a^12*b*c*d^2))","B"
721,1,137273,454,43.673163,"\text{Not used}","int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^2),x)","\frac{\frac{2\,a^6\,d^4-4\,a^4\,b^2\,d^4+8\,a^3\,b^3\,c^3\,d-8\,a^3\,b^3\,c\,d^3-4\,a^2\,b^4\,c^4+4\,a^2\,b^4\,c^2\,d^2+2\,a^2\,b^4\,d^4-5\,a\,b^5\,c^3\,d+5\,a\,b^5\,c\,d^3+b^6\,c^4-b^6\,c^2\,d^2}{\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2-a^4\,d^2-2\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2+b^4\,c^2-b^4\,d^2\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a^7\,d^5+8\,a^6\,b\,c\,d^4-4\,a^5\,b^2\,d^5+16\,a^4\,b^3\,c^3\,d^2-32\,a^4\,b^3\,c\,d^4+15\,a^3\,b^4\,c^4\,d-15\,a^3\,b^4\,c^2\,d^3+2\,a^3\,b^4\,d^5-11\,a^2\,b^5\,c^5+a^2\,b^5\,c^3\,d^2+18\,a^2\,b^5\,c\,d^4-12\,a\,b^6\,c^4\,d+12\,a\,b^6\,c^2\,d^3+2\,b^7\,c^5-2\,b^7\,c^3\,d^2\right)}{a\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2-a^4\,d^2-2\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2+b^4\,c^2-b^4\,d^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,a^7\,d^5-4\,a^5\,b^2\,d^5+9\,a^3\,b^4\,c^4\,d-9\,a^3\,b^4\,c^2\,d^3+2\,a^3\,b^4\,d^5-5\,a^2\,b^5\,c^5+5\,a^2\,b^5\,c^3\,d^2-6\,a\,b^6\,c^4\,d+6\,a\,b^6\,c^2\,d^3+2\,b^7\,c^5-2\,b^7\,c^3\,d^2\right)}{a\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2-a^4\,d^2-2\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2+b^4\,c^2-b^4\,d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a^8\,c\,d^4+4\,a^7\,b\,d^5+8\,a^5\,b^3\,c^4\,d-8\,a^5\,b^3\,c^2\,d^3-8\,a^5\,b^3\,d^5-4\,a^4\,b^4\,c^5+27\,a^4\,b^4\,c^3\,d^2-29\,a^4\,b^4\,c\,d^4-8\,a^3\,b^5\,c^4\,d+8\,a^3\,b^5\,c^2\,d^3+4\,a^3\,b^5\,d^5-3\,a^2\,b^6\,c^5-11\,a^2\,b^6\,c^3\,d^2+18\,a^2\,b^6\,c\,d^4-3\,a\,b^7\,c^4\,d+3\,a\,b^7\,c^2\,d^3+b^8\,c^5-b^8\,c^3\,d^2\right)}{a^2\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2-a^4\,d^2-2\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2+b^4\,c^2-b^4\,d^2\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(-2\,a^8\,c\,d^4-8\,a^7\,b\,d^5+4\,a^6\,b^2\,c\,d^4-8\,a^5\,b^3\,c^4\,d+8\,a^5\,b^3\,c^2\,d^3+16\,a^5\,b^3\,d^5+4\,a^4\,b^4\,c^5-22\,a^4\,b^4\,c^3\,d^2+16\,a^4\,b^4\,c\,d^4-a^3\,b^5\,c^4\,d+a^3\,b^5\,c^2\,d^3-8\,a^3\,b^5\,d^5+7\,a^2\,b^6\,c^5+5\,a^2\,b^6\,c^3\,d^2-12\,a^2\,b^6\,c\,d^4+6\,a\,b^7\,c^4\,d-6\,a\,b^7\,c^2\,d^3-2\,b^8\,c^5+2\,b^8\,c^3\,d^2\right)}{a^2\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2-a^4\,d^2-2\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2+b^4\,c^2-b^4\,d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(d\,a^2+2\,c\,a\,b+2\,d\,b^2\right)\,\left(2\,a^6\,d^4-4\,a^4\,b^2\,d^4+8\,a^3\,b^3\,c^3\,d-8\,a^3\,b^3\,c\,d^3-4\,a^2\,b^4\,c^4+4\,a^2\,b^4\,c^2\,d^2+2\,a^2\,b^4\,d^4-5\,a\,b^5\,c^3\,d+5\,a\,b^5\,c\,d^3+b^6\,c^4-b^6\,c^2\,d^2\right)}{a^2\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2-a^4\,d^2-2\,a^2\,b^2\,c^2+2\,a^2\,b^2\,d^2+b^4\,c^2-b^4\,d^2\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c\,a^2+8\,d\,a\,b+4\,c\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c\,a^2+8\,d\,a\,b+4\,c\,b^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,d\,a^2+8\,c\,a\,b+8\,d\,b^2\right)+a^2\,c+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,d\,a^2+4\,b\,c\,a\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,d\,a^2+4\,b\,c\,a\right)+a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\right)}-\frac{d^3\,\mathrm{atan}\left(\frac{\frac{d^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(4\,a^{15}\,b\,c^3\,d^{11}-44\,a^{14}\,b^2\,c^4\,d^{10}+24\,a^{14}\,b^2\,c^2\,d^{12}+172\,a^{13}\,b^3\,c^5\,d^9-184\,a^{13}\,b^3\,c^3\,d^{11}+36\,a^{13}\,b^3\,c\,d^{13}-148\,a^{12}\,b^4\,c^6\,d^8+248\,a^{12}\,b^4\,c^4\,d^{10}-60\,a^{12}\,b^4\,c^2\,d^{12}-400\,a^{11}\,b^5\,c^7\,d^7+248\,a^{11}\,b^5\,c^5\,d^9+180\,a^{11}\,b^5\,c^3\,d^{11}-144\,a^{11}\,b^5\,c\,d^{13}+1056\,a^{10}\,b^6\,c^8\,d^6-1336\,a^{10}\,b^6\,c^6\,d^8+100\,a^{10}\,b^6\,c^4\,d^{10}+216\,a^{10}\,b^6\,c^2\,d^{12}-1088\,a^9\,b^7\,c^9\,d^5+2648\,a^9\,b^7\,c^7\,d^7-1544\,a^9\,b^7\,c^5\,d^9-88\,a^9\,b^7\,c^3\,d^{11}+216\,a^9\,b^7\,c\,d^{13}+628\,a^8\,b^8\,c^{10}\,d^4-3012\,a^8\,b^8\,c^8\,d^6+2885\,a^8\,b^8\,c^6\,d^8-270\,a^8\,b^8\,c^4\,d^{10}-375\,a^8\,b^8\,c^2\,d^{12}-220\,a^7\,b^9\,c^{11}\,d^3+1860\,a^7\,b^9\,c^9\,d^5-2979\,a^7\,b^9\,c^7\,d^7+1386\,a^7\,b^9\,c^5\,d^9+61\,a^7\,b^9\,c^3\,d^{11}-144\,a^7\,b^9\,c\,d^{13}+44\,a^6\,b^{10}\,c^{12}\,d^2-552\,a^6\,b^{10}\,c^{10}\,d^4+2161\,a^6\,b^{10}\,c^8\,d^6-2046\,a^6\,b^{10}\,c^6\,d^8+233\,a^6\,b^{10}\,c^4\,d^{10}+276\,a^6\,b^{10}\,c^2\,d^{12}-4\,a^5\,b^{11}\,c^{13}\,d+40\,a^5\,b^{11}\,c^{11}\,d^3-895\,a^5\,b^{11}\,c^9\,d^5+1354\,a^5\,b^{11}\,c^7\,d^7-535\,a^5\,b^{11}\,c^5\,d^9-36\,a^5\,b^{11}\,c^3\,d^{11}+36\,a^5\,b^{11}\,c\,d^{13}+20\,a^4\,b^{12}\,c^{12}\,d^2+99\,a^4\,b^{12}\,c^{10}\,d^4-602\,a^4\,b^{12}\,c^8\,d^6+699\,a^4\,b^{12}\,c^6\,d^8-168\,a^4\,b^{12}\,c^4\,d^{10}-72\,a^4\,b^{12}\,c^2\,d^{12}-4\,a^3\,b^{13}\,c^{13}\,d+19\,a^3\,b^{13}\,c^{11}\,d^3+190\,a^3\,b^{13}\,c^9\,d^5-305\,a^3\,b^{13}\,c^7\,d^7+120\,a^3\,b^{13}\,c^5\,d^9-a^2\,b^{14}\,c^{12}\,d^2+14\,a^2\,b^{14}\,c^{10}\,d^4+19\,a^2\,b^{14}\,c^8\,d^6-108\,a^2\,b^{14}\,c^6\,d^8+72\,a^2\,b^{14}\,c^4\,d^{10}-a\,b^{15}\,c^{13}\,d-10\,a\,b^{15}\,c^{11}\,d^3-13\,a\,b^{15}\,c^9\,d^5+60\,a\,b^{15}\,c^7\,d^7-36\,a\,b^{15}\,c^5\,d^9\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}\,d^{13}-9\,a^{16}\,b\,c^5\,d^8+18\,a^{16}\,b\,c^3\,d^{10}-9\,a^{16}\,b\,c\,d^{12}+36\,a^{15}\,b^2\,c^6\,d^7-76\,a^{15}\,b^2\,c^4\,d^9+44\,a^{15}\,b^2\,c^2\,d^{11}-4\,a^{15}\,b^2\,d^{13}-84\,a^{14}\,b^3\,c^7\,d^6+204\,a^{14}\,b^3\,c^5\,d^8-156\,a^{14}\,b^3\,c^3\,d^{10}+36\,a^{14}\,b^3\,c\,d^{12}+126\,a^{13}\,b^4\,c^8\,d^5-396\,a^{13}\,b^4\,c^6\,d^7+420\,a^{13}\,b^4\,c^4\,d^9-156\,a^{13}\,b^4\,c^2\,d^{11}+6\,a^{13}\,b^4\,d^{13}-126\,a^{12}\,b^5\,c^9\,d^4+588\,a^{12}\,b^5\,c^7\,d^6-852\,a^{12}\,b^5\,c^5\,d^8+444\,a^{12}\,b^5\,c^3\,d^{10}-54\,a^{12}\,b^5\,c\,d^{12}+84\,a^{11}\,b^6\,c^{10}\,d^3-672\,a^{11}\,b^6\,c^8\,d^5+1308\,a^{11}\,b^6\,c^6\,d^7-940\,a^{11}\,b^6\,c^4\,d^9+224\,a^{11}\,b^6\,c^2\,d^{11}-4\,a^{11}\,b^6\,d^{13}-36\,a^{10}\,b^7\,c^{11}\,d^2+576\,a^{10}\,b^7\,c^9\,d^4-1548\,a^{10}\,b^7\,c^7\,d^6+1548\,a^{10}\,b^7\,c^5\,d^8-576\,a^{10}\,b^7\,c^3\,d^{10}+36\,a^{10}\,b^7\,c\,d^{12}+9\,a^9\,b^8\,c^{12}\,d-354\,a^9\,b^8\,c^{10}\,d^3+1437\,a^9\,b^8\,c^8\,d^5-1992\,a^9\,b^8\,c^6\,d^7+1045\,a^9\,b^8\,c^4\,d^9-146\,a^9\,b^8\,c^2\,d^{11}+a^9\,b^8\,d^{13}-a^8\,b^9\,c^{13}+146\,a^8\,b^9\,c^{11}\,d^2-1045\,a^8\,b^9\,c^9\,d^4+1992\,a^8\,b^9\,c^7\,d^6-1437\,a^8\,b^9\,c^5\,d^8+354\,a^8\,b^9\,c^3\,d^{10}-9\,a^8\,b^9\,c\,d^{12}-36\,a^7\,b^{10}\,c^{12}\,d+576\,a^7\,b^{10}\,c^{10}\,d^3-1548\,a^7\,b^{10}\,c^8\,d^5+1548\,a^7\,b^{10}\,c^6\,d^7-576\,a^7\,b^{10}\,c^4\,d^9+36\,a^7\,b^{10}\,c^2\,d^{11}+4\,a^6\,b^{11}\,c^{13}-224\,a^6\,b^{11}\,c^{11}\,d^2+940\,a^6\,b^{11}\,c^9\,d^4-1308\,a^6\,b^{11}\,c^7\,d^6+672\,a^6\,b^{11}\,c^5\,d^8-84\,a^6\,b^{11}\,c^3\,d^{10}+54\,a^5\,b^{12}\,c^{12}\,d-444\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{16}\,c^3\,d^{11}-44\,a^{15}\,b\,c^4\,d^{10}+24\,a^{15}\,b\,c^2\,d^{12}+172\,a^{14}\,b^2\,c^5\,d^9-192\,a^{14}\,b^2\,c^3\,d^{11}+36\,a^{14}\,b^2\,c\,d^{13}-292\,a^{13}\,b^3\,c^6\,d^8+624\,a^{13}\,b^3\,c^4\,d^{10}-252\,a^{13}\,b^3\,c^2\,d^{12}+368\,a^{12}\,b^4\,c^7\,d^7-1920\,a^{12}\,b^4\,c^5\,d^9+1892\,a^{12}\,b^4\,c^3\,d^{11}-504\,a^{12}\,b^4\,c\,d^{13}-688\,a^{11}\,b^5\,c^8\,d^6+4344\,a^{11}\,b^5\,c^6\,d^8-5932\,a^{11}\,b^5\,c^4\,d^{10}+2232\,a^{11}\,b^5\,c^2\,d^{12}+1120\,a^{10}\,b^6\,c^9\,d^5-6184\,a^{10}\,b^6\,c^7\,d^7+11320\,a^{10}\,b^6\,c^5\,d^9-7104\,a^{10}\,b^6\,c^3\,d^{11}+1224\,a^{10}\,b^6\,c\,d^{13}-1088\,a^9\,b^7\,c^{10}\,d^4+6104\,a^9\,b^7\,c^8\,d^6-15576\,a^9\,b^7\,c^6\,d^8+14976\,a^9\,b^7\,c^4\,d^{10}-4632\,a^9\,b^7\,c^2\,d^{12}+628\,a^8\,b^8\,c^{11}\,d^3-4524\,a^8\,b^8\,c^9\,d^5+14693\,a^8\,b^8\,c^7\,d^7-19912\,a^8\,b^8\,c^5\,d^9+10105\,a^8\,b^8\,c^3\,d^{11}-1314\,a^8\,b^8\,c\,d^{13}-220\,a^7\,b^9\,c^{12}\,d^2+2300\,a^7\,b^9\,c^{10}\,d^4-8939\,a^7\,b^9\,c^8\,d^6+18608\,a^7\,b^9\,c^6\,d^8-15815\,a^7\,b^9\,c^4\,d^{10}+4470\,a^7\,b^9\,c^2\,d^{12}+44\,a^6\,b^{10}\,c^{13}\,d-640\,a^6\,b^{10}\,c^{11}\,d^3+3649\,a^6\,b^{10}\,c^9\,d^5-12464\,a^6\,b^{10}\,c^7\,d^7+16053\,a^6\,b^{10}\,c^5\,d^9-7294\,a^6\,b^{10}\,c^3\,d^{11}+684\,a^6\,b^{10}\,c\,d^{13}-4\,a^5\,b^{11}\,c^{14}+48\,a^5\,b^{11}\,c^{12}\,d^2-975\,a^5\,b^{11}\,c^{10}\,d^4+5064\,a^5\,b^{11}\,c^8\,d^6-10619\,a^5\,b^{11}\,c^6\,d^8+8378\,a^5\,b^{11}\,c^4\,d^{10}-2148\,a^5\,b^{11}\,c^2\,d^{12}+20\,a^4\,b^{12}\,c^{13}\,d+59\,a^4\,b^{12}\,c^{11}\,d^3-1056\,a^4\,b^{12}\,c^9\,d^5+5107\,a^4\,b^{12}\,c^7\,d^7-6574\,a^4\,b^{12}\,c^5\,d^9+2688\,a^4\,b^{12}\,c^3\,d^{11}-144\,a^4\,b^{12}\,c\,d^{13}-4\,a^3\,b^{13}\,c^{14}+27\,a^3\,b^{13}\,c^{12}\,d^2+152\,a^3\,b^{13}\,c^{10}\,d^4-1485\,a^3\,b^{13}\,c^8\,d^6+2938\,a^3\,b^{13}\,c^6\,d^8-2016\,a^3\,b^{13}\,c^4\,d^{10}+432\,a^3\,b^{13}\,c^2\,d^{12}-a^2\,b^{14}\,c^{13}\,d+16\,a^2\,b^{14}\,c^{11}\,d^3+55\,a^2\,b^{14}\,c^9\,d^5-818\,a^2\,b^{14}\,c^7\,d^7+1140\,a^2\,b^{14}\,c^5\,d^9-432\,a^2\,b^{14}\,c^3\,d^{11}-a\,b^{15}\,c^{14}-8\,a\,b^{15}\,c^{12}\,d^2+7\,a\,b^{15}\,c^{10}\,d^4+214\,a\,b^{15}\,c^8\,d^6-348\,a\,b^{15}\,c^6\,d^8+144\,a\,b^{15}\,c^4\,d^{10}\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}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0\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}\right)\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)\,1{}\mathrm{i}}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}-\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{15}\,b\,c^3\,d^{11}-44\,a^{14}\,b^2\,c^4\,d^{10}+24\,a^{14}\,b^2\,c^2\,d^{12}+172\,a^{13}\,b^3\,c^5\,d^9-184\,a^{13}\,b^3\,c^3\,d^{11}+36\,a^{13}\,b^3\,c\,d^{13}-148\,a^{12}\,b^4\,c^6\,d^8+248\,a^{12}\,b^4\,c^4\,d^{10}-60\,a^{12}\,b^4\,c^2\,d^{12}-400\,a^{11}\,b^5\,c^7\,d^7+248\,a^{11}\,b^5\,c^5\,d^9+180\,a^{11}\,b^5\,c^3\,d^{11}-144\,a^{11}\,b^5\,c\,d^{13}+1056\,a^{10}\,b^6\,c^8\,d^6-1336\,a^{10}\,b^6\,c^6\,d^8+100\,a^{10}\,b^6\,c^4\,d^{10}+216\,a^{10}\,b^6\,c^2\,d^{12}-1088\,a^9\,b^7\,c^9\,d^5+2648\,a^9\,b^7\,c^7\,d^7-1544\,a^9\,b^7\,c^5\,d^9-88\,a^9\,b^7\,c^3\,d^{11}+216\,a^9\,b^7\,c\,d^{13}+628\,a^8\,b^8\,c^{10}\,d^4-3012\,a^8\,b^8\,c^8\,d^6+2885\,a^8\,b^8\,c^6\,d^8-270\,a^8\,b^8\,c^4\,d^{10}-375\,a^8\,b^8\,c^2\,d^{12}-220\,a^7\,b^9\,c^{11}\,d^3+1860\,a^7\,b^9\,c^9\,d^5-2979\,a^7\,b^9\,c^7\,d^7+1386\,a^7\,b^9\,c^5\,d^9+61\,a^7\,b^9\,c^3\,d^{11}-144\,a^7\,b^9\,c\,d^{13}+44\,a^6\,b^{10}\,c^{12}\,d^2-552\,a^6\,b^{10}\,c^{10}\,d^4+2161\,a^6\,b^{10}\,c^8\,d^6-2046\,a^6\,b^{10}\,c^6\,d^8+233\,a^6\,b^{10}\,c^4\,d^{10}+276\,a^6\,b^{10}\,c^2\,d^{12}-4\,a^5\,b^{11}\,c^{13}\,d+40\,a^5\,b^{11}\,c^{11}\,d^3-895\,a^5\,b^{11}\,c^9\,d^5+1354\,a^5\,b^{11}\,c^7\,d^7-535\,a^5\,b^{11}\,c^5\,d^9-36\,a^5\,b^{11}\,c^3\,d^{11}+36\,a^5\,b^{11}\,c\,d^{13}+20\,a^4\,b^{12}\,c^{12}\,d^2+99\,a^4\,b^{12}\,c^{10}\,d^4-602\,a^4\,b^{12}\,c^8\,d^6+699\,a^4\,b^{12}\,c^6\,d^8-168\,a^4\,b^{12}\,c^4\,d^{10}-72\,a^4\,b^{12}\,c^2\,d^{12}-4\,a^3\,b^{13}\,c^{13}\,d+19\,a^3\,b^{13}\,c^{11}\,d^3+190\,a^3\,b^{13}\,c^9\,d^5-305\,a^3\,b^{13}\,c^7\,d^7+120\,a^3\,b^{13}\,c^5\,d^9-a^2\,b^{14}\,c^{12}\,d^2+14\,a^2\,b^{14}\,c^{10}\,d^4+19\,a^2\,b^{14}\,c^8\,d^6-108\,a^2\,b^{14}\,c^6\,d^8+72\,a^2\,b^{14}\,c^4\,d^{10}-a\,b^{15}\,c^{13}\,d-10\,a\,b^{15}\,c^{11}\,d^3-13\,a\,b^{15}\,c^9\,d^5+60\,a\,b^{15}\,c^7\,d^7-36\,a\,b^{15}\,c^5\,d^9\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}\,d^{13}-9\,a^{16}\,b\,c^5\,d^8+18\,a^{16}\,b\,c^3\,d^{10}-9\,a^{16}\,b\,c\,d^{12}+36\,a^{15}\,b^2\,c^6\,d^7-76\,a^{15}\,b^2\,c^4\,d^9+44\,a^{15}\,b^2\,c^2\,d^{11}-4\,a^{15}\,b^2\,d^{13}-84\,a^{14}\,b^3\,c^7\,d^6+204\,a^{14}\,b^3\,c^5\,d^8-156\,a^{14}\,b^3\,c^3\,d^{10}+36\,a^{14}\,b^3\,c\,d^{12}+126\,a^{13}\,b^4\,c^8\,d^5-396\,a^{13}\,b^4\,c^6\,d^7+420\,a^{13}\,b^4\,c^4\,d^9-156\,a^{13}\,b^4\,c^2\,d^{11}+6\,a^{13}\,b^4\,d^{13}-126\,a^{12}\,b^5\,c^9\,d^4+588\,a^{12}\,b^5\,c^7\,d^6-852\,a^{12}\,b^5\,c^5\,d^8+444\,a^{12}\,b^5\,c^3\,d^{10}-54\,a^{12}\,b^5\,c\,d^{12}+84\,a^{11}\,b^6\,c^{10}\,d^3-672\,a^{11}\,b^6\,c^8\,d^5+1308\,a^{11}\,b^6\,c^6\,d^7-940\,a^{11}\,b^6\,c^4\,d^9+224\,a^{11}\,b^6\,c^2\,d^{11}-4\,a^{11}\,b^6\,d^{13}-36\,a^{10}\,b^7\,c^{11}\,d^2+576\,a^{10}\,b^7\,c^9\,d^4-1548\,a^{10}\,b^7\,c^7\,d^6+1548\,a^{10}\,b^7\,c^5\,d^8-576\,a^{10}\,b^7\,c^3\,d^{10}+36\,a^{10}\,b^7\,c\,d^{12}+9\,a^9\,b^8\,c^{12}\,d-354\,a^9\,b^8\,c^{10}\,d^3+1437\,a^9\,b^8\,c^8\,d^5-1992\,a^9\,b^8\,c^6\,d^7+1045\,a^9\,b^8\,c^4\,d^9-146\,a^9\,b^8\,c^2\,d^{11}+a^9\,b^8\,d^{13}-a^8\,b^9\,c^{13}+146\,a^8\,b^9\,c^{11}\,d^2-1045\,a^8\,b^9\,c^9\,d^4+1992\,a^8\,b^9\,c^7\,d^6-1437\,a^8\,b^9\,c^5\,d^8+354\,a^8\,b^9\,c^3\,d^{10}-9\,a^8\,b^9\,c\,d^{12}-36\,a^7\,b^{10}\,c^{12}\,d+576\,a^7\,b^{10}\,c^{10}\,d^3-1548\,a^7\,b^{10}\,c^8\,d^5+1548\,a^7\,b^{10}\,c^6\,d^7-576\,a^7\,b^{10}\,c^4\,d^9+36\,a^7\,b^{10}\,c^2\,d^{11}+4\,a^6\,b^{11}\,c^{13}-224\,a^6\,b^{11}\,c^{11}\,d^2+940\,a^6\,b^{11}\,c^9\,d^4-1308\,a^6\,b^{11}\,c^7\,d^6+672\,a^6\,b^{11}\,c^5\,d^8-84\,a^6\,b^{11}\,c^3\,d^{10}+54\,a^5\,b^{12}\,c^{12}\,d-444\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{16}\,c^3\,d^{11}-44\,a^{15}\,b\,c^4\,d^{10}+24\,a^{15}\,b\,c^2\,d^{12}+172\,a^{14}\,b^2\,c^5\,d^9-192\,a^{14}\,b^2\,c^3\,d^{11}+36\,a^{14}\,b^2\,c\,d^{13}-292\,a^{13}\,b^3\,c^6\,d^8+624\,a^{13}\,b^3\,c^4\,d^{10}-252\,a^{13}\,b^3\,c^2\,d^{12}+368\,a^{12}\,b^4\,c^7\,d^7-1920\,a^{12}\,b^4\,c^5\,d^9+1892\,a^{12}\,b^4\,c^3\,d^{11}-504\,a^{12}\,b^4\,c\,d^{13}-688\,a^{11}\,b^5\,c^8\,d^6+4344\,a^{11}\,b^5\,c^6\,d^8-5932\,a^{11}\,b^5\,c^4\,d^{10}+2232\,a^{11}\,b^5\,c^2\,d^{12}+1120\,a^{10}\,b^6\,c^9\,d^5-6184\,a^{10}\,b^6\,c^7\,d^7+11320\,a^{10}\,b^6\,c^5\,d^9-7104\,a^{10}\,b^6\,c^3\,d^{11}+1224\,a^{10}\,b^6\,c\,d^{13}-1088\,a^9\,b^7\,c^{10}\,d^4+6104\,a^9\,b^7\,c^8\,d^6-15576\,a^9\,b^7\,c^6\,d^8+14976\,a^9\,b^7\,c^4\,d^{10}-4632\,a^9\,b^7\,c^2\,d^{12}+628\,a^8\,b^8\,c^{11}\,d^3-4524\,a^8\,b^8\,c^9\,d^5+14693\,a^8\,b^8\,c^7\,d^7-19912\,a^8\,b^8\,c^5\,d^9+10105\,a^8\,b^8\,c^3\,d^{11}-1314\,a^8\,b^8\,c\,d^{13}-220\,a^7\,b^9\,c^{12}\,d^2+2300\,a^7\,b^9\,c^{10}\,d^4-8939\,a^7\,b^9\,c^8\,d^6+18608\,a^7\,b^9\,c^6\,d^8-15815\,a^7\,b^9\,c^4\,d^{10}+4470\,a^7\,b^9\,c^2\,d^{12}+44\,a^6\,b^{10}\,c^{13}\,d-640\,a^6\,b^{10}\,c^{11}\,d^3+3649\,a^6\,b^{10}\,c^9\,d^5-12464\,a^6\,b^{10}\,c^7\,d^7+16053\,a^6\,b^{10}\,c^5\,d^9-7294\,a^6\,b^{10}\,c^3\,d^{11}+684\,a^6\,b^{10}\,c\,d^{13}-4\,a^5\,b^{11}\,c^{14}+48\,a^5\,b^{11}\,c^{12}\,d^2-975\,a^5\,b^{11}\,c^{10}\,d^4+5064\,a^5\,b^{11}\,c^8\,d^6-10619\,a^5\,b^{11}\,c^6\,d^8+8378\,a^5\,b^{11}\,c^4\,d^{10}-2148\,a^5\,b^{11}\,c^2\,d^{12}+20\,a^4\,b^{12}\,c^{13}\,d+59\,a^4\,b^{12}\,c^{11}\,d^3-1056\,a^4\,b^{12}\,c^9\,d^5+5107\,a^4\,b^{12}\,c^7\,d^7-6574\,a^4\,b^{12}\,c^5\,d^9+2688\,a^4\,b^{12}\,c^3\,d^{11}-144\,a^4\,b^{12}\,c\,d^{13}-4\,a^3\,b^{13}\,c^{14}+27\,a^3\,b^{13}\,c^{12}\,d^2+152\,a^3\,b^{13}\,c^{10}\,d^4-1485\,a^3\,b^{13}\,c^8\,d^6+2938\,a^3\,b^{13}\,c^6\,d^8-2016\,a^3\,b^{13}\,c^4\,d^{10}+432\,a^3\,b^{13}\,c^2\,d^{12}-a^2\,b^{14}\,c^{13}\,d+16\,a^2\,b^{14}\,c^{11}\,d^3+55\,a^2\,b^{14}\,c^9\,d^5-818\,a^2\,b^{14}\,c^7\,d^7+1140\,a^2\,b^{14}\,c^5\,d^9-432\,a^2\,b^{14}\,c^3\,d^{11}-a\,b^{15}\,c^{14}-8\,a\,b^{15}\,c^{12}\,d^2+7\,a\,b^{15}\,c^{10}\,d^4+214\,a\,b^{15}\,c^8\,d^6-348\,a\,b^{15}\,c^6\,d^8+144\,a\,b^{15}\,c^4\,d^{10}\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}\,d^{13}-9\,a^{16}\,b\,c^5\,d^8+18\,a^{16}\,b\,c^3\,d^{10}-9\,a^{16}\,b\,c\,d^{12}+36\,a^{15}\,b^2\,c^6\,d^7-76\,a^{15}\,b^2\,c^4\,d^9+44\,a^{15}\,b^2\,c^2\,d^{11}-4\,a^{15}\,b^2\,d^{13}-84\,a^{14}\,b^3\,c^7\,d^6+204\,a^{14}\,b^3\,c^5\,d^8-156\,a^{14}\,b^3\,c^3\,d^{10}+36\,a^{14}\,b^3\,c\,d^{12}+126\,a^{13}\,b^4\,c^8\,d^5-396\,a^{13}\,b^4\,c^6\,d^7+420\,a^{13}\,b^4\,c^4\,d^9-156\,a^{13}\,b^4\,c^2\,d^{11}+6\,a^{13}\,b^4\,d^{13}-126\,a^{12}\,b^5\,c^9\,d^4+588\,a^{12}\,b^5\,c^7\,d^6-852\,a^{12}\,b^5\,c^5\,d^8+444\,a^{12}\,b^5\,c^3\,d^{10}-54\,a^{12}\,b^5\,c\,d^{12}+84\,a^{11}\,b^6\,c^{10}\,d^3-672\,a^{11}\,b^6\,c^8\,d^5+1308\,a^{11}\,b^6\,c^6\,d^7-940\,a^{11}\,b^6\,c^4\,d^9+224\,a^{11}\,b^6\,c^2\,d^{11}-4\,a^{11}\,b^6\,d^{13}-36\,a^{10}\,b^7\,c^{11}\,d^2+576\,a^{10}\,b^7\,c^9\,d^4-1548\,a^{10}\,b^7\,c^7\,d^6+1548\,a^{10}\,b^7\,c^5\,d^8-576\,a^{10}\,b^7\,c^3\,d^{10}+36\,a^{10}\,b^7\,c\,d^{12}+9\,a^9\,b^8\,c^{12}\,d-354\,a^9\,b^8\,c^{10}\,d^3+1437\,a^9\,b^8\,c^8\,d^5-1992\,a^9\,b^8\,c^6\,d^7+1045\,a^9\,b^8\,c^4\,d^9-146\,a^9\,b^8\,c^2\,d^{11}+a^9\,b^8\,d^{13}-a^8\,b^9\,c^{13}+146\,a^8\,b^9\,c^{11}\,d^2-1045\,a^8\,b^9\,c^9\,d^4+1992\,a^8\,b^9\,c^7\,d^6-1437\,a^8\,b^9\,c^5\,d^8+354\,a^8\,b^9\,c^3\,d^{10}-9\,a^8\,b^9\,c\,d^{12}-36\,a^7\,b^{10}\,c^{12}\,d+576\,a^7\,b^{10}\,c^{10}\,d^3-1548\,a^7\,b^{10}\,c^8\,d^5+1548\,a^7\,b^{10}\,c^6\,d^7-576\,a^7\,b^{10}\,c^4\,d^9+36\,a^7\,b^{10}\,c^2\,d^{11}+4\,a^6\,b^{11}\,c^{13}-224\,a^6\,b^{11}\,c^{11}\,d^2+940\,a^6\,b^{11}\,c^9\,d^4-1308\,a^6\,b^{11}\,c^7\,d^6+672\,a^6\,b^{11}\,c^5\,d^8-84\,a^6\,b^{11}\,c^3\,d^{10}+54\,a^5\,b^{12}\,c^{12}\,d-444\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(-4\,a^{19}\,c^5\,d^{11}+4\,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\,a^7\,b^{15}\,c^{10}\,d^8+45408\,a^7\,b^{15}\,c^8\,d^{10}-7392\,a^7\,b^{15}\,c^6\,d^{12}-1144\,a^6\,b^{16}\,c^{17}\,d+13112\,a^6\,b^{16}\,c^{15}\,d^3-40876\,a^6\,b^{16}\,c^{13}\,d^5+54384\,a^6\,b^{16}\,c^{11}\,d^7-32868\,a^6\,b^{16}\,c^9\,d^9+7392\,a^6\,b^{16}\,c^7\,d^{11}+104\,a^5\,b^{17}\,c^{18}-3432\,a^5\,b^{17}\,c^{16}\,d^2+14692\,a^5\,b^{17}\,c^{14}\,d^4-24784\,a^5\,b^{17}\,c^{12}\,d^6+18700\,a^5\,b^{17}\,c^{10}\,d^8-5280\,a^5\,b^{17}\,c^8\,d^{10}+616\,a^4\,b^{18}\,c^{17}\,d-4048\,a^4\,b^{18}\,c^{15}\,d^3+8888\,a^4\,b^{18}\,c^{13}\,d^5-8096\,a^4\,b^{18}\,c^{11}\,d^7+2640\,a^4\,b^{18}\,c^9\,d^9-56\,a^3\,b^{19}\,c^{18}+848\,a^3\,b^{19}\,c^{16}\,d^2-2408\,a^3\,b^{19}\,c^{14}\,d^4+2496\,a^3\,b^{19}\,c^{12}\,d^6-880\,a^3\,b^{19}\,c^{10}\,d^8-132\,a^2\,b^{20}\,c^{17}\,d+440\,a^2\,b^{20}\,c^{15}\,d^3-484\,a^2\,b^{20}\,c^{13}\,d^5+176\,a^2\,b^{20}\,c^{11}\,d^7+12\,a\,b^{21}\,c^{18}-40\,a\,b^{21}\,c^{16}\,d^2+44\,a\,b^{21}\,c^{14}\,d^4-16\,a\,b^{21}\,c^{12}\,d^6\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}\,d^{13}-9\,a^{16}\,b\,c^5\,d^8+18\,a^{16}\,b\,c^3\,d^{10}-9\,a^{16}\,b\,c\,d^{12}+36\,a^{15}\,b^2\,c^6\,d^7-76\,a^{15}\,b^2\,c^4\,d^9+44\,a^{15}\,b^2\,c^2\,d^{11}-4\,a^{15}\,b^2\,d^{13}-84\,a^{14}\,b^3\,c^7\,d^6+204\,a^{14}\,b^3\,c^5\,d^8-156\,a^{14}\,b^3\,c^3\,d^{10}+36\,a^{14}\,b^3\,c\,d^{12}+126\,a^{13}\,b^4\,c^8\,d^5-396\,a^{13}\,b^4\,c^6\,d^7+420\,a^{13}\,b^4\,c^4\,d^9-156\,a^{13}\,b^4\,c^2\,d^{11}+6\,a^{13}\,b^4\,d^{13}-126\,a^{12}\,b^5\,c^9\,d^4+588\,a^{12}\,b^5\,c^7\,d^6-852\,a^{12}\,b^5\,c^5\,d^8+444\,a^{12}\,b^5\,c^3\,d^{10}-54\,a^{12}\,b^5\,c\,d^{12}+84\,a^{11}\,b^6\,c^{10}\,d^3-672\,a^{11}\,b^6\,c^8\,d^5+1308\,a^{11}\,b^6\,c^6\,d^7-940\,a^{11}\,b^6\,c^4\,d^9+224\,a^{11}\,b^6\,c^2\,d^{11}-4\,a^{11}\,b^6\,d^{13}-36\,a^{10}\,b^7\,c^{11}\,d^2+576\,a^{10}\,b^7\,c^9\,d^4-1548\,a^{10}\,b^7\,c^7\,d^6+1548\,a^{10}\,b^7\,c^5\,d^8-576\,a^{10}\,b^7\,c^3\,d^{10}+36\,a^{10}\,b^7\,c\,d^{12}+9\,a^9\,b^8\,c^{12}\,d-354\,a^9\,b^8\,c^{10}\,d^3+1437\,a^9\,b^8\,c^8\,d^5-1992\,a^9\,b^8\,c^6\,d^7+1045\,a^9\,b^8\,c^4\,d^9-146\,a^9\,b^8\,c^2\,d^{11}+a^9\,b^8\,d^{13}-a^8\,b^9\,c^{13}+146\,a^8\,b^9\,c^{11}\,d^2-1045\,a^8\,b^9\,c^9\,d^4+1992\,a^8\,b^9\,c^7\,d^6-1437\,a^8\,b^9\,c^5\,d^8+354\,a^8\,b^9\,c^3\,d^{10}-9\,a^8\,b^9\,c\,d^{12}-36\,a^7\,b^{10}\,c^{12}\,d+576\,a^7\,b^{10}\,c^{10}\,d^3-1548\,a^7\,b^{10}\,c^8\,d^5+1548\,a^7\,b^{10}\,c^6\,d^7-576\,a^7\,b^{10}\,c^4\,d^9+36\,a^7\,b^{10}\,c^2\,d^{11}+4\,a^6\,b^{11}\,c^{13}-224\,a^6\,b^{11}\,c^{11}\,d^2+940\,a^6\,b^{11}\,c^9\,d^4-1308\,a^6\,b^{11}\,c^7\,d^6+672\,a^6\,b^{11}\,c^5\,d^8-84\,a^6\,b^{11}\,c^3\,d^{10}+54\,a^5\,b^{12}\,c^{12}\,d-444\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}\right)\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}\right)\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}-\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,a^{15}\,b\,c^3\,d^{11}-44\,a^{14}\,b^2\,c^4\,d^{10}+24\,a^{14}\,b^2\,c^2\,d^{12}+172\,a^{13}\,b^3\,c^5\,d^9-184\,a^{13}\,b^3\,c^3\,d^{11}+36\,a^{13}\,b^3\,c\,d^{13}-148\,a^{12}\,b^4\,c^6\,d^8+248\,a^{12}\,b^4\,c^4\,d^{10}-60\,a^{12}\,b^4\,c^2\,d^{12}-400\,a^{11}\,b^5\,c^7\,d^7+248\,a^{11}\,b^5\,c^5\,d^9+180\,a^{11}\,b^5\,c^3\,d^{11}-144\,a^{11}\,b^5\,c\,d^{13}+1056\,a^{10}\,b^6\,c^8\,d^6-1336\,a^{10}\,b^6\,c^6\,d^8+100\,a^{10}\,b^6\,c^4\,d^{10}+216\,a^{10}\,b^6\,c^2\,d^{12}-1088\,a^9\,b^7\,c^9\,d^5+2648\,a^9\,b^7\,c^7\,d^7-1544\,a^9\,b^7\,c^5\,d^9-88\,a^9\,b^7\,c^3\,d^{11}+216\,a^9\,b^7\,c\,d^{13}+628\,a^8\,b^8\,c^{10}\,d^4-3012\,a^8\,b^8\,c^8\,d^6+2885\,a^8\,b^8\,c^6\,d^8-270\,a^8\,b^8\,c^4\,d^{10}-375\,a^8\,b^8\,c^2\,d^{12}-220\,a^7\,b^9\,c^{11}\,d^3+1860\,a^7\,b^9\,c^9\,d^5-2979\,a^7\,b^9\,c^7\,d^7+1386\,a^7\,b^9\,c^5\,d^9+61\,a^7\,b^9\,c^3\,d^{11}-144\,a^7\,b^9\,c\,d^{13}+44\,a^6\,b^{10}\,c^{12}\,d^2-552\,a^6\,b^{10}\,c^{10}\,d^4+2161\,a^6\,b^{10}\,c^8\,d^6-2046\,a^6\,b^{10}\,c^6\,d^8+233\,a^6\,b^{10}\,c^4\,d^{10}+276\,a^6\,b^{10}\,c^2\,d^{12}-4\,a^5\,b^{11}\,c^{13}\,d+40\,a^5\,b^{11}\,c^{11}\,d^3-895\,a^5\,b^{11}\,c^9\,d^5+1354\,a^5\,b^{11}\,c^7\,d^7-535\,a^5\,b^{11}\,c^5\,d^9-36\,a^5\,b^{11}\,c^3\,d^{11}+36\,a^5\,b^{11}\,c\,d^{13}+20\,a^4\,b^{12}\,c^{12}\,d^2+99\,a^4\,b^{12}\,c^{10}\,d^4-602\,a^4\,b^{12}\,c^8\,d^6+699\,a^4\,b^{12}\,c^6\,d^8-168\,a^4\,b^{12}\,c^4\,d^{10}-72\,a^4\,b^{12}\,c^2\,d^{12}-4\,a^3\,b^{13}\,c^{13}\,d+19\,a^3\,b^{13}\,c^{11}\,d^3+190\,a^3\,b^{13}\,c^9\,d^5-305\,a^3\,b^{13}\,c^7\,d^7+120\,a^3\,b^{13}\,c^5\,d^9-a^2\,b^{14}\,c^{12}\,d^2+14\,a^2\,b^{14}\,c^{10}\,d^4+19\,a^2\,b^{14}\,c^8\,d^6-108\,a^2\,b^{14}\,c^6\,d^8+72\,a^2\,b^{14}\,c^4\,d^{10}-a\,b^{15}\,c^{13}\,d-10\,a\,b^{15}\,c^{11}\,d^3-13\,a\,b^{15}\,c^9\,d^5+60\,a\,b^{15}\,c^7\,d^7-36\,a\,b^{15}\,c^5\,d^9\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}\,d^{13}-9\,a^{16}\,b\,c^5\,d^8+18\,a^{16}\,b\,c^3\,d^{10}-9\,a^{16}\,b\,c\,d^{12}+36\,a^{15}\,b^2\,c^6\,d^7-76\,a^{15}\,b^2\,c^4\,d^9+44\,a^{15}\,b^2\,c^2\,d^{11}-4\,a^{15}\,b^2\,d^{13}-84\,a^{14}\,b^3\,c^7\,d^6+204\,a^{14}\,b^3\,c^5\,d^8-156\,a^{14}\,b^3\,c^3\,d^{10}+36\,a^{14}\,b^3\,c\,d^{12}+126\,a^{13}\,b^4\,c^8\,d^5-396\,a^{13}\,b^4\,c^6\,d^7+420\,a^{13}\,b^4\,c^4\,d^9-156\,a^{13}\,b^4\,c^2\,d^{11}+6\,a^{13}\,b^4\,d^{13}-126\,a^{12}\,b^5\,c^9\,d^4+588\,a^{12}\,b^5\,c^7\,d^6-852\,a^{12}\,b^5\,c^5\,d^8+444\,a^{12}\,b^5\,c^3\,d^{10}-54\,a^{12}\,b^5\,c\,d^{12}+84\,a^{11}\,b^6\,c^{10}\,d^3-672\,a^{11}\,b^6\,c^8\,d^5+1308\,a^{11}\,b^6\,c^6\,d^7-940\,a^{11}\,b^6\,c^4\,d^9+224\,a^{11}\,b^6\,c^2\,d^{11}-4\,a^{11}\,b^6\,d^{13}-36\,a^{10}\,b^7\,c^{11}\,d^2+576\,a^{10}\,b^7\,c^9\,d^4-1548\,a^{10}\,b^7\,c^7\,d^6+1548\,a^{10}\,b^7\,c^5\,d^8-576\,a^{10}\,b^7\,c^3\,d^{10}+36\,a^{10}\,b^7\,c\,d^{12}+9\,a^9\,b^8\,c^{12}\,d-354\,a^9\,b^8\,c^{10}\,d^3+1437\,a^9\,b^8\,c^8\,d^5-1992\,a^9\,b^8\,c^6\,d^7+1045\,a^9\,b^8\,c^4\,d^9-146\,a^9\,b^8\,c^2\,d^{11}+a^9\,b^8\,d^{13}-a^8\,b^9\,c^{13}+146\,a^8\,b^9\,c^{11}\,d^2-1045\,a^8\,b^9\,c^9\,d^4+1992\,a^8\,b^9\,c^7\,d^6-1437\,a^8\,b^9\,c^5\,d^8+354\,a^8\,b^9\,c^3\,d^{10}-9\,a^8\,b^9\,c\,d^{12}-36\,a^7\,b^{10}\,c^{12}\,d+576\,a^7\,b^{10}\,c^{10}\,d^3-1548\,a^7\,b^{10}\,c^8\,d^5+1548\,a^7\,b^{10}\,c^6\,d^7-576\,a^7\,b^{10}\,c^4\,d^9+36\,a^7\,b^{10}\,c^2\,d^{11}+4\,a^6\,b^{11}\,c^{13}-224\,a^6\,b^{11}\,c^{11}\,d^2+940\,a^6\,b^{11}\,c^9\,d^4-1308\,a^6\,b^{11}\,c^7\,d^6+672\,a^6\,b^{11}\,c^5\,d^8-84\,a^6\,b^{11}\,c^3\,d^{10}+54\,a^5\,b^{12}\,c^{12}\,d-444\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^{16}\,c^3\,d^{11}-44\,a^{15}\,b\,c^4\,d^{10}+24\,a^{15}\,b\,c^2\,d^{12}+172\,a^{14}\,b^2\,c^5\,d^9-192\,a^{14}\,b^2\,c^3\,d^{11}+36\,a^{14}\,b^2\,c\,d^{13}-292\,a^{13}\,b^3\,c^6\,d^8+624\,a^{13}\,b^3\,c^4\,d^{10}-252\,a^{13}\,b^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44\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{22}\,c^7\,d^{11}-28\,a^{22}\,c^5\,d^{13}+32\,a^{22}\,c^3\,d^{15}-12\,a^{22}\,c\,d^{17}-88\,a^{21}\,b\,c^8\,d^{10}+308\,a^{21}\,b\,c^6\,d^{12}-352\,a^{21}\,b\,c^4\,d^{14}+132\,a^{21}\,b\,c^2\,d^{16}+440\,a^{20}\,b^2\,c^9\,d^9-1584\,a^{20}\,b^2\,c^7\,d^{11}+1912\,a^{20}\,b^2\,c^5\,d^{13}-832\,a^{20}\,b^2\,c^3\,d^{15}+64\,a^{20}\,b^2\,c\,d^{17}-1320\,a^{19}\,b^3\,c^{10}\,d^8+5104\,a^{19}\,b^3\,c^8\,d^{10}-6952\,a^{19}\,b^3\,c^6\,d^{12}+3872\,a^{19}\,b^3\,c^4\,d^{14}-704\,a^{19}\,b^3\,c^2\,d^{16}+2640\,a^{18}\,b^4\,c^{11}\,d^7-11660\,a^{18}\,b^4\,c^9\,d^9+19016\,a^{18}\,b^4\,c^7\,d^{11}-13748\,a^{18}\,b^4\,c^5\,d^{13}+3888\,a^{18}\,b^4\,c^3\,d^{15}-136\,a^{18}\,b^4\,c\,d^{17}-3696\,a^{17}\,b^5\,c^{12}\,d^6+20196\,a^{17}\,b^5\,c^{10}\,d^8-40920\,a^{17}\,b^5\,c^8\,d^{10}+37532\,a^{17}\,b^5\,c^6\,d^{12}-14608\,a^{17}\,b^5\,c^4\,d^{14}+1496\,a^{17}\,b^5\,c^2\,d^{16}+3696\,a^{16}\,b^6\,c^{13}\,d^5-27456\,a^{16}\,b^6\,c^{11}\,d^7+70224\,a^{16}\,b^6\,c^9\,d^9-80448\,a^{16}\,b^6\,c^7\,d^{11}+41712\,a^{16}\,b^6\,c^5\,d^{13}-7872\,a^{16}\,b^6\,c^3\,d^{15}+144\,a^{16}\,b^6\,c\,d^{17}-2640\,a^{15}\,b^7\,c^{14}\,d^4+29568\,a^{15}\,b^7\,c^{12}\,d^6-96624\,a^{15}\,b^7\,c^{10}\,d^8+138688\,a^{15}\,b^7\,c^8\,d^{10}-94160\,a^{15}\,b^7\,c^6\,d^{12}+26752\,a^{15}\,b^7\,c^4\,d^{14}-1584\,a^{15}\,b^7\,c^2\,d^{16}+1320\,a^{14}\,b^8\,c^{15}\,d^3-24948\,a^{14}\,b^8\,c^{13}\,d^5+107184\,a^{14}\,b^8\,c^{11}\,d^7-195404\,a^{14}\,b^8\,c^9\,d^9+170424\,a^{14}\,b^8\,c^7\,d^{11}-66628\,a^{14}\,b^8\,c^5\,d^{13}+8128\,a^{14}\,b^8\,c^3\,d^{15}-76\,a^{14}\,b^8\,c\,d^{17}-440\,a^{13}\,b^9\,c^{16}\,d^2+16060\,a^{13}\,b^9\,c^{14}\,d^4-96272\,a^{13}\,b^9\,c^{12}\,d^6+226116\,a^{13}\,b^9\,c^{10}\,d^8-249832\,a^{13}\,b^9\,c^8\,d^{10}+129580\,a^{13}\,b^9\,c^6\,d^{12}-26048\,a^{13}\,b^9\,c^4\,d^{14}+836\,a^{13}\,b^9\,c^2\,d^{16}+88\,a^{12}\,b^{10}\,c^{17}\,d-7568\,a^{12}\,b^{10}\,c^{15}\,d^3+69784\,a^{12}\,b^{10}\,c^{13}\,d^5-214368\,a^{12}\,b^{10}\,c^{11}\,d^7+299816\,a^{12}\,b^{10}\,c^9\,d^9-202544\,a^{12}\,b^{10}\,c^7\,d^{11}+59000\,a^{12}\,b^{10}\,c^5\,d^{13}-4224\,a^{12}\,b^{10}\,c^3\,d^{15}+16\,a^{12}\,b^{10}\,c\,d^{17}-8\,a^{11}\,b^{11}\,c^{18}+2448\,a^{11}\,b^{11}\,c^{16}\,d^2-40072\,a^{11}\,b^{11}\,c^{14}\,d^4+165760\,a^{11}\,b^{11}\,c^{12}\,d^6-296824\,a^{11}\,b^{11}\,c^{10}\,d^8+257136\,a^{11}\,b^{11}\,c^8\,d^{10}-101288\,a^{11}\,b^{11}\,c^6\,d^{12}+13024\,a^{11}\,b^{11}\,c^4\,d^{14}-176\,a^{11}\,b^{11}\,c^2\,d^{16}-484\,a^{10}\,b^{12}\,c^{17}\,d+17512\,a^{10}\,b^{12}\,c^{15}\,d^3-104060\,a^{10}\,b^{12}\,c^{13}\,d^5+242528\,a^{10}\,b^{12}\,c^{11}\,d^7-266244\,a^{10}\,b^{12}\,c^9\,d^9+137368\,a^{10}\,b^{12}\,c^7\,d^{11}-27500\,a^{10}\,b^{12}\,c^5\,d^{13}+880\,a^{10}\,b^{12}\,c^3\,d^{15}+44\,a^9\,b^{13}\,c^{18}-5432\,a^9\,b^{13}\,c^{16}\,d^2+52532\,a^9\,b^{13}\,c^{14}\,d^4-162336\,a^9\,b^{13}\,c^{12}\,d^6+225676\,a^9\,b^{13}\,c^{10}\,d^8-150216\,a^9\,b^{13}\,c^8\,d^{10}+42372\,a^9\,b^{13}\,c^6\,d^{12}-2640\,a^9\,b^{13}\,c^4\,d^{14}+1056\,a^8\,b^{14}\,c^{17}\,d-20768\,a^8\,b^{14}\,c^{15}\,d^3+88000\,a^8\,b^{14}\,c^{13}\,d^5-156992\,a^8\,b^{14}\,c^{11}\,d^7+133056\,a^8\,b^{14}\,c^9\,d^9-49632\,a^8\,b^{14}\,c^7\,d^{11}+5280\,a^8\,b^{14}\,c^5\,d^{13}-96\,a^7\,b^{15}\,c^{18}+6048\,a^7\,b^{15}\,c^{16}\,d^2-38208\,a^7\,b^{15}\,c^{14}\,d^4+89280\,a^7\,b^{15}\,c^{12}\,d^6-95040\,a^7\,b^{15}\,c^{10}\,d^8+45408\,a^7\,b^{15}\,c^8\,d^{10}-7392\,a^7\,b^{15}\,c^6\,d^{12}-1144\,a^6\,b^{16}\,c^{17}\,d+13112\,a^6\,b^{16}\,c^{15}\,d^3-40876\,a^6\,b^{16}\,c^{13}\,d^5+54384\,a^6\,b^{16}\,c^{11}\,d^7-32868\,a^6\,b^{16}\,c^9\,d^9+7392\,a^6\,b^{16}\,c^7\,d^{11}+104\,a^5\,b^{17}\,c^{18}-3432\,a^5\,b^{17}\,c^{16}\,d^2+14692\,a^5\,b^{17}\,c^{14}\,d^4-24784\,a^5\,b^{17}\,c^{12}\,d^6+18700\,a^5\,b^{17}\,c^{10}\,d^8-5280\,a^5\,b^{17}\,c^8\,d^{10}+616\,a^4\,b^{18}\,c^{17}\,d-4048\,a^4\,b^{18}\,c^{15}\,d^3+8888\,a^4\,b^{18}\,c^{13}\,d^5-8096\,a^4\,b^{18}\,c^{11}\,d^7+2640\,a^4\,b^{18}\,c^9\,d^9-56\,a^3\,b^{19}\,c^{18}+848\,a^3\,b^{19}\,c^{16}\,d^2-2408\,a^3\,b^{19}\,c^{14}\,d^4+2496\,a^3\,b^{19}\,c^{12}\,d^6-880\,a^3\,b^{19}\,c^{10}\,d^8-132\,a^2\,b^{20}\,c^{17}\,d+440\,a^2\,b^{20}\,c^{15}\,d^3-484\,a^2\,b^{20}\,c^{13}\,d^5+176\,a^2\,b^{20}\,c^{11}\,d^7+12\,a\,b^{21}\,c^{18}-40\,a\,b^{21}\,c^{16}\,d^2+44\,a\,b^{21}\,c^{14}\,d^4-16\,a\,b^{21}\,c^{12}\,d^6\right)}{a^{17}\,c^4\,d^9-2\,a^{17}\,c^2\,d^{11}+a^{17}\,d^{13}-9\,a^{16}\,b\,c^5\,d^8+18\,a^{16}\,b\,c^3\,d^{10}-9\,a^{16}\,b\,c\,d^{12}+36\,a^{15}\,b^2\,c^6\,d^7-76\,a^{15}\,b^2\,c^4\,d^9+44\,a^{15}\,b^2\,c^2\,d^{11}-4\,a^{15}\,b^2\,d^{13}-84\,a^{14}\,b^3\,c^7\,d^6+204\,a^{14}\,b^3\,c^5\,d^8-156\,a^{14}\,b^3\,c^3\,d^{10}+36\,a^{14}\,b^3\,c\,d^{12}+126\,a^{13}\,b^4\,c^8\,d^5-396\,a^{13}\,b^4\,c^6\,d^7+420\,a^{13}\,b^4\,c^4\,d^9-156\,a^{13}\,b^4\,c^2\,d^{11}+6\,a^{13}\,b^4\,d^{13}-126\,a^{12}\,b^5\,c^9\,d^4+588\,a^{12}\,b^5\,c^7\,d^6-852\,a^{12}\,b^5\,c^5\,d^8+444\,a^{12}\,b^5\,c^3\,d^{10}-54\,a^{12}\,b^5\,c\,d^{12}+84\,a^{11}\,b^6\,c^{10}\,d^3-672\,a^{11}\,b^6\,c^8\,d^5+1308\,a^{11}\,b^6\,c^6\,d^7-940\,a^{11}\,b^6\,c^4\,d^9+224\,a^{11}\,b^6\,c^2\,d^{11}-4\,a^{11}\,b^6\,d^{13}-36\,a^{10}\,b^7\,c^{11}\,d^2+576\,a^{10}\,b^7\,c^9\,d^4-1548\,a^{10}\,b^7\,c^7\,d^6+1548\,a^{10}\,b^7\,c^5\,d^8-576\,a^{10}\,b^7\,c^3\,d^{10}+36\,a^{10}\,b^7\,c\,d^{12}+9\,a^9\,b^8\,c^{12}\,d-354\,a^9\,b^8\,c^{10}\,d^3+1437\,a^9\,b^8\,c^8\,d^5-1992\,a^9\,b^8\,c^6\,d^7+1045\,a^9\,b^8\,c^4\,d^9-146\,a^9\,b^8\,c^2\,d^{11}+a^9\,b^8\,d^{13}-a^8\,b^9\,c^{13}+146\,a^8\,b^9\,c^{11}\,d^2-1045\,a^8\,b^9\,c^9\,d^4+1992\,a^8\,b^9\,c^7\,d^6-1437\,a^8\,b^9\,c^5\,d^8+354\,a^8\,b^9\,c^3\,d^{10}-9\,a^8\,b^9\,c\,d^{12}-36\,a^7\,b^{10}\,c^{12}\,d+576\,a^7\,b^{10}\,c^{10}\,d^3-1548\,a^7\,b^{10}\,c^8\,d^5+1548\,a^7\,b^{10}\,c^6\,d^7-576\,a^7\,b^{10}\,c^4\,d^9+36\,a^7\,b^{10}\,c^2\,d^{11}+4\,a^6\,b^{11}\,c^{13}-224\,a^6\,b^{11}\,c^{11}\,d^2+940\,a^6\,b^{11}\,c^9\,d^4-1308\,a^6\,b^{11}\,c^7\,d^6+672\,a^6\,b^{11}\,c^5\,d^8-84\,a^6\,b^{11}\,c^3\,d^{10}+54\,a^5\,b^{12}\,c^{12}\,d-444\,a^5\,b^{12}\,c^{10}\,d^3+852\,a^5\,b^{12}\,c^8\,d^5-588\,a^5\,b^{12}\,c^6\,d^7+126\,a^5\,b^{12}\,c^4\,d^9-6\,a^4\,b^{13}\,c^{13}+156\,a^4\,b^{13}\,c^{11}\,d^2-420\,a^4\,b^{13}\,c^9\,d^4+396\,a^4\,b^{13}\,c^7\,d^6-126\,a^4\,b^{13}\,c^5\,d^8-36\,a^3\,b^{14}\,c^{12}\,d+156\,a^3\,b^{14}\,c^{10}\,d^3-204\,a^3\,b^{14}\,c^8\,d^5+84\,a^3\,b^{14}\,c^6\,d^7+4\,a^2\,b^{15}\,c^{13}-44\,a^2\,b^{15}\,c^{11}\,d^2+76\,a^2\,b^{15}\,c^9\,d^4-36\,a^2\,b^{15}\,c^7\,d^6+9\,a\,b^{16}\,c^{12}\,d-18\,a\,b^{16}\,c^{10}\,d^3+9\,a\,b^{16}\,c^8\,d^5-b^{17}\,c^{13}+2\,b^{17}\,c^{11}\,d^2-b^{17}\,c^9\,d^4}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}\right)\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}\right)\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)}{2\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4\,d^2-8\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2-15\,a^2\,b^2\,d^2+2\,a\,b^3\,c\,d+b^4\,c^2+6\,b^4\,d^2\right)\,1{}\mathrm{i}}{f\,\left(a^{14}\,d^4-4\,a^{13}\,b\,c\,d^3+6\,a^{12}\,b^2\,c^2\,d^2-5\,a^{12}\,b^2\,d^4-4\,a^{11}\,b^3\,c^3\,d+20\,a^{11}\,b^3\,c\,d^3+a^{10}\,b^4\,c^4-30\,a^{10}\,b^4\,c^2\,d^2+10\,a^{10}\,b^4\,d^4+20\,a^9\,b^5\,c^3\,d-40\,a^9\,b^5\,c\,d^3-5\,a^8\,b^6\,c^4+60\,a^8\,b^6\,c^2\,d^2-10\,a^8\,b^6\,d^4-40\,a^7\,b^7\,c^3\,d+40\,a^7\,b^7\,c\,d^3+10\,a^6\,b^8\,c^4-60\,a^6\,b^8\,c^2\,d^2+5\,a^6\,b^8\,d^4+40\,a^5\,b^9\,c^3\,d-20\,a^5\,b^9\,c\,d^3-10\,a^4\,b^{10}\,c^4+30\,a^4\,b^{10}\,c^2\,d^2-a^4\,b^{10}\,d^4-20\,a^3\,b^{11}\,c^3\,d+4\,a^3\,b^{11}\,c\,d^3+5\,a^2\,b^{12}\,c^4-6\,a^2\,b^{12}\,c^2\,d^2+4\,a\,b^{13}\,c^3\,d-b^{14}\,c^4\right)}","Not used",1,"((2*a^6*d^4 + b^6*c^4 - 4*a^2*b^4*c^4 + 2*a^2*b^4*d^4 - 4*a^4*b^2*d^4 - b^6*c^2*d^2 - 8*a^3*b^3*c*d^3 + 8*a^3*b^3*c^3*d + 4*a^2*b^4*c^2*d^2 + 5*a*b^5*c*d^3 - 5*a*b^5*c^3*d)/((a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*c^2 - a^4*d^2 + b^4*c^2 - b^4*d^2 - 2*a^2*b^2*c^2 + 2*a^2*b^2*d^2)) + (tan(e/2 + (f*x)/2)*(2*a^7*d^5 + 2*b^7*c^5 - 11*a^2*b^5*c^5 + 2*a^3*b^4*d^5 - 4*a^5*b^2*d^5 - 2*b^7*c^3*d^2 + 12*a*b^6*c^2*d^3 + 18*a^2*b^5*c*d^4 + 15*a^3*b^4*c^4*d - 32*a^4*b^3*c*d^4 + a^2*b^5*c^3*d^2 - 15*a^3*b^4*c^2*d^3 + 16*a^4*b^3*c^3*d^2 - 12*a*b^6*c^4*d + 8*a^6*b*c*d^4))/(a*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*c^2 - a^4*d^2 + b^4*c^2 - b^4*d^2 - 2*a^2*b^2*c^2 + 2*a^2*b^2*d^2)) + (tan(e/2 + (f*x)/2)^5*(2*a^7*d^5 + 2*b^7*c^5 - 5*a^2*b^5*c^5 + 2*a^3*b^4*d^5 - 4*a^5*b^2*d^5 - 2*b^7*c^3*d^2 + 6*a*b^6*c^2*d^3 + 9*a^3*b^4*c^4*d + 5*a^2*b^5*c^3*d^2 - 9*a^3*b^4*c^2*d^3 - 6*a*b^6*c^4*d))/(a*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*c^2 - a^4*d^2 + b^4*c^2 - b^4*d^2 - 2*a^2*b^2*c^2 + 2*a^2*b^2*d^2)) + (2*tan(e/2 + (f*x)/2)^2*(b^8*c^5 + 4*a^7*b*d^5 + 2*a^8*c*d^4 - 3*a^2*b^6*c^5 - 4*a^4*b^4*c^5 + 4*a^3*b^5*d^5 - 8*a^5*b^3*d^5 - b^8*c^3*d^2 + 3*a*b^7*c^2*d^3 + 18*a^2*b^6*c*d^4 - 8*a^3*b^5*c^4*d - 29*a^4*b^4*c*d^4 + 8*a^5*b^3*c^4*d - 11*a^2*b^6*c^3*d^2 + 8*a^3*b^5*c^2*d^3 + 27*a^4*b^4*c^3*d^2 - 8*a^5*b^3*c^2*d^3 - 3*a*b^7*c^4*d))/(a^2*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*c^2 - a^4*d^2 + b^4*c^2 - b^4*d^2 - 2*a^2*b^2*c^2 + 2*a^2*b^2*d^2)) - (tan(e/2 + (f*x)/2)^4*(7*a^2*b^6*c^5 - 8*a^7*b*d^5 - 2*a^8*c*d^4 - 2*b^8*c^5 + 4*a^4*b^4*c^5 - 8*a^3*b^5*d^5 + 16*a^5*b^3*d^5 + 2*b^8*c^3*d^2 - 6*a*b^7*c^2*d^3 - 12*a^2*b^6*c*d^4 - a^3*b^5*c^4*d + 16*a^4*b^4*c*d^4 - 8*a^5*b^3*c^4*d + 4*a^6*b^2*c*d^4 + 5*a^2*b^6*c^3*d^2 + a^3*b^5*c^2*d^3 - 22*a^4*b^4*c^3*d^2 + 8*a^5*b^3*c^2*d^3 + 6*a*b^7*c^4*d))/(a^2*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*c^2 - a^4*d^2 + b^4*c^2 - b^4*d^2 - 2*a^2*b^2*c^2 + 2*a^2*b^2*d^2)) + (2*tan(e/2 + (f*x)/2)^3*(a^2*d + 2*b^2*d + 2*a*b*c)*(2*a^6*d^4 + b^6*c^4 - 4*a^2*b^4*c^4 + 2*a^2*b^4*d^4 - 4*a^4*b^2*d^4 - b^6*c^2*d^2 - 8*a^3*b^3*c*d^3 + 8*a^3*b^3*c^3*d + 4*a^2*b^4*c^2*d^2 + 5*a*b^5*c*d^3 - 5*a*b^5*c^3*d))/(a^2*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*c^2 - a^4*d^2 + b^4*c^2 - b^4*d^2 - 2*a^2*b^2*c^2 + 2*a^2*b^2*d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(3*a^2*c + 4*b^2*c + 8*a*b*d) + tan(e/2 + (f*x)/2)^4*(3*a^2*c + 4*b^2*c + 8*a*b*d) + tan(e/2 + (f*x)/2)^3*(4*a^2*d + 8*b^2*d + 8*a*b*c) + a^2*c + tan(e/2 + (f*x)/2)*(2*a^2*d + 4*a*b*c) + tan(e/2 + (f*x)/2)^5*(2*a^2*d + 4*a*b*c) + a^2*c*tan(e/2 + (f*x)/2)^6)) - (d^3*atan(((d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 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126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 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9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (d^3*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 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257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d)*1i)/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9) - (d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 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444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^16 - 12*a^5*b^14*c^16 + 8*a^7*b^12*c^16 + 8*a^19*c^2*d^14 - 8*a^19*c^4*d^12 + 12*a*b^18*c^10*d^6 - 28*a*b^18*c^12*d^4 + 12*a*b^18*c^14*d^2 - 20*a^2*b^17*c^15*d - 48*a^4*b^15*c^15*d + 156*a^6*b^13*c^15*d - 88*a^8*b^11*c^15*d + 12*a^10*b^9*c*d^15 - 48*a^12*b^7*c*d^15 + 84*a^14*b^5*c*d^15 - 72*a^16*b^3*c*d^15 - 112*a^18*b*c^3*d^13 + 88*a^18*b*c^5*d^11 - 84*a^2*b^17*c^9*d^7 + 212*a^2*b^17*c^11*d^5 - 108*a^2*b^17*c^13*d^3 + 240*a^3*b^16*c^8*d^8 - 744*a^3*b^16*c^10*d^6 + 584*a^3*b^16*c^12*d^4 - 80*a^3*b^16*c^14*d^2 - 336*a^4*b^15*c^7*d^9 + 1632*a^4*b^15*c^9*d^7 - 2176*a^4*b^15*c^11*d^5 + 928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (d^3*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 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24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 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3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d)*1i)/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))/((16*(63*a*b^12*c^5*d^7 - 216*a*b^12*c^3*d^9 + 41*a*b^12*c^7*d^5 + 4*a*b^12*c^9*d^3 - 486*a^3*b^10*c*d^11 + 864*a^5*b^8*c*d^11 - 702*a^7*b^6*c*d^11 + 216*a^9*b^4*c*d^11 + 162*a^2*b^11*c^2*d^10 - 261*a^2*b^11*c^4*d^8 + 66*a^2*b^11*c^6*d^6 + 19*a^2*b^11*c^8*d^4 + 1197*a^3*b^10*c^3*d^9 - 696*a^3*b^10*c^5*d^7 - 21*a^3*b^10*c^7*d^5 + 16*a^3*b^10*c^9*d^3 - 783*a^4*b^9*c^2*d^10 + 1444*a^4*b^9*c^4*d^8 - 583*a^4*b^9*c^6*d^6 - 20*a^4*b^9*c^8*d^4 - 2511*a^5*b^8*c^3*d^9 + 1913*a^5*b^8*c^5*d^7 - 312*a^5*b^8*c^7*d^5 + 16*a^5*b^8*c^9*d^3 + 1278*a^6*b^7*c^2*d^10 - 2508*a^6*b^7*c^4*d^8 + 1232*a^6*b^7*c^6*d^6 - 116*a^6*b^7*c^8*d^4 + 2328*a^7*b^6*c^3*d^9 - 1936*a^7*b^6*c^5*d^7 + 364*a^7*b^6*c^7*d^5 - 828*a^8*b^5*c^2*d^10 + 1518*a^8*b^5*c^4*d^8 - 580*a^8*b^5*c^6*d^6 - 750*a^9*b^4*c^3*d^9 + 476*a^9*b^4*c^5*d^7 + 144*a^10*b^3*c^2*d^10 - 184*a^10*b^3*c^4*d^8 + 24*a^11*b^2*c^3*d^9 + 108*a*b^12*c*d^11))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (16*tan(e/2 + (f*x)/2)*(108*a*b^12*c^2*d^10 - 162*a*b^12*c^4*d^8 + 18*a*b^12*c^6*d^6 + 8*a*b^12*c^8*d^4 + 108*a^2*b^11*c*d^11 - 486*a^4*b^9*c*d^11 + 756*a^6*b^7*c*d^11 - 432*a^8*b^5*c*d^11 - 162*a^2*b^11*c^3*d^9 + 36*a^2*b^11*c^5*d^7 + 38*a^2*b^11*c^7*d^5 - 270*a^3*b^10*c^2*d^10 + 396*a^3*b^10*c^4*d^8 - 42*a^3*b^10*c^6*d^6 + 32*a^3*b^10*c^8*d^4 + 864*a^4*b^9*c^3*d^9 - 398*a^4*b^9*c^5*d^7 - 40*a^4*b^9*c^7*d^5 + 90*a^5*b^8*c^2*d^10 + 82*a^5*b^8*c^4*d^8 - 432*a^5*b^8*c^6*d^6 + 32*a^5*b^8*c^8*d^4 - 1632*a^6*b^7*c^3*d^9 + 1216*a^6*b^7*c^5*d^7 - 232*a^6*b^7*c^7*d^5 + 216*a^7*b^6*c^2*d^10 - 596*a^7*b^6*c^4*d^8 + 600*a^7*b^6*c^6*d^6 + 900*a^8*b^5*c^3*d^9 - 584*a^8*b^5*c^5*d^7 - 80*a^9*b^4*c^4*d^8 + 48*a^10*b^3*c^3*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 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1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 + 4038*a^15*b^4*c^7*d^9 - 1320*a^15*b^4*c^9*d^7 - 244*a^16*b^3*c^2*d^14 + 1084*a^16*b^3*c^4*d^12 - 1500*a^16*b^3*c^6*d^10 + 660*a^16*b^3*c^8*d^8 - 176*a^17*b^2*c^3*d^13 + 372*a^17*b^2*c^5*d^11 - 220*a^17*b^2*c^7*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^16 - 12*a^5*b^14*c^16 + 8*a^7*b^12*c^16 + 8*a^19*c^2*d^14 - 8*a^19*c^4*d^12 + 12*a*b^18*c^10*d^6 - 28*a*b^18*c^12*d^4 + 12*a*b^18*c^14*d^2 - 20*a^2*b^17*c^15*d - 48*a^4*b^15*c^15*d + 156*a^6*b^13*c^15*d - 88*a^8*b^11*c^15*d + 12*a^10*b^9*c*d^15 - 48*a^12*b^7*c*d^15 + 84*a^14*b^5*c*d^15 - 72*a^16*b^3*c*d^15 - 112*a^18*b*c^3*d^13 + 88*a^18*b*c^5*d^11 - 84*a^2*b^17*c^9*d^7 + 212*a^2*b^17*c^11*d^5 - 108*a^2*b^17*c^13*d^3 + 240*a^3*b^16*c^8*d^8 - 744*a^3*b^16*c^10*d^6 + 584*a^3*b^16*c^12*d^4 - 80*a^3*b^16*c^14*d^2 - 336*a^4*b^15*c^7*d^9 + 1632*a^4*b^15*c^9*d^7 - 2176*a^4*b^15*c^11*d^5 + 928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (d^3*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(12*a*b^21*c^18 - 12*a^22*c*d^17 - 56*a^3*b^19*c^18 + 104*a^5*b^17*c^18 - 96*a^7*b^15*c^18 + 44*a^9*b^13*c^18 - 8*a^11*b^11*c^18 + 32*a^22*c^3*d^15 - 28*a^22*c^5*d^13 + 8*a^22*c^7*d^11 - 16*a*b^21*c^12*d^6 + 44*a*b^21*c^14*d^4 - 40*a*b^21*c^16*d^2 - 132*a^2*b^20*c^17*d + 616*a^4*b^18*c^17*d - 1144*a^6*b^16*c^17*d + 1056*a^8*b^14*c^17*d - 484*a^10*b^12*c^17*d + 16*a^12*b^10*c*d^17 + 88*a^12*b^10*c^17*d - 76*a^14*b^8*c*d^17 + 144*a^16*b^6*c*d^17 - 136*a^18*b^4*c*d^17 + 64*a^20*b^2*c*d^17 + 132*a^21*b*c^2*d^16 - 352*a^21*b*c^4*d^14 + 308*a^21*b*c^6*d^12 - 88*a^21*b*c^8*d^10 + 176*a^2*b^20*c^11*d^7 - 484*a^2*b^20*c^13*d^5 + 440*a^2*b^20*c^15*d^3 - 880*a^3*b^19*c^10*d^8 + 2496*a^3*b^19*c^12*d^6 - 2408*a^3*b^19*c^14*d^4 + 848*a^3*b^19*c^16*d^2 + 2640*a^4*b^18*c^9*d^9 - 8096*a^4*b^18*c^11*d^7 + 8888*a^4*b^18*c^13*d^5 - 4048*a^4*b^18*c^15*d^3 - 5280*a^5*b^17*c^8*d^10 + 18700*a^5*b^17*c^10*d^8 - 24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9) - (d^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (d^3*(-(c + 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282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 + 4038*a^15*b^4*c^7*d^9 - 1320*a^15*b^4*c^9*d^7 - 244*a^16*b^3*c^2*d^14 + 1084*a^16*b^3*c^4*d^12 - 1500*a^16*b^3*c^6*d^10 + 660*a^16*b^3*c^8*d^8 - 176*a^17*b^2*c^3*d^13 + 372*a^17*b^2*c^5*d^11 - 220*a^17*b^2*c^7*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 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928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 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576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (d^3*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 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512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(12*a*b^21*c^18 - 12*a^22*c*d^17 - 56*a^3*b^19*c^18 + 104*a^5*b^17*c^18 - 96*a^7*b^15*c^18 + 44*a^9*b^13*c^18 - 8*a^11*b^11*c^18 + 32*a^22*c^3*d^15 - 28*a^22*c^5*d^13 + 8*a^22*c^7*d^11 - 16*a*b^21*c^12*d^6 + 44*a*b^21*c^14*d^4 - 40*a*b^21*c^16*d^2 - 132*a^2*b^20*c^17*d + 616*a^4*b^18*c^17*d - 1144*a^6*b^16*c^17*d + 1056*a^8*b^14*c^17*d - 484*a^10*b^12*c^17*d + 16*a^12*b^10*c*d^17 + 88*a^12*b^10*c^17*d - 76*a^14*b^8*c*d^17 + 144*a^16*b^6*c*d^17 - 136*a^18*b^4*c*d^17 + 64*a^20*b^2*c*d^17 + 132*a^21*b*c^2*d^16 - 352*a^21*b*c^4*d^14 + 308*a^21*b*c^6*d^12 - 88*a^21*b*c^8*d^10 + 176*a^2*b^20*c^11*d^7 - 484*a^2*b^20*c^13*d^5 + 440*a^2*b^20*c^15*d^3 - 880*a^3*b^19*c^10*d^8 + 2496*a^3*b^19*c^12*d^6 - 2408*a^3*b^19*c^14*d^4 + 848*a^3*b^19*c^16*d^2 + 2640*a^4*b^18*c^9*d^9 - 8096*a^4*b^18*c^11*d^7 + 8888*a^4*b^18*c^13*d^5 - 4048*a^4*b^18*c^15*d^3 - 5280*a^5*b^17*c^8*d^10 + 18700*a^5*b^17*c^10*d^8 - 24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9))*(3*b*d^2 - 4*b*c^2 + a*c*d))/(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9)))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*b*d^2 - 4*b*c^2 + a*c*d)*2i)/(f*(a^4*d^10 - b^4*c^10 - 3*a^4*c^2*d^8 + 3*a^4*c^4*d^6 - a^4*c^6*d^4 + b^4*c^4*d^6 - 3*b^4*c^6*d^4 + 3*b^4*c^8*d^2 - 4*a*b^3*c^3*d^7 + 12*a*b^3*c^5*d^5 - 12*a*b^3*c^7*d^3 + 12*a^3*b*c^3*d^7 - 12*a^3*b*c^5*d^5 + 4*a^3*b*c^7*d^3 + 6*a^2*b^2*c^2*d^8 - 18*a^2*b^2*c^4*d^6 + 18*a^2*b^2*c^6*d^4 - 6*a^2*b^2*c^8*d^2 + 4*a*b^3*c^9*d - 4*a^3*b*c*d^9)) + (b^2*atan(((b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 + 4038*a^15*b^4*c^7*d^9 - 1320*a^15*b^4*c^9*d^7 - 244*a^16*b^3*c^2*d^14 + 1084*a^16*b^3*c^4*d^12 - 1500*a^16*b^3*c^6*d^10 + 660*a^16*b^3*c^8*d^8 - 176*a^17*b^2*c^3*d^13 + 372*a^17*b^2*c^5*d^11 - 220*a^17*b^2*c^7*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 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48*a^4*b^15*c^15*d + 156*a^6*b^13*c^15*d - 88*a^8*b^11*c^15*d + 12*a^10*b^9*c*d^15 - 48*a^12*b^7*c*d^15 + 84*a^14*b^5*c*d^15 - 72*a^16*b^3*c*d^15 - 112*a^18*b*c^3*d^13 + 88*a^18*b*c^5*d^11 - 84*a^2*b^17*c^9*d^7 + 212*a^2*b^17*c^11*d^5 - 108*a^2*b^17*c^13*d^3 + 240*a^3*b^16*c^8*d^8 - 744*a^3*b^16*c^10*d^6 + 584*a^3*b^16*c^12*d^4 - 80*a^3*b^16*c^14*d^2 - 336*a^4*b^15*c^7*d^9 + 1632*a^4*b^15*c^9*d^7 - 2176*a^4*b^15*c^11*d^5 + 928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 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24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(12*a*b^21*c^18 - 12*a^22*c*d^17 - 56*a^3*b^19*c^18 + 104*a^5*b^17*c^18 - 96*a^7*b^15*c^18 + 44*a^9*b^13*c^18 - 8*a^11*b^11*c^18 + 32*a^22*c^3*d^15 - 28*a^22*c^5*d^13 + 8*a^22*c^7*d^11 - 16*a*b^21*c^12*d^6 + 44*a*b^21*c^14*d^4 - 40*a*b^21*c^16*d^2 - 132*a^2*b^20*c^17*d + 616*a^4*b^18*c^17*d - 1144*a^6*b^16*c^17*d + 1056*a^8*b^14*c^17*d - 484*a^10*b^12*c^17*d + 16*a^12*b^10*c*d^17 + 88*a^12*b^10*c^17*d - 76*a^14*b^8*c*d^17 + 144*a^16*b^6*c*d^17 - 136*a^18*b^4*c*d^17 + 64*a^20*b^2*c*d^17 + 132*a^21*b*c^2*d^16 - 352*a^21*b*c^4*d^14 + 308*a^21*b*c^6*d^12 - 88*a^21*b*c^8*d^10 + 176*a^2*b^20*c^11*d^7 - 484*a^2*b^20*c^13*d^5 + 440*a^2*b^20*c^15*d^3 - 880*a^3*b^19*c^10*d^8 + 2496*a^3*b^19*c^12*d^6 - 2408*a^3*b^19*c^14*d^4 + 848*a^3*b^19*c^16*d^2 + 2640*a^4*b^18*c^9*d^9 - 8096*a^4*b^18*c^11*d^7 + 8888*a^4*b^18*c^13*d^5 - 4048*a^4*b^18*c^15*d^3 - 5280*a^5*b^17*c^8*d^10 + 18700*a^5*b^17*c^10*d^8 - 24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d)*1i)/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)) - (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 + 4038*a^15*b^4*c^7*d^9 - 1320*a^15*b^4*c^9*d^7 - 244*a^16*b^3*c^2*d^14 + 1084*a^16*b^3*c^4*d^12 - 1500*a^16*b^3*c^6*d^10 + 660*a^16*b^3*c^8*d^8 - 176*a^17*b^2*c^3*d^13 + 372*a^17*b^2*c^5*d^11 - 220*a^17*b^2*c^7*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^16 - 12*a^5*b^14*c^16 + 8*a^7*b^12*c^16 + 8*a^19*c^2*d^14 - 8*a^19*c^4*d^12 + 12*a*b^18*c^10*d^6 - 28*a*b^18*c^12*d^4 + 12*a*b^18*c^14*d^2 - 20*a^2*b^17*c^15*d - 48*a^4*b^15*c^15*d + 156*a^6*b^13*c^15*d - 88*a^8*b^11*c^15*d + 12*a^10*b^9*c*d^15 - 48*a^12*b^7*c*d^15 + 84*a^14*b^5*c*d^15 - 72*a^16*b^3*c*d^15 - 112*a^18*b*c^3*d^13 + 88*a^18*b*c^5*d^11 - 84*a^2*b^17*c^9*d^7 + 212*a^2*b^17*c^11*d^5 - 108*a^2*b^17*c^13*d^3 + 240*a^3*b^16*c^8*d^8 - 744*a^3*b^16*c^10*d^6 + 584*a^3*b^16*c^12*d^4 - 80*a^3*b^16*c^14*d^2 - 336*a^4*b^15*c^7*d^9 + 1632*a^4*b^15*c^9*d^7 - 2176*a^4*b^15*c^11*d^5 + 928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 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1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (b^2*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(12*a*b^21*c^18 - 12*a^22*c*d^17 - 56*a^3*b^19*c^18 + 104*a^5*b^17*c^18 - 96*a^7*b^15*c^18 + 44*a^9*b^13*c^18 - 8*a^11*b^11*c^18 + 32*a^22*c^3*d^15 - 28*a^22*c^5*d^13 + 8*a^22*c^7*d^11 - 16*a*b^21*c^12*d^6 + 44*a*b^21*c^14*d^4 - 40*a*b^21*c^16*d^2 - 132*a^2*b^20*c^17*d + 616*a^4*b^18*c^17*d - 1144*a^6*b^16*c^17*d + 1056*a^8*b^14*c^17*d - 484*a^10*b^12*c^17*d + 16*a^12*b^10*c*d^17 + 88*a^12*b^10*c^17*d - 76*a^14*b^8*c*d^17 + 144*a^16*b^6*c*d^17 - 136*a^18*b^4*c*d^17 + 64*a^20*b^2*c*d^17 + 132*a^21*b*c^2*d^16 - 352*a^21*b*c^4*d^14 + 308*a^21*b*c^6*d^12 - 88*a^21*b*c^8*d^10 + 176*a^2*b^20*c^11*d^7 - 484*a^2*b^20*c^13*d^5 + 440*a^2*b^20*c^15*d^3 - 880*a^3*b^19*c^10*d^8 + 2496*a^3*b^19*c^12*d^6 - 2408*a^3*b^19*c^14*d^4 + 848*a^3*b^19*c^16*d^2 + 2640*a^4*b^18*c^9*d^9 - 8096*a^4*b^18*c^11*d^7 + 8888*a^4*b^18*c^13*d^5 - 4048*a^4*b^18*c^15*d^3 - 5280*a^5*b^17*c^8*d^10 + 18700*a^5*b^17*c^10*d^8 - 24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d)*1i)/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))/((16*(63*a*b^12*c^5*d^7 - 216*a*b^12*c^3*d^9 + 41*a*b^12*c^7*d^5 + 4*a*b^12*c^9*d^3 - 486*a^3*b^10*c*d^11 + 864*a^5*b^8*c*d^11 - 702*a^7*b^6*c*d^11 + 216*a^9*b^4*c*d^11 + 162*a^2*b^11*c^2*d^10 - 261*a^2*b^11*c^4*d^8 + 66*a^2*b^11*c^6*d^6 + 19*a^2*b^11*c^8*d^4 + 1197*a^3*b^10*c^3*d^9 - 696*a^3*b^10*c^5*d^7 - 21*a^3*b^10*c^7*d^5 + 16*a^3*b^10*c^9*d^3 - 783*a^4*b^9*c^2*d^10 + 1444*a^4*b^9*c^4*d^8 - 583*a^4*b^9*c^6*d^6 - 20*a^4*b^9*c^8*d^4 - 2511*a^5*b^8*c^3*d^9 + 1913*a^5*b^8*c^5*d^7 - 312*a^5*b^8*c^7*d^5 + 16*a^5*b^8*c^9*d^3 + 1278*a^6*b^7*c^2*d^10 - 2508*a^6*b^7*c^4*d^8 + 1232*a^6*b^7*c^6*d^6 - 116*a^6*b^7*c^8*d^4 + 2328*a^7*b^6*c^3*d^9 - 1936*a^7*b^6*c^5*d^7 + 364*a^7*b^6*c^7*d^5 - 828*a^8*b^5*c^2*d^10 + 1518*a^8*b^5*c^4*d^8 - 580*a^8*b^5*c^6*d^6 - 750*a^9*b^4*c^3*d^9 + 476*a^9*b^4*c^5*d^7 + 144*a^10*b^3*c^2*d^10 - 184*a^10*b^3*c^4*d^8 + 24*a^11*b^2*c^3*d^9 + 108*a*b^12*c*d^11))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (16*tan(e/2 + (f*x)/2)*(108*a*b^12*c^2*d^10 - 162*a*b^12*c^4*d^8 + 18*a*b^12*c^6*d^6 + 8*a*b^12*c^8*d^4 + 108*a^2*b^11*c*d^11 - 486*a^4*b^9*c*d^11 + 756*a^6*b^7*c*d^11 - 432*a^8*b^5*c*d^11 - 162*a^2*b^11*c^3*d^9 + 36*a^2*b^11*c^5*d^7 + 38*a^2*b^11*c^7*d^5 - 270*a^3*b^10*c^2*d^10 + 396*a^3*b^10*c^4*d^8 - 42*a^3*b^10*c^6*d^6 + 32*a^3*b^10*c^8*d^4 + 864*a^4*b^9*c^3*d^9 - 398*a^4*b^9*c^5*d^7 - 40*a^4*b^9*c^7*d^5 + 90*a^5*b^8*c^2*d^10 + 82*a^5*b^8*c^4*d^8 - 432*a^5*b^8*c^6*d^6 + 32*a^5*b^8*c^8*d^4 - 1632*a^6*b^7*c^3*d^9 + 1216*a^6*b^7*c^5*d^7 - 232*a^6*b^7*c^7*d^5 + 216*a^7*b^6*c^2*d^10 - 596*a^7*b^6*c^4*d^8 + 600*a^7*b^6*c^6*d^6 + 900*a^8*b^5*c^3*d^9 - 584*a^8*b^5*c^5*d^7 - 80*a^9*b^4*c^4*d^8 + 48*a^10*b^3*c^3*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 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54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 + 4038*a^15*b^4*c^7*d^9 - 1320*a^15*b^4*c^9*d^7 - 244*a^16*b^3*c^2*d^14 + 1084*a^16*b^3*c^4*d^12 - 1500*a^16*b^3*c^6*d^10 + 660*a^16*b^3*c^8*d^8 - 176*a^17*b^2*c^3*d^13 + 372*a^17*b^2*c^5*d^11 - 220*a^17*b^2*c^7*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^16 - 12*a^5*b^14*c^16 + 8*a^7*b^12*c^16 + 8*a^19*c^2*d^14 - 8*a^19*c^4*d^12 + 12*a*b^18*c^10*d^6 - 28*a*b^18*c^12*d^4 + 12*a*b^18*c^14*d^2 - 20*a^2*b^17*c^15*d - 48*a^4*b^15*c^15*d + 156*a^6*b^13*c^15*d - 88*a^8*b^11*c^15*d + 12*a^10*b^9*c*d^15 - 48*a^12*b^7*c*d^15 + 84*a^14*b^5*c*d^15 - 72*a^16*b^3*c*d^15 - 112*a^18*b*c^3*d^13 + 88*a^18*b*c^5*d^11 - 84*a^2*b^17*c^9*d^7 + 212*a^2*b^17*c^11*d^5 - 108*a^2*b^17*c^13*d^3 + 240*a^3*b^16*c^8*d^8 - 744*a^3*b^16*c^10*d^6 + 584*a^3*b^16*c^12*d^4 - 80*a^3*b^16*c^14*d^2 - 336*a^4*b^15*c^7*d^9 + 1632*a^4*b^15*c^9*d^7 - 2176*a^4*b^15*c^11*d^5 + 928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (b^2*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(12*a*b^21*c^18 - 12*a^22*c*d^17 - 56*a^3*b^19*c^18 + 104*a^5*b^17*c^18 - 96*a^7*b^15*c^18 + 44*a^9*b^13*c^18 - 8*a^11*b^11*c^18 + 32*a^22*c^3*d^15 - 28*a^22*c^5*d^13 + 8*a^22*c^7*d^11 - 16*a*b^21*c^12*d^6 + 44*a*b^21*c^14*d^4 - 40*a*b^21*c^16*d^2 - 132*a^2*b^20*c^17*d + 616*a^4*b^18*c^17*d - 1144*a^6*b^16*c^17*d + 1056*a^8*b^14*c^17*d - 484*a^10*b^12*c^17*d + 16*a^12*b^10*c*d^17 + 88*a^12*b^10*c^17*d - 76*a^14*b^8*c*d^17 + 144*a^16*b^6*c*d^17 - 136*a^18*b^4*c*d^17 + 64*a^20*b^2*c*d^17 + 132*a^21*b*c^2*d^16 - 352*a^21*b*c^4*d^14 + 308*a^21*b*c^6*d^12 - 88*a^21*b*c^8*d^10 + 176*a^2*b^20*c^11*d^7 - 484*a^2*b^20*c^13*d^5 + 440*a^2*b^20*c^15*d^3 - 880*a^3*b^19*c^10*d^8 + 2496*a^3*b^19*c^12*d^6 - 2408*a^3*b^19*c^14*d^4 + 848*a^3*b^19*c^16*d^2 + 2640*a^4*b^18*c^9*d^9 - 8096*a^4*b^18*c^11*d^7 + 8888*a^4*b^18*c^13*d^5 - 4048*a^4*b^18*c^15*d^3 - 5280*a^5*b^17*c^8*d^10 + 18700*a^5*b^17*c^10*d^8 - 24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)) - (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(60*a*b^15*c^7*d^7 - 36*a*b^15*c^5*d^9 - 13*a*b^15*c^9*d^5 - 10*a*b^15*c^11*d^3 - 4*a^3*b^13*c^13*d + 36*a^5*b^11*c*d^13 - 4*a^5*b^11*c^13*d - 144*a^7*b^9*c*d^13 + 216*a^9*b^7*c*d^13 - 144*a^11*b^5*c*d^13 + 36*a^13*b^3*c*d^13 + 4*a^15*b*c^3*d^11 + 72*a^2*b^14*c^4*d^10 - 108*a^2*b^14*c^6*d^8 + 19*a^2*b^14*c^8*d^6 + 14*a^2*b^14*c^10*d^4 - a^2*b^14*c^12*d^2 + 120*a^3*b^13*c^5*d^9 - 305*a^3*b^13*c^7*d^7 + 190*a^3*b^13*c^9*d^5 + 19*a^3*b^13*c^11*d^3 - 72*a^4*b^12*c^2*d^12 - 168*a^4*b^12*c^4*d^10 + 699*a^4*b^12*c^6*d^8 - 602*a^4*b^12*c^8*d^6 + 99*a^4*b^12*c^10*d^4 + 20*a^4*b^12*c^12*d^2 - 36*a^5*b^11*c^3*d^11 - 535*a^5*b^11*c^5*d^9 + 1354*a^5*b^11*c^7*d^7 - 895*a^5*b^11*c^9*d^5 + 40*a^5*b^11*c^11*d^3 + 276*a^6*b^10*c^2*d^12 + 233*a^6*b^10*c^4*d^10 - 2046*a^6*b^10*c^6*d^8 + 2161*a^6*b^10*c^8*d^6 - 552*a^6*b^10*c^10*d^4 + 44*a^6*b^10*c^12*d^2 + 61*a^7*b^9*c^3*d^11 + 1386*a^7*b^9*c^5*d^9 - 2979*a^7*b^9*c^7*d^7 + 1860*a^7*b^9*c^9*d^5 - 220*a^7*b^9*c^11*d^3 - 375*a^8*b^8*c^2*d^12 - 270*a^8*b^8*c^4*d^10 + 2885*a^8*b^8*c^6*d^8 - 3012*a^8*b^8*c^8*d^6 + 628*a^8*b^8*c^10*d^4 - 88*a^9*b^7*c^3*d^11 - 1544*a^9*b^7*c^5*d^9 + 2648*a^9*b^7*c^7*d^7 - 1088*a^9*b^7*c^9*d^5 + 216*a^10*b^6*c^2*d^12 + 100*a^10*b^6*c^4*d^10 - 1336*a^10*b^6*c^6*d^8 + 1056*a^10*b^6*c^8*d^6 + 180*a^11*b^5*c^3*d^11 + 248*a^11*b^5*c^5*d^9 - 400*a^11*b^5*c^7*d^7 - 60*a^12*b^4*c^2*d^12 + 248*a^12*b^4*c^4*d^10 - 148*a^12*b^4*c^6*d^8 - 184*a^13*b^3*c^3*d^11 + 172*a^13*b^3*c^5*d^9 + 24*a^14*b^2*c^2*d^12 - 44*a^14*b^2*c^4*d^10 - a*b^15*c^13*d))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(4*a^16*c^3*d^11 - 4*a^3*b^13*c^14 - 4*a^5*b^11*c^14 - a*b^15*c^14 + 144*a*b^15*c^4*d^10 - 348*a*b^15*c^6*d^8 + 214*a*b^15*c^8*d^6 + 7*a*b^15*c^10*d^4 - 8*a*b^15*c^12*d^2 - a^2*b^14*c^13*d - 144*a^4*b^12*c*d^13 + 20*a^4*b^12*c^13*d + 684*a^6*b^10*c*d^13 + 44*a^6*b^10*c^13*d - 1314*a^8*b^8*c*d^13 + 1224*a^10*b^6*c*d^13 - 504*a^12*b^4*c*d^13 + 36*a^14*b^2*c*d^13 + 24*a^15*b*c^2*d^12 - 44*a^15*b*c^4*d^10 - 432*a^2*b^14*c^3*d^11 + 1140*a^2*b^14*c^5*d^9 - 818*a^2*b^14*c^7*d^7 + 55*a^2*b^14*c^9*d^5 + 16*a^2*b^14*c^11*d^3 + 432*a^3*b^13*c^2*d^12 - 2016*a^3*b^13*c^4*d^10 + 2938*a^3*b^13*c^6*d^8 - 1485*a^3*b^13*c^8*d^6 + 152*a^3*b^13*c^10*d^4 + 27*a^3*b^13*c^12*d^2 + 2688*a^4*b^12*c^3*d^11 - 6574*a^4*b^12*c^5*d^9 + 5107*a^4*b^12*c^7*d^7 - 1056*a^4*b^12*c^9*d^5 + 59*a^4*b^12*c^11*d^3 - 2148*a^5*b^11*c^2*d^12 + 8378*a^5*b^11*c^4*d^10 - 10619*a^5*b^11*c^6*d^8 + 5064*a^5*b^11*c^8*d^6 - 975*a^5*b^11*c^10*d^4 + 48*a^5*b^11*c^12*d^2 - 7294*a^6*b^10*c^3*d^11 + 16053*a^6*b^10*c^5*d^9 - 12464*a^6*b^10*c^7*d^7 + 3649*a^6*b^10*c^9*d^5 - 640*a^6*b^10*c^11*d^3 + 4470*a^7*b^9*c^2*d^12 - 15815*a^7*b^9*c^4*d^10 + 18608*a^7*b^9*c^6*d^8 - 8939*a^7*b^9*c^8*d^6 + 2300*a^7*b^9*c^10*d^4 - 220*a^7*b^9*c^12*d^2 + 10105*a^8*b^8*c^3*d^11 - 19912*a^8*b^8*c^5*d^9 + 14693*a^8*b^8*c^7*d^7 - 4524*a^8*b^8*c^9*d^5 + 628*a^8*b^8*c^11*d^3 - 4632*a^9*b^7*c^2*d^12 + 14976*a^9*b^7*c^4*d^10 - 15576*a^9*b^7*c^6*d^8 + 6104*a^9*b^7*c^8*d^6 - 1088*a^9*b^7*c^10*d^4 - 7104*a^10*b^6*c^3*d^11 + 11320*a^10*b^6*c^5*d^9 - 6184*a^10*b^6*c^7*d^7 + 1120*a^10*b^6*c^9*d^5 + 2232*a^11*b^5*c^2*d^12 - 5932*a^11*b^5*c^4*d^10 + 4344*a^11*b^5*c^6*d^8 - 688*a^11*b^5*c^8*d^6 + 1892*a^12*b^4*c^3*d^11 - 1920*a^12*b^4*c^5*d^9 + 368*a^12*b^4*c^7*d^7 - 252*a^13*b^3*c^2*d^12 + 624*a^13*b^3*c^4*d^10 - 292*a^13*b^3*c^6*d^8 - 192*a^14*b^2*c^3*d^11 + 172*a^14*b^2*c^5*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*(2*a^2*b^17*c^16 - 6*a^6*b^13*c^16 + 4*a^8*b^11*c^16 + 4*a^19*c^3*d^13 - 4*a^19*c^5*d^11 + 12*a*b^18*c^9*d^7 - 28*a*b^18*c^11*d^5 + 16*a*b^18*c^13*d^3 - 10*a^3*b^16*c^15*d - 24*a^5*b^14*c^15*d + 78*a^7*b^12*c^15*d + 12*a^9*b^10*c*d^15 - 44*a^9*b^10*c^15*d - 54*a^11*b^8*c*d^15 + 96*a^13*b^6*c*d^15 - 78*a^15*b^4*c*d^15 + 24*a^17*b^2*c*d^15 + 12*a^18*b*c^2*d^14 - 56*a^18*b*c^4*d^12 + 44*a^18*b*c^6*d^10 - 96*a^2*b^17*c^8*d^8 + 234*a^2*b^17*c^10*d^6 - 146*a^2*b^17*c^12*d^4 + 6*a^2*b^17*c^14*d^2 + 336*a^3*b^16*c^7*d^9 - 918*a^3*b^16*c^9*d^7 + 726*a^3*b^16*c^11*d^5 - 134*a^3*b^16*c^13*d^3 - 672*a^4*b^15*c^6*d^10 + 2280*a^4*b^15*c^8*d^8 - 2520*a^4*b^15*c^10*d^6 + 952*a^4*b^15*c^12*d^4 - 40*a^4*b^15*c^14*d^2 + 840*a^5*b^14*c^5*d^11 - 4032*a^5*b^14*c^7*d^9 + 6360*a^5*b^14*c^9*d^7 - 3768*a^5*b^14*c^11*d^5 + 624*a^5*b^14*c^13*d^3 - 672*a^6*b^13*c^4*d^12 + 5292*a^6*b^13*c^6*d^10 - 11772*a^6*b^13*c^8*d^8 + 10050*a^6*b^13*c^10*d^6 - 3174*a^6*b^13*c^12*d^4 + 282*a^6*b^13*c^14*d^2 + 336*a^7*b^12*c^3*d^13 - 5124*a^7*b^12*c^5*d^11 + 16212*a^7*b^12*c^7*d^9 - 19602*a^7*b^12*c^9*d^7 + 9670*a^7*b^12*c^11*d^5 - 1570*a^7*b^12*c^13*d^3 - 96*a^8*b^11*c^2*d^14 + 3528*a^8*b^11*c^4*d^12 - 16872*a^8*b^11*c^6*d^10 + 28848*a^8*b^11*c^8*d^8 - 20340*a^8*b^11*c^10*d^6 + 5396*a^8*b^11*c^12*d^4 - 468*a^8*b^11*c^14*d^2 - 1620*a^9*b^10*c^3*d^13 + 13320*a^9*b^10*c^5*d^11 - 32304*a^9*b^10*c^7*d^9 + 31560*a^9*b^10*c^9*d^7 - 12648*a^9*b^10*c^11*d^5 + 1724*a^9*b^10*c^13*d^3 + 442*a^10*b^9*c^2*d^14 - 7810*a^10*b^9*c^4*d^12 + 27546*a^10*b^9*c^6*d^10 - 37338*a^10*b^9*c^8*d^8 + 21288*a^10*b^9*c^10*d^6 - 4348*a^10*b^9*c^12*d^4 + 220*a^10*b^9*c^14*d^2 + 3206*a^11*b^8*c^3*d^13 - 17850*a^11*b^8*c^5*d^11 + 34018*a^11*b^8*c^7*d^9 - 26556*a^11*b^8*c^9*d^7 + 7896*a^11*b^8*c^11*d^5 - 660*a^11*b^8*c^13*d^3 - 816*a^12*b^7*c^2*d^14 + 8696*a^12*b^7*c^4*d^12 - 23696*a^12*b^7*c^6*d^10 + 25056*a^12*b^7*c^8*d^8 - 10560*a^12*b^7*c^10*d^6 + 1320*a^12*b^7*c^12*d^4 - 3064*a^13*b^6*c^3*d^13 + 12400*a^13*b^6*c^5*d^11 - 18048*a^13*b^6*c^7*d^9 + 10464*a^13*b^6*c^9*d^7 - 1848*a^13*b^6*c^11*d^5 + 702*a^14*b^5*c^2*d^14 - 4770*a^14*b^5*c^4*d^12 + 9858*a^14*b^5*c^6*d^10 - 7638*a^14*b^5*c^8*d^8 + 1848*a^14*b^5*c^10*d^6 + 1314*a^15*b^4*c^3*d^13 - 3954*a^15*b^4*c^5*d^11 + 4038*a^15*b^4*c^7*d^9 - 1320*a^15*b^4*c^9*d^7 - 244*a^16*b^3*c^2*d^14 + 1084*a^16*b^3*c^4*d^12 - 1500*a^16*b^3*c^6*d^10 + 660*a^16*b^3*c^8*d^8 - 176*a^17*b^2*c^3*d^13 + 372*a^17*b^2*c^5*d^11 - 220*a^17*b^2*c^7*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 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1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (8*tan(e/2 + (f*x)/2)*(4*a*b^18*c^16 - 12*a^5*b^14*c^16 + 8*a^7*b^12*c^16 + 8*a^19*c^2*d^14 - 8*a^19*c^4*d^12 + 12*a*b^18*c^10*d^6 - 28*a*b^18*c^12*d^4 + 12*a*b^18*c^14*d^2 - 20*a^2*b^17*c^15*d - 48*a^4*b^15*c^15*d + 156*a^6*b^13*c^15*d - 88*a^8*b^11*c^15*d + 12*a^10*b^9*c*d^15 - 48*a^12*b^7*c*d^15 + 84*a^14*b^5*c*d^15 - 72*a^16*b^3*c*d^15 - 112*a^18*b*c^3*d^13 + 88*a^18*b*c^5*d^11 - 84*a^2*b^17*c^9*d^7 + 212*a^2*b^17*c^11*d^5 - 108*a^2*b^17*c^13*d^3 + 240*a^3*b^16*c^8*d^8 - 744*a^3*b^16*c^10*d^6 + 584*a^3*b^16*c^12*d^4 - 80*a^3*b^16*c^14*d^2 - 336*a^4*b^15*c^7*d^9 + 1632*a^4*b^15*c^9*d^7 - 2176*a^4*b^15*c^11*d^5 + 928*a^4*b^15*c^13*d^3 + 168*a^5*b^14*c^6*d^10 - 2472*a^5*b^14*c^8*d^8 + 5460*a^5*b^14*c^10*d^6 - 3708*a^5*b^14*c^12*d^4 + 564*a^5*b^14*c^14*d^2 + 168*a^6*b^13*c^5*d^11 + 2520*a^6*b^13*c^7*d^9 - 9204*a^6*b^13*c^9*d^7 + 9180*a^6*b^13*c^11*d^5 - 2820*a^6*b^13*c^13*d^3 - 336*a^7*b^12*c^4*d^12 - 1344*a^7*b^12*c^6*d^10 + 10416*a^7*b^12*c^8*d^8 - 15960*a^7*b^12*c^10*d^6 + 8152*a^7*b^12*c^12*d^4 - 936*a^7*b^12*c^14*d^2 + 240*a^8*b^11*c^3*d^13 - 336*a^8*b^11*c^5*d^11 - 7488*a^8*b^11*c^7*d^9 + 19800*a^8*b^11*c^9*d^7 - 15416*a^8*b^11*c^11*d^5 + 3288*a^8*b^11*c^13*d^3 - 84*a^9*b^10*c^2*d^14 + 1188*a^9*b^10*c^4*d^12 + 2292*a^9*b^10*c^6*d^10 - 16596*a^9*b^10*c^8*d^8 + 20136*a^9*b^10*c^10*d^6 - 7376*a^9*b^10*c^12*d^4 + 440*a^9*b^10*c^14*d^2 - 908*a^10*b^9*c^3*d^13 + 1740*a^10*b^9*c^5*d^11 + 7556*a^10*b^9*c^7*d^9 - 18048*a^10*b^9*c^9*d^7 + 10936*a^10*b^9*c^11*d^5 - 1288*a^10*b^9*c^13*d^3 + 328*a^11*b^8*c^2*d^14 - 2808*a^11*b^8*c^4*d^12 + 1088*a^11*b^8*c^6*d^10 + 9600*a^11*b^8*c^8*d^8 - 10584*a^11*b^8*c^10*d^6 + 2376*a^11*b^8*c^12*d^4 + 1792*a^12*b^7*c^3*d^13 - 4720*a^12*b^7*c^5*d^11 - 144*a^12*b^7*c^7*d^9 + 5856*a^12*b^7*c^9*d^7 - 2736*a^12*b^7*c^11*d^5 - 596*a^13*b^6*c^2*d^14 + 3980*a^13*b^6*c^4*d^12 - 4908*a^13*b^6*c^6*d^10 - 156*a^13*b^6*c^8*d^8 + 1680*a^13*b^6*c^10*d^6 - 1932*a^14*b^5*c^3*d^13 + 4812*a^14*b^5*c^5*d^11 - 3012*a^14*b^5*c^7*d^9 + 48*a^14*b^5*c^9*d^7 + 552*a^15*b^4*c^2*d^14 - 2616*a^15*b^4*c^4*d^12 + 3096*a^15*b^4*c^6*d^10 - 1032*a^15*b^4*c^8*d^8 + 920*a^16*b^3*c^3*d^13 - 1752*a^16*b^3*c^5*d^11 + 904*a^16*b^3*c^7*d^9 - 208*a^17*b^2*c^2*d^14 + 600*a^17*b^2*c^4*d^12 - 392*a^17*b^2*c^6*d^10 + 24*a^18*b*c*d^15))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) + (b^2*((8*(16*a^4*b^18*c^18 - 4*a^2*b^20*c^18 - 24*a^6*b^16*c^18 + 16*a^8*b^14*c^18 - 4*a^10*b^12*c^18 + 4*a^22*c^2*d^16 - 8*a^22*c^4*d^14 + 4*a^22*c^6*d^12 + 4*a*b^21*c^13*d^5 - 8*a*b^21*c^15*d^3 + 24*a^3*b^19*c^17*d - 136*a^5*b^17*c^17*d + 224*a^7*b^15*c^17*d - 156*a^9*b^13*c^17*d + 40*a^11*b^11*c^17*d - 4*a^13*b^9*c*d^17 + 16*a^15*b^7*c*d^17 - 24*a^17*b^5*c*d^17 + 16*a^19*b^3*c*d^17 - 32*a^21*b*c^3*d^15 + 76*a^21*b*c^5*d^13 - 40*a^21*b*c^7*d^11 - 40*a^2*b^20*c^12*d^6 + 76*a^2*b^20*c^14*d^4 - 32*a^2*b^20*c^16*d^2 + 176*a^3*b^19*c^11*d^7 - 328*a^3*b^19*c^13*d^5 + 128*a^3*b^19*c^15*d^3 - 440*a^4*b^18*c^10*d^8 + 864*a^4*b^18*c^12*d^6 - 392*a^4*b^18*c^14*d^4 - 48*a^4*b^18*c^16*d^2 + 660*a^5*b^17*c^9*d^9 - 1584*a^5*b^17*c^11*d^7 + 1052*a^5*b^17*c^13*d^5 + 8*a^5*b^17*c^15*d^3 - 528*a^6*b^16*c^8*d^10 + 2156*a^6*b^16*c^10*d^8 - 2264*a^6*b^16*c^12*d^6 + 148*a^6*b^16*c^14*d^4 + 512*a^6*b^16*c^16*d^2 - 2112*a^7*b^15*c^9*d^9 + 3520*a^7*b^15*c^11*d^7 - 480*a^7*b^15*c^13*d^5 - 1152*a^7*b^15*c^15*d^3 + 528*a^8*b^14*c^6*d^12 + 1056*a^8*b^14*c^8*d^10 - 3696*a^8*b^14*c^10*d^8 + 1216*a^8*b^14*c^12*d^6 + 1808*a^8*b^14*c^14*d^4 - 928*a^8*b^14*c^16*d^2 - 660*a^9*b^13*c^5*d^13 + 792*a^9*b^13*c^7*d^11 + 2244*a^9*b^13*c^9*d^9 - 2288*a^9*b^13*c^11*d^7 - 2180*a^9*b^13*c^13*d^5 + 2248*a^9*b^13*c^15*d^3 + 440*a^10*b^12*c^4*d^14 - 2332*a^10*b^12*c^6*d^12 + 176*a^10*b^12*c^8*d^10 + 2684*a^10*b^12*c^10*d^8 + 1896*a^10*b^12*c^12*d^6 - 3532*a^10*b^12*c^14*d^4 + 672*a^10*b^12*c^16*d^2 - 176*a^11*b^11*c^3*d^15 + 2552*a^11*b^11*c^5*d^13 - 2464*a^11*b^11*c^7*d^11 - 1496*a^11*b^11*c^9*d^9 - 528*a^11*b^11*c^11*d^7 + 3736*a^11*b^11*c^13*d^5 - 1664*a^11*b^11*c^15*d^3 + 40*a^12*b^10*c^2*d^16 - 1664*a^12*b^10*c^4*d^14 + 3736*a^12*b^10*c^6*d^12 - 528*a^12*b^10*c^8*d^10 - 1496*a^12*b^10*c^10*d^8 - 2464*a^12*b^10*c^12*d^6 + 2552*a^12*b^10*c^14*d^4 - 176*a^12*b^10*c^16*d^2 + 672*a^13*b^9*c^3*d^15 - 3532*a^13*b^9*c^5*d^13 + 1896*a^13*b^9*c^7*d^11 + 2684*a^13*b^9*c^9*d^9 + 176*a^13*b^9*c^11*d^7 - 2332*a^13*b^9*c^13*d^5 + 440*a^13*b^9*c^15*d^3 - 156*a^14*b^8*c^2*d^16 + 2248*a^14*b^8*c^4*d^14 - 2180*a^14*b^8*c^6*d^12 - 2288*a^14*b^8*c^8*d^10 + 2244*a^14*b^8*c^10*d^8 + 792*a^14*b^8*c^12*d^6 - 660*a^14*b^8*c^14*d^4 - 928*a^15*b^7*c^3*d^15 + 1808*a^15*b^7*c^5*d^13 + 1216*a^15*b^7*c^7*d^11 - 3696*a^15*b^7*c^9*d^9 + 1056*a^15*b^7*c^11*d^7 + 528*a^15*b^7*c^13*d^5 + 224*a^16*b^6*c^2*d^16 - 1152*a^16*b^6*c^4*d^14 - 480*a^16*b^6*c^6*d^12 + 3520*a^16*b^6*c^8*d^10 - 2112*a^16*b^6*c^10*d^8 + 512*a^17*b^5*c^3*d^15 + 148*a^17*b^5*c^5*d^13 - 2264*a^17*b^5*c^7*d^11 + 2156*a^17*b^5*c^9*d^9 - 528*a^17*b^5*c^11*d^7 - 136*a^18*b^4*c^2*d^16 + 8*a^18*b^4*c^4*d^14 + 1052*a^18*b^4*c^6*d^12 - 1584*a^18*b^4*c^8*d^10 + 660*a^18*b^4*c^10*d^8 - 48*a^19*b^3*c^3*d^15 - 392*a^19*b^3*c^5*d^13 + 864*a^19*b^3*c^7*d^11 - 440*a^19*b^3*c^9*d^9 + 24*a^20*b^2*c^2*d^16 + 128*a^20*b^2*c^4*d^14 - 328*a^20*b^2*c^6*d^12 + 176*a^20*b^2*c^8*d^10 + 4*a*b^21*c^17*d - 4*a^21*b*c*d^17))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12) - (8*tan(e/2 + (f*x)/2)*(12*a*b^21*c^18 - 12*a^22*c*d^17 - 56*a^3*b^19*c^18 + 104*a^5*b^17*c^18 - 96*a^7*b^15*c^18 + 44*a^9*b^13*c^18 - 8*a^11*b^11*c^18 + 32*a^22*c^3*d^15 - 28*a^22*c^5*d^13 + 8*a^22*c^7*d^11 - 16*a*b^21*c^12*d^6 + 44*a*b^21*c^14*d^4 - 40*a*b^21*c^16*d^2 - 132*a^2*b^20*c^17*d + 616*a^4*b^18*c^17*d - 1144*a^6*b^16*c^17*d + 1056*a^8*b^14*c^17*d - 484*a^10*b^12*c^17*d + 16*a^12*b^10*c*d^17 + 88*a^12*b^10*c^17*d - 76*a^14*b^8*c*d^17 + 144*a^16*b^6*c*d^17 - 136*a^18*b^4*c*d^17 + 64*a^20*b^2*c*d^17 + 132*a^21*b*c^2*d^16 - 352*a^21*b*c^4*d^14 + 308*a^21*b*c^6*d^12 - 88*a^21*b*c^8*d^10 + 176*a^2*b^20*c^11*d^7 - 484*a^2*b^20*c^13*d^5 + 440*a^2*b^20*c^15*d^3 - 880*a^3*b^19*c^10*d^8 + 2496*a^3*b^19*c^12*d^6 - 2408*a^3*b^19*c^14*d^4 + 848*a^3*b^19*c^16*d^2 + 2640*a^4*b^18*c^9*d^9 - 8096*a^4*b^18*c^11*d^7 + 8888*a^4*b^18*c^13*d^5 - 4048*a^4*b^18*c^15*d^3 - 5280*a^5*b^17*c^8*d^10 + 18700*a^5*b^17*c^10*d^8 - 24784*a^5*b^17*c^12*d^6 + 14692*a^5*b^17*c^14*d^4 - 3432*a^5*b^17*c^16*d^2 + 7392*a^6*b^16*c^7*d^11 - 32868*a^6*b^16*c^9*d^9 + 54384*a^6*b^16*c^11*d^7 - 40876*a^6*b^16*c^13*d^5 + 13112*a^6*b^16*c^15*d^3 - 7392*a^7*b^15*c^6*d^12 + 45408*a^7*b^15*c^8*d^10 - 95040*a^7*b^15*c^10*d^8 + 89280*a^7*b^15*c^12*d^6 - 38208*a^7*b^15*c^14*d^4 + 6048*a^7*b^15*c^16*d^2 + 5280*a^8*b^14*c^5*d^13 - 49632*a^8*b^14*c^7*d^11 + 133056*a^8*b^14*c^9*d^9 - 156992*a^8*b^14*c^11*d^7 + 88000*a^8*b^14*c^13*d^5 - 20768*a^8*b^14*c^15*d^3 - 2640*a^9*b^13*c^4*d^14 + 42372*a^9*b^13*c^6*d^12 - 150216*a^9*b^13*c^8*d^10 + 225676*a^9*b^13*c^10*d^8 - 162336*a^9*b^13*c^12*d^6 + 52532*a^9*b^13*c^14*d^4 - 5432*a^9*b^13*c^16*d^2 + 880*a^10*b^12*c^3*d^15 - 27500*a^10*b^12*c^5*d^13 + 137368*a^10*b^12*c^7*d^11 - 266244*a^10*b^12*c^9*d^9 + 242528*a^10*b^12*c^11*d^7 - 104060*a^10*b^12*c^13*d^5 + 17512*a^10*b^12*c^15*d^3 - 176*a^11*b^11*c^2*d^16 + 13024*a^11*b^11*c^4*d^14 - 101288*a^11*b^11*c^6*d^12 + 257136*a^11*b^11*c^8*d^10 - 296824*a^11*b^11*c^10*d^8 + 165760*a^11*b^11*c^12*d^6 - 40072*a^11*b^11*c^14*d^4 + 2448*a^11*b^11*c^16*d^2 - 4224*a^12*b^10*c^3*d^15 + 59000*a^12*b^10*c^5*d^13 - 202544*a^12*b^10*c^7*d^11 + 299816*a^12*b^10*c^9*d^9 - 214368*a^12*b^10*c^11*d^7 + 69784*a^12*b^10*c^13*d^5 - 7568*a^12*b^10*c^15*d^3 + 836*a^13*b^9*c^2*d^16 - 26048*a^13*b^9*c^4*d^14 + 129580*a^13*b^9*c^6*d^12 - 249832*a^13*b^9*c^8*d^10 + 226116*a^13*b^9*c^10*d^8 - 96272*a^13*b^9*c^12*d^6 + 16060*a^13*b^9*c^14*d^4 - 440*a^13*b^9*c^16*d^2 + 8128*a^14*b^8*c^3*d^15 - 66628*a^14*b^8*c^5*d^13 + 170424*a^14*b^8*c^7*d^11 - 195404*a^14*b^8*c^9*d^9 + 107184*a^14*b^8*c^11*d^7 - 24948*a^14*b^8*c^13*d^5 + 1320*a^14*b^8*c^15*d^3 - 1584*a^15*b^7*c^2*d^16 + 26752*a^15*b^7*c^4*d^14 - 94160*a^15*b^7*c^6*d^12 + 138688*a^15*b^7*c^8*d^10 - 96624*a^15*b^7*c^10*d^8 + 29568*a^15*b^7*c^12*d^6 - 2640*a^15*b^7*c^14*d^4 - 7872*a^16*b^6*c^3*d^15 + 41712*a^16*b^6*c^5*d^13 - 80448*a^16*b^6*c^7*d^11 + 70224*a^16*b^6*c^9*d^9 - 27456*a^16*b^6*c^11*d^7 + 3696*a^16*b^6*c^13*d^5 + 1496*a^17*b^5*c^2*d^16 - 14608*a^17*b^5*c^4*d^14 + 37532*a^17*b^5*c^6*d^12 - 40920*a^17*b^5*c^8*d^10 + 20196*a^17*b^5*c^10*d^8 - 3696*a^17*b^5*c^12*d^6 + 3888*a^18*b^4*c^3*d^15 - 13748*a^18*b^4*c^5*d^13 + 19016*a^18*b^4*c^7*d^11 - 11660*a^18*b^4*c^9*d^9 + 2640*a^18*b^4*c^11*d^7 - 704*a^19*b^3*c^2*d^16 + 3872*a^19*b^3*c^4*d^14 - 6952*a^19*b^3*c^6*d^12 + 5104*a^19*b^3*c^8*d^10 - 1320*a^19*b^3*c^10*d^8 - 832*a^20*b^2*c^3*d^15 + 1912*a^20*b^2*c^5*d^13 - 1584*a^20*b^2*c^7*d^11 + 440*a^20*b^2*c^9*d^9))/(a^17*d^13 - b^17*c^13 + 4*a^2*b^15*c^13 - 6*a^4*b^13*c^13 + 4*a^6*b^11*c^13 - a^8*b^9*c^13 + a^9*b^8*d^13 - 4*a^11*b^6*d^13 + 6*a^13*b^4*d^13 - 4*a^15*b^2*d^13 - 2*a^17*c^2*d^11 + a^17*c^4*d^9 - b^17*c^9*d^4 + 2*b^17*c^11*d^2 + 9*a*b^16*c^8*d^5 - 18*a*b^16*c^10*d^3 - 36*a^3*b^14*c^12*d + 54*a^5*b^12*c^12*d - 36*a^7*b^10*c^12*d - 9*a^8*b^9*c*d^12 + 9*a^9*b^8*c^12*d + 36*a^10*b^7*c*d^12 - 54*a^12*b^5*c*d^12 + 36*a^14*b^3*c*d^12 + 18*a^16*b*c^3*d^10 - 9*a^16*b*c^5*d^8 - 36*a^2*b^15*c^7*d^6 + 76*a^2*b^15*c^9*d^4 - 44*a^2*b^15*c^11*d^2 + 84*a^3*b^14*c^6*d^7 - 204*a^3*b^14*c^8*d^5 + 156*a^3*b^14*c^10*d^3 - 126*a^4*b^13*c^5*d^8 + 396*a^4*b^13*c^7*d^6 - 420*a^4*b^13*c^9*d^4 + 156*a^4*b^13*c^11*d^2 + 126*a^5*b^12*c^4*d^9 - 588*a^5*b^12*c^6*d^7 + 852*a^5*b^12*c^8*d^5 - 444*a^5*b^12*c^10*d^3 - 84*a^6*b^11*c^3*d^10 + 672*a^6*b^11*c^5*d^8 - 1308*a^6*b^11*c^7*d^6 + 940*a^6*b^11*c^9*d^4 - 224*a^6*b^11*c^11*d^2 + 36*a^7*b^10*c^2*d^11 - 576*a^7*b^10*c^4*d^9 + 1548*a^7*b^10*c^6*d^7 - 1548*a^7*b^10*c^8*d^5 + 576*a^7*b^10*c^10*d^3 + 354*a^8*b^9*c^3*d^10 - 1437*a^8*b^9*c^5*d^8 + 1992*a^8*b^9*c^7*d^6 - 1045*a^8*b^9*c^9*d^4 + 146*a^8*b^9*c^11*d^2 - 146*a^9*b^8*c^2*d^11 + 1045*a^9*b^8*c^4*d^9 - 1992*a^9*b^8*c^6*d^7 + 1437*a^9*b^8*c^8*d^5 - 354*a^9*b^8*c^10*d^3 - 576*a^10*b^7*c^3*d^10 + 1548*a^10*b^7*c^5*d^8 - 1548*a^10*b^7*c^7*d^6 + 576*a^10*b^7*c^9*d^4 - 36*a^10*b^7*c^11*d^2 + 224*a^11*b^6*c^2*d^11 - 940*a^11*b^6*c^4*d^9 + 1308*a^11*b^6*c^6*d^7 - 672*a^11*b^6*c^8*d^5 + 84*a^11*b^6*c^10*d^3 + 444*a^12*b^5*c^3*d^10 - 852*a^12*b^5*c^5*d^8 + 588*a^12*b^5*c^7*d^6 - 126*a^12*b^5*c^9*d^4 - 156*a^13*b^4*c^2*d^11 + 420*a^13*b^4*c^4*d^9 - 396*a^13*b^4*c^6*d^7 + 126*a^13*b^4*c^8*d^5 - 156*a^14*b^3*c^3*d^10 + 204*a^14*b^3*c^5*d^8 - 84*a^14*b^3*c^7*d^6 + 44*a^15*b^2*c^2*d^11 - 76*a^15*b^2*c^4*d^9 + 36*a^15*b^2*c^6*d^7 + 9*a*b^16*c^12*d - 9*a^16*b*c*d^12))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3)))*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d))/(2*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3))))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4*d^2 + b^4*c^2 + 6*b^4*d^2 + 2*a^2*b^2*c^2 - 15*a^2*b^2*d^2 + 2*a*b^3*c*d - 8*a^3*b*c*d)*1i)/(f*(a^14*d^4 - b^14*c^4 + 5*a^2*b^12*c^4 - 10*a^4*b^10*c^4 + 10*a^6*b^8*c^4 - 5*a^8*b^6*c^4 + a^10*b^4*c^4 - a^4*b^10*d^4 + 5*a^6*b^8*d^4 - 10*a^8*b^6*d^4 + 10*a^10*b^4*d^4 - 5*a^12*b^2*d^4 + 4*a^3*b^11*c*d^3 - 20*a^3*b^11*c^3*d - 20*a^5*b^9*c*d^3 + 40*a^5*b^9*c^3*d + 40*a^7*b^7*c*d^3 - 40*a^7*b^7*c^3*d - 40*a^9*b^5*c*d^3 + 20*a^9*b^5*c^3*d + 20*a^11*b^3*c*d^3 - 4*a^11*b^3*c^3*d - 6*a^2*b^12*c^2*d^2 + 30*a^4*b^10*c^2*d^2 - 60*a^6*b^8*c^2*d^2 + 60*a^8*b^6*c^2*d^2 - 30*a^10*b^4*c^2*d^2 + 6*a^12*b^2*c^2*d^2 + 4*a*b^13*c^3*d - 4*a^13*b*c*d^3))","B"
722,1,571173,669,80.303368,"\text{Not used}","int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^3),x)","-\frac{\frac{-4\,a^7\,c^2\,d^5+a^7\,d^7+10\,a^6\,b\,c^3\,d^4-7\,a^6\,b\,c\,d^6+8\,a^5\,b^2\,c^2\,d^5-2\,a^5\,b^2\,d^7-20\,a^4\,b^3\,c^3\,d^4+14\,a^4\,b^3\,c\,d^6+10\,a^3\,b^4\,c^6\,d-20\,a^3\,b^4\,c^4\,d^3+6\,a^3\,b^4\,c^2\,d^5+a^3\,b^4\,d^7-4\,a^2\,b^5\,c^7+8\,a^2\,b^5\,c^5\,d^2+6\,a^2\,b^5\,c^3\,d^4-7\,a^2\,b^5\,c\,d^6-7\,a\,b^6\,c^6\,d+14\,a\,b^6\,c^4\,d^3-7\,a\,b^6\,c^2\,d^5+b^7\,c^7-2\,b^7\,c^5\,d^2+b^7\,c^3\,d^4}{\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(11\,a^8\,c^2\,d^6-2\,a^8\,d^8-13\,a^7\,b\,c^3\,d^5+16\,a^7\,b\,c\,d^7-40\,a^6\,b^2\,c^4\,d^4+6\,a^6\,b^2\,c^2\,d^6+4\,a^6\,b^2\,d^8+26\,a^5\,b^3\,c^3\,d^5-32\,a^5\,b^3\,c\,d^7-40\,a^4\,b^4\,c^6\,d^2+160\,a^4\,b^4\,c^4\,d^4-85\,a^4\,b^4\,c^2\,d^6-2\,a^4\,b^4\,d^8-13\,a^3\,b^5\,c^7\,d+26\,a^3\,b^5\,c^5\,d^3-26\,a^3\,b^5\,c^3\,d^5+16\,a^3\,b^5\,c\,d^7+11\,a^2\,b^6\,c^8+6\,a^2\,b^6\,c^6\,d^2-85\,a^2\,b^6\,c^4\,d^4+56\,a^2\,b^6\,c^2\,d^6+16\,a\,b^7\,c^7\,d-32\,a\,b^7\,c^5\,d^3+16\,a\,b^7\,c^3\,d^5-2\,b^8\,c^8+4\,b^8\,c^6\,d^2-2\,b^8\,c^4\,d^4\right)}{a\,c\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(-21\,a^9\,c^3\,d^6+6\,a^9\,c\,d^8+35\,a^8\,b\,c^4\,d^5-64\,a^8\,b\,c^2\,d^7+8\,a^8\,b\,d^9+40\,a^7\,b^2\,c^5\,d^4+74\,a^7\,b^2\,c^3\,d^6-60\,a^7\,b^2\,c\,d^8-26\,a^6\,b^3\,c^4\,d^5+96\,a^6\,b^3\,c^2\,d^7-16\,a^6\,b^3\,d^9+40\,a^5\,b^4\,c^7\,d^2-160\,a^5\,b^4\,c^5\,d^4-45\,a^5\,b^4\,c^3\,d^6+102\,a^5\,b^4\,c\,d^8+35\,a^4\,b^5\,c^8\,d-26\,a^4\,b^5\,c^6\,d^3-106\,a^4\,b^5\,c^4\,d^5+44\,a^4\,b^5\,c^2\,d^7+8\,a^4\,b^5\,d^9-21\,a^3\,b^6\,c^9+74\,a^3\,b^6\,c^7\,d^2-45\,a^3\,b^6\,c^5\,d^4+64\,a^3\,b^6\,c^3\,d^6-48\,a^3\,b^6\,c\,d^8-64\,a^2\,b^7\,c^8\,d+96\,a^2\,b^7\,c^6\,d^3+44\,a^2\,b^7\,c^4\,d^5-64\,a^2\,b^7\,c^2\,d^7+6\,a\,b^8\,c^9-60\,a\,b^8\,c^7\,d^2+102\,a\,b^8\,c^5\,d^4-48\,a\,b^8\,c^3\,d^6+8\,b^9\,c^8\,d-16\,b^9\,c^6\,d^3+8\,b^9\,c^4\,d^5\right)}{a^2\,c^2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-27\,a^9\,c^3\,d^6+6\,a^9\,c\,d^8+37\,a^8\,b\,c^4\,d^5-72\,a^8\,b\,c^2\,d^7+8\,a^8\,b\,d^9+80\,a^7\,b^2\,c^5\,d^4+34\,a^7\,b^2\,c^3\,d^6-60\,a^7\,b^2\,c\,d^8+42\,a^6\,b^3\,c^4\,d^5+64\,a^6\,b^3\,c^2\,d^7-16\,a^6\,b^3\,d^9+80\,a^5\,b^4\,c^7\,d^2-320\,a^5\,b^4\,c^5\,d^4+93\,a^5\,b^4\,c^3\,d^6+102\,a^5\,b^4\,c\,d^8+37\,a^4\,b^5\,c^8\,d+42\,a^4\,b^5\,c^6\,d^3-390\,a^4\,b^5\,c^4\,d^5+204\,a^4\,b^5\,c^2\,d^7+8\,a^4\,b^5\,d^9-27\,a^3\,b^6\,c^9+34\,a^3\,b^6\,c^7\,d^2+93\,a^3\,b^6\,c^5\,d^4-40\,a^3\,b^6\,c^3\,d^6-48\,a^3\,b^6\,c\,d^8-72\,a^2\,b^7\,c^8\,d+64\,a^2\,b^7\,c^6\,d^3+204\,a^2\,b^7\,c^4\,d^5-160\,a^2\,b^7\,c^2\,d^7+6\,a\,b^8\,c^9-60\,a\,b^8\,c^7\,d^2+102\,a\,b^8\,c^5\,d^4-48\,a\,b^8\,c^3\,d^6+8\,b^9\,c^8\,d-16\,b^9\,c^6\,d^3+8\,b^9\,c^4\,d^5\right)}{a^2\,c^2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,a^9\,c^4\,d^5+7\,a^9\,c^2\,d^7-2\,a^9\,d^9-10\,a^8\,b\,c^5\,d^4+7\,a^8\,b\,c^3\,d^6+6\,a^8\,b\,c\,d^8-52\,a^7\,b^2\,c^4\,d^5+18\,a^7\,b^2\,c^2\,d^7+4\,a^7\,b^2\,d^9+20\,a^6\,b^3\,c^5\,d^4-14\,a^6\,b^3\,c^3\,d^6-12\,a^6\,b^3\,c\,d^8-10\,a^5\,b^4\,c^8\,d+20\,a^5\,b^4\,c^6\,d^3+82\,a^5\,b^4\,c^4\,d^5-57\,a^5\,b^4\,c^2\,d^7-2\,a^5\,b^4\,d^9+4\,a^4\,b^5\,c^9-52\,a^4\,b^5\,c^7\,d^2+82\,a^4\,b^5\,c^5\,d^4-37\,a^4\,b^5\,c^3\,d^6+6\,a^4\,b^5\,c\,d^8+7\,a^3\,b^6\,c^8\,d-14\,a^3\,b^6\,c^6\,d^3-37\,a^3\,b^6\,c^4\,d^5+32\,a^3\,b^6\,c^2\,d^7+7\,a^2\,b^7\,c^9+18\,a^2\,b^7\,c^7\,d^2-57\,a^2\,b^7\,c^5\,d^4+32\,a^2\,b^7\,c^3\,d^6+6\,a\,b^8\,c^8\,d-12\,a\,b^8\,c^6\,d^3+6\,a\,b^8\,c^4\,d^5-2\,b^9\,c^9+4\,b^9\,c^7\,d^2-2\,b^9\,c^5\,d^4\right)}{a^2\,c^2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(12\,a^9\,c^4\,d^5+5\,a^9\,c^2\,d^7-2\,a^9\,d^9-30\,a^8\,b\,c^5\,d^4+45\,a^8\,b\,c^3\,d^6+6\,a^8\,b\,c\,d^8-124\,a^7\,b^2\,c^4\,d^5+66\,a^7\,b^2\,c^2\,d^7+4\,a^7\,b^2\,d^9+20\,a^6\,b^3\,c^5\,d^4-62\,a^6\,b^3\,c^3\,d^6-12\,a^6\,b^3\,c\,d^8-30\,a^5\,b^4\,c^8\,d+20\,a^5\,b^4\,c^6\,d^3+262\,a^5\,b^4\,c^4\,d^5-187\,a^5\,b^4\,c^2\,d^7-2\,a^5\,b^4\,d^9+12\,a^4\,b^5\,c^9-124\,a^4\,b^5\,c^7\,d^2+262\,a^4\,b^5\,c^5\,d^4-111\,a^4\,b^5\,c^3\,d^6+6\,a^4\,b^5\,c\,d^8+45\,a^3\,b^6\,c^8\,d-62\,a^3\,b^6\,c^6\,d^3-111\,a^3\,b^6\,c^4\,d^5+104\,a^3\,b^6\,c^2\,d^7+5\,a^2\,b^7\,c^9+66\,a^2\,b^7\,c^7\,d^2-187\,a^2\,b^7\,c^5\,d^4+104\,a^2\,b^7\,c^3\,d^6+6\,a\,b^8\,c^8\,d-12\,a\,b^8\,c^6\,d^3+6\,a\,b^8\,c^4\,d^5-2\,b^9\,c^9+4\,b^9\,c^7\,d^2-2\,b^9\,c^5\,d^4\right)}{a^2\,c^2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(5\,a^8\,c^2\,d^6-2\,a^8\,d^8-11\,a^7\,b\,c^3\,d^5+8\,a^7\,b\,c\,d^7-10\,a^6\,b^2\,c^2\,d^6+4\,a^6\,b^2\,d^8+22\,a^5\,b^3\,c^3\,d^5-16\,a^5\,b^3\,c\,d^7+5\,a^4\,b^4\,c^2\,d^6-2\,a^4\,b^4\,d^8-11\,a^3\,b^5\,c^7\,d+22\,a^3\,b^5\,c^5\,d^3-22\,a^3\,b^5\,c^3\,d^5+8\,a^3\,b^5\,c\,d^7+5\,a^2\,b^6\,c^8-10\,a^2\,b^6\,c^6\,d^2+5\,a^2\,b^6\,c^4\,d^4+8\,a\,b^7\,c^7\,d-16\,a\,b^7\,c^5\,d^3+8\,a\,b^7\,c^3\,d^5-2\,b^8\,c^8+4\,b^8\,c^6\,d^2-2\,b^8\,c^4\,d^4\right)}{a\,c\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a^2\,c^2+4\,a^2\,d^2+16\,a\,b\,c\,d+4\,b^2\,c^2+8\,b^2\,d^2\right)\,\left(-4\,a^7\,c^2\,d^5+a^7\,d^7+10\,a^6\,b\,c^3\,d^4-7\,a^6\,b\,c\,d^6+8\,a^5\,b^2\,c^2\,d^5-2\,a^5\,b^2\,d^7-20\,a^4\,b^3\,c^3\,d^4+14\,a^4\,b^3\,c\,d^6+10\,a^3\,b^4\,c^6\,d-20\,a^3\,b^4\,c^4\,d^3+6\,a^3\,b^4\,c^2\,d^5+a^3\,b^4\,d^7-4\,a^2\,b^5\,c^7+8\,a^2\,b^5\,c^5\,d^2+6\,a^2\,b^5\,c^3\,d^4-7\,a^2\,b^5\,c\,d^6-7\,a\,b^6\,c^6\,d+14\,a\,b^6\,c^4\,d^3-7\,a\,b^6\,c^2\,d^5+b^7\,c^7-2\,b^7\,c^5\,d^2+b^7\,c^3\,d^4\right)}{a^2\,c^2\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)\,\left(a^4\,c^4-2\,a^4\,c^2\,d^2+a^4\,d^4-2\,a^2\,b^2\,c^4+4\,a^2\,b^2\,c^2\,d^2-2\,a^2\,b^2\,d^4+b^4\,c^4-2\,b^4\,c^2\,d^2+b^4\,d^4\right)}}{f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,d\,a^2\,c+4\,b\,a\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,a^2\,c^2+8\,a^2\,d^2+32\,a\,b\,c\,d+8\,b^2\,c^2+16\,b^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,a^2\,c^2+4\,a^2\,d^2+16\,a\,b\,c\,d+4\,b^2\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,a^2\,c^2+4\,a^2\,d^2+16\,a\,b\,c\,d+4\,b^2\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,a^2\,c\,d+12\,a\,b\,c^2+16\,a\,b\,d^2+16\,b^2\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(12\,a^2\,c\,d+12\,a\,b\,c^2+16\,a\,b\,d^2+16\,b^2\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(4\,d\,a^2\,c+4\,b\,a\,c^2\right)+a^2\,c^2+a^2\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{\frac{\sqrt{\frac{{\left(16\,a^{24}\,c^4\,d^{20}+16\,a^{24}\,c^2\,d^{22}+4\,a^{24}\,d^{24}-320\,a^{23}\,b\,c^5\,d^{19}-176\,a^{23}\,b\,c^3\,d^{21}-8\,a^{23}\,b\,c\,d^{23}+3040\,a^{22}\,b^2\,c^6\,d^{18}+176\,a^{22}\,b^2\,c^4\,d^{20}-196\,a^{22}\,b^2\,c^2\,d^{22}+76\,a^{22}\,b^2\,d^{24}-17920\,a^{21}\,b^3\,c^7\,d^{17}+8160\,a^{21}\,b^3\,c^5\,d^{19}-288\,a^{21}\,b^3\,c^3\,d^{21}-536\,a^{21}\,b^3\,c\,d^{23}+72560\,a^{20}\,b^4\,c^8\,d^{16}-72240\,a^{20}\,b^4\,c^6\,d^{18}+21124\,a^{20}\,b^4\,c^4\,d^{20}-1564\,a^{20}\,b^4\,c^2\,d^{22}+136\,a^{20}\,b^4\,d^{24}-212032\,a^{19}\,b^5\,c^9\,d^{15}+336688\,a^{19}\,b^5\,c^7\,d^{17}-170968\,a^{19}\,b^5\,c^5\,d^{19}+37680\,a^{19}\,b^5\,c^3\,d^{21}-2960\,a^{19}\,b^5\,c\,d^{23}+460480\,a^{18}\,b^6\,c^{10}\,d^{14}-1058448\,a^{18}\,b^6\,c^8\,d^{16}+793756\,a^{18}\,b^6\,c^6\,d^{18}-276020\,a^{18}\,b^6\,c^4\,d^{20}+44120\,a^{18}\,b^6\,c^2\,d^{22}-3560\,a^{18}\,b^6\,d^{24}-762560\,a^{17}\,b^7\,c^{11}\,d^{13}+2478528\,a^{17}\,b^7\,c^9\,d^{15}-2621008\,a^{17}\,b^7\,c^7\,d^{17}+1310168\,a^{17}\,b^7\,c^5\,d^{19}-335040\,a^{17}\,b^7\,c^3\,d^{21}+40720\,a^{17}\,b^7\,c\,d^{23}+999040\,a^{16}\,b^8\,c^{12}\,d^{12}-4591360\,a^{16}\,b^8\,c^{10}\,d^{14}+6661036\,a^{16}\,b^8\,c^8\,d^{16}-4506428\,a^{16}\,b^8\,c^6\,d^{18}+1586920\,a^{16}\,b^8\,c^4\,d^{20}-263320\,a^{16}\,b^8\,c^2\,d^{22}+9460\,a^{16}\,b^8\,d^{24}-1104320\,a^{15}\,b^9\,c^{13}\,d^{11}+6995840\,a^{15}\,b^9\,c^{11}\,d^{13}-13462088\,a^{15}\,b^9\,c^9\,d^{15}+11779808\,a^{15}\,b^9\,c^7\,d^{17}-5365072\,a^{15}\,b^9\,c^5\,d^{19}+1210560\,a^{15}\,b^9\,c^3\,d^{21}-101240\,a^{15}\,b^9\,c\,d^{23}+1124032\,a^{14}\,b^{10}\,c^{14}\,d^{10}-8958208\,a^{14}\,b^{10}\,c^{12}\,d^{12}+21989928\,a^{14}\,b^{10}\,c^{10}\,d^{14}-24199280\,a^{14}\,b^{10}\,c^8\,d^{16}+13887520\,a^{14}\,b^{10}\,c^6\,d^{18}-4147952\,a^{14}\,b^{10}\,c^4\,d^{20}+547088\,a^{14}\,b^{10}\,c^2\,d^{22}-10568\,a^{14}\,b^{10}\,d^{24}-1104320\,a^{13}\,b^{11}\,c^{15}\,d^9+9722048\,a^{13}\,b^{11}\,c^{13}\,d^{11}-29358696\,a^{13}\,b^{11}\,c^{11}\,d^{13}+39987520\,a^{13}\,b^{11}\,c^9\,d^{15}-28461040\,a^{13}\,b^{11}\,c^7\,d^{17}+10875200\,a^{13}\,b^{11}\,c^5\,d^{19}-2002728\,a^{13}\,b^{11}\,c^3\,d^{21}+109456\,a^{13}\,b^{11}\,c\,d^{23}+999040\,a^{12}\,b^{12}\,c^{16}\,d^8-8958208\,a^{12}\,b^{12}\,c^{14}\,d^{10}+32294808\,a^{12}\,b^{12}\,c^{12}\,d^{12}-53854288\,a^{12}\,b^{12}\,c^{10}\,d^{14}+46972560\,a^{12}\,b^{12}\,c^8\,d^{16}-22419600\,a^{12}\,b^{12}\,c^6\,d^{18}+5501328\,a^{12}\,b^{12}\,c^4\,d^{20}-541208\,a^{12}\,b^{12}\,c^2\,d^{22}+5568\,a^{12}\,b^{12}\,d^{24}-762560\,a^{11}\,b^{13}\,c^{17}\,d^7+6995840\,a^{11}\,b^{13}\,c^{15}\,d^9-29358696\,a^{11}\,b^{13}\,c^{13}\,d^{11}+59445728\,a^{11}\,b^{13}\,c^{11}\,d^{13}-63124080\,a^{11}\,b^{13}\,c^9\,d^{15}+37153600\,a^{11}\,b^{13}\,c^7\,d^{17}-11781560\,a^{11}\,b^{13}\,c^5\,d^{19}+1720736\,a^{11}\,b^{13}\,c^3\,d^{21}-56448\,a^{11}\,b^{13}\,c\,d^{23}+460480\,a^{10}\,b^{14}\,c^{18}\,d^6-4591360\,a^{10}\,b^{14}\,c^{16}\,d^8+21989928\,a^{10}\,b^{14}\,c^{14}\,d^{10}-53854288\,a^{10}\,b^{14}\,c^{12}\,d^{12}+69593872\,a^{10}\,b^{14}\,c^{10}\,d^{14}-50137600\,a^{10}\,b^{14}\,c^8\,d^{16}+20019440\,a^{10}\,b^{14}\,c^6\,d^{18}-3975688\,a^{10}\,b^{14}\,c^4\,d^{20}+263808\,a^{10}\,b^{14}\,c^2\,d^{22}-1152\,a^{10}\,b^{14}\,d^{24}-212032\,a^9\,b^{15}\,c^{19}\,d^5+2478528\,a^9\,b^{15}\,c^{17}\,d^7-13462088\,a^9\,b^{15}\,c^{15}\,d^9+39987520\,a^9\,b^{15}\,c^{13}\,d^{11}-63124080\,a^9\,b^{15}\,c^{11}\,d^{13}+55383904\,a^9\,b^{15}\,c^9\,d^{15}-27336616\,a^9\,b^{15}\,c^7\,d^{17}+7078256\,a^9\,b^{15}\,c^5\,d^{19}-758400\,a^9\,b^{15}\,c^3\,d^{21}+11520\,a^9\,b^{15}\,c\,d^{23}+72560\,a^8\,b^{16}\,c^{20}\,d^4-1058448\,a^8\,b^{16}\,c^{18}\,d^6+6661036\,a^8\,b^{16}\,c^{16}\,d^8-24199280\,a^8\,b^{16}\,c^{14}\,d^{10}+46972560\,a^8\,b^{16}\,c^{12}\,d^{12}-50137600\,a^8\,b^{16}\,c^{10}\,d^{14}+30289656\,a^8\,b^{16}\,c^8\,d^{16}-9955992\,a^8\,b^{16}\,c^6\,d^{18}+1512000\,a^8\,b^{16}\,c^4\,d^{20}-51840\,a^8\,b^{16}\,c^2\,d^{22}-17920\,a^7\,b^{17}\,c^{21}\,d^3+336688\,a^7\,b^{17}\,c^{19}\,d^5-2621008\,a^7\,b^{17}\,c^{17}\,d^7+11779808\,a^7\,b^{17}\,c^{15}\,d^9-28461040\,a^7\,b^{17}\,c^{13}\,d^{11}+37153600\,a^7\,b^{17}\,c^{11}\,d^{13}-27336616\,a^7\,b^{17}\,c^9\,d^{15}+11150016\,a^7\,b^{17}\,c^7\,d^{17}-2232576\,a^7\,b^{17}\,c^5\,d^{19}+138240\,a^7\,b^{17}\,c^3\,d^{21}+3040\,a^6\,b^{18}\,c^{22}\,d^2-72240\,a^6\,b^{18}\,c^{20}\,d^4+793756\,a^6\,b^{18}\,c^{18}\,d^6-4506428\,a^6\,b^{18}\,c^{16}\,d^8+13887520\,a^6\,b^{18}\,c^{14}\,d^{10}-22419600\,a^6\,b^{18}\,c^{12}\,d^{12}+20019440\,a^6\,b^{18}\,c^{10}\,d^{14}-9955992\,a^6\,b^{18}\,c^8\,d^{16}+2532096\,a^6\,b^{18}\,c^6\,d^{18}-241920\,a^6\,b^{18}\,c^4\,d^{20}-320\,a^5\,b^{19}\,c^{23}\,d+8160\,a^5\,b^{19}\,c^{21}\,d^3-170968\,a^5\,b^{19}\,c^{19}\,d^5+1310168\,a^5\,b^{19}\,c^{17}\,d^7-5365072\,a^5\,b^{19}\,c^{15}\,d^9+10875200\,a^5\,b^{19}\,c^{13}\,d^{11}-11781560\,a^5\,b^{19}\,c^{11}\,d^{13}+7078256\,a^5\,b^{19}\,c^9\,d^{15}-2232576\,a^5\,b^{19}\,c^7\,d^{17}+290304\,a^5\,b^{19}\,c^5\,d^{19}+16\,a^4\,b^{20}\,c^{24}+176\,a^4\,b^{20}\,c^{22}\,d^2+21124\,a^4\,b^{20}\,c^{20}\,d^4-276020\,a^4\,b^{20}\,c^{18}\,d^6+1586920\,a^4\,b^{20}\,c^{16}\,d^8-4147952\,a^4\,b^{20}\,c^{14}\,d^{10}+5501328\,a^4\,b^{20}\,c^{12}\,d^{12}-3975688\,a^4\,b^{20}\,c^{10}\,d^{14}+1512000\,a^4\,b^{20}\,c^8\,d^{16}-241920\,a^4\,b^{20}\,c^6\,d^{18}-176\,a^3\,b^{21}\,c^{23}\,d-288\,a^3\,b^{21}\,c^{21}\,d^3+37680\,a^3\,b^{21}\,c^{19}\,d^5-335040\,a^3\,b^{21}\,c^{17}\,d^7+1210560\,a^3\,b^{21}\,c^{15}\,d^9-2002728\,a^3\,b^{21}\,c^{13}\,d^{11}+1720736\,a^3\,b^{21}\,c^{11}\,d^{13}-758400\,a^3\,b^{21}\,c^9\,d^{15}+138240\,a^3\,b^{21}\,c^7\,d^{17}+16\,a^2\,b^{22}\,c^{24}-196\,a^2\,b^{22}\,c^{22}\,d^2-1564\,a^2\,b^{22}\,c^{20}\,d^4+44120\,a^2\,b^{22}\,c^{18}\,d^6-263320\,a^2\,b^{22}\,c^{16}\,d^8+547088\,a^2\,b^{22}\,c^{14}\,d^{10}-541208\,a^2\,b^{22}\,c^{12}\,d^{12}+263808\,a^2\,b^{22}\,c^{10}\,d^{14}-51840\,a^2\,b^{22}\,c^8\,d^{16}-8\,a\,b^{23}\,c^{23}\,d-536\,a\,b^{23}\,c^{21}\,d^3-2960\,a\,b^{23}\,c^{19}\,d^5+40720\,a\,b^{23}\,c^{17}\,d^7-101240\,a\,b^{23}\,c^{15}\,d^9+109456\,a\,b^{23}\,c^{13}\,d^{11}-56448\,a\,b^{23}\,c^{11}\,d^{13}+11520\,a\,b^{23}\,c^9\,d^{15}+4\,b^{24}\,c^{24}+76\,b^{24}\,c^{22}\,d^2+136\,b^{24}\,c^{20}\,d^4-3560\,b^{24}\,c^{18}\,d^6+9460\,b^{24}\,c^{16}\,d^8-10568\,b^{24}\,c^{14}\,d^{10}+5568\,b^{24}\,c^{12}\,d^{12}-1152\,b^{24}\,c^{10}\,d^{14}\right)}^2}{4}-\left(1600\,a^{12}\,b^6\,c^4\,d^{14}+1600\,a^{12}\,b^6\,c^2\,d^{16}+400\,a^{12}\,b^6\,d^{18}-17600\,a^{11}\,b^7\,c^5\,d^{13}-3200\,a^{11}\,b^7\,c^3\,d^{15}+2800\,a^{11}\,b^7\,c\,d^{17}+88720\,a^{10}\,b^8\,c^6\,d^{12}-64720\,a^{10}\,b^8\,c^4\,d^{14}-5260\,a^{10}\,b^8\,c^2\,d^{16}+8440\,a^{10}\,b^8\,d^{18}-239360\,a^9\,b^9\,c^7\,d^{11}+406880\,a^9\,b^9\,c^5\,d^{13}-182200\,a^9\,b^9\,c^3\,d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1}\,c^{21}\,d^3+37680\,a^3\,b^{21}\,c^{19}\,d^5-335040\,a^3\,b^{21}\,c^{17}\,d^7+1210560\,a^3\,b^{21}\,c^{15}\,d^9-2002728\,a^3\,b^{21}\,c^{13}\,d^{11}+1720736\,a^3\,b^{21}\,c^{11}\,d^{13}-758400\,a^3\,b^{21}\,c^9\,d^{15}+138240\,a^3\,b^{21}\,c^7\,d^{17}+16\,a^2\,b^{22}\,c^{24}-196\,a^2\,b^{22}\,c^{22}\,d^2-1564\,a^2\,b^{22}\,c^{20}\,d^4+44120\,a^2\,b^{22}\,c^{18}\,d^6-263320\,a^2\,b^{22}\,c^{16}\,d^8+547088\,a^2\,b^{22}\,c^{14}\,d^{10}-541208\,a^2\,b^{22}\,c^{12}\,d^{12}+263808\,a^2\,b^{22}\,c^{10}\,d^{14}-51840\,a^2\,b^{22}\,c^8\,d^{16}-8\,a\,b^{23}\,c^{23}\,d-536\,a\,b^{23}\,c^{21}\,d^3-2960\,a\,b^{23}\,c^{19}\,d^5+40720\,a\,b^{23}\,c^{17}\,d^7-101240\,a\,b^{23}\,c^{15}\,d^9+109456\,a\,b^{23}\,c^{13}\,d^{11}-56448\,a\,b^{23}\,c^{11}\,d^{13}+11520\,a\,b^{23}\,c^9\,d^{15}+4\,b^{24}\,c^{24}+76\,b^{24}\,c^{22}\,d^2+136\,b^{24}\,c^{20}\,d^4-3560\,b^{24}\,c^{18}\,d^6+9460\,b^{24}\,c^{16}\,d^8-10568\,b^{24}\,c^{14}\,d^{10}+5568\,b^{24}\,c^{12}\,d^{12}-1152\,b^{24}\,c^{10}\,d^{14}\right)}^2}{4}-\left(1600\,a^{12}\,b^6\,c^4\,d^{14}+1600\,a^{12}\,b^6\,c^2\,d^{16}+400\,a^{12}\,b^6\,d^{18}-17600\,a^{11}\,b^7\,c^5\,d^{13}-3200\,a^{11}\,b^7\,c^3\,d^{15}+2800\,a^{11}\,b^7\,c\,d^{17}+88720\,a^{10}\,b^8\,c^6\,d^{12}-64720\,a^{10}\,b^8\,c^4\,d^{14}-5260\,a^{10}\,b^8\,c^2\,d^{16}+8440\,a^{10}\,b^8\,d^{18}-239360\,a^9\,b^9\,c^7\,d^{11}+406880\,a^9\,b^9\,c^5\,d^{13}-182200\,a^9\,b^9\,c^3\,d^{15}+20260\,a^9\,b^9\,c\,d^{17}+354016\,a^8\,b^{10}\,c^8\,d^{10}-1026928\,a^8\,b^{10}\,c^6\,d^{12}+900624\,a^8\,b^{10}\,c^4\,d^{14}-308392\,a^8\,b^{10}\,c^2\,d^{16}+31081\,a^8\,b^{10}\,d^{18}-239360\,a^7\,b^{11}\,c^9\,d^9+1206848\,a^7\,b^{11}\,c^7\,d^{11}-1641528\,a^7\,b^{11}\,c^5\,d^{13}+838256\,a^7\,b^{11}\,c^3\,d^{15}-141104\,a^7\,b^{11}\,c\,d^{17}+88720\,a^6\,b^{12}\,c^{10}\,d^8-1026928\,a^6\,b^{12}\,c^8\,d^{10}+2430936\,a^6\,b^{12}\,c^6\,d^{12}-2218576\,a^6\,b^{12}\,c^4\,d^{14}+901948\,a^6\,b^{12}\,c^2\,d^{16}-136032\,a^6\,b^{12}\,d^{18}-17600\,a^5\,b^{13}\,c^{11}\,d^7+406880\,a^5\,b^{13}\,c^9\,d^9-1641528\,a^5\,b^{13}\,c^7\,d^{11}+2158808\,a^5\,b^{13}\,c^5\,d^{13}-1158992\,a^5\,b^{13}\,c^3\,d^{15}+216576\,a^5\,b^{13}\,c\,d^{17}+1600\,a^4\,b^{14}\,c^{12}\,d^6-64720\,a^4\,b^{14}\,c^{10}\,d^8+900624\,a^4\,b^{14}\,c^8\,d^{10}-2218576\,a^4\,b^{14}\,c^6\,d^{12}+2185654\,a^4\,b^{14}\,c^4\,d^{14}-989856\,a^4\,b^{14}\,c^2\,d^{16}+173664\,a^4\,b^{14}\,d^{18}-3200\,a^3\,b^{15}\,c^{11}\,d^7-182200\,a^3\,b^{15}\,c^9\,d^9+838256\,a^3\,b^{15}\,c^7\,d^{11}-1158992\,a^3\,b^{15}\,c^5\,d^{13}+657408\,a^3\,b^{15}\,c^3\,d^{15}-131328\,a^3\,b^{15}\,c\,d^{17}+1600\,a^2\,b^{16}\,c^{12}\,d^6-5260\,a^2\,b^{16}\,c^{10}\,d^8-308392\,a^2\,b^{16}\,c^8\,d^{10}+901948\,a^2\,b^{16}\,c^6\,d^{12}-989856\,a^2\,b^{16}\,c^4\,d^{14}+495936\,a^2\,b^{16}\,c^2\,d^{16}-96768\,a^2\,b^{16}\,d^{18}+2800\,a\,b^{17}\,c^{11}\,d^7+20260\,a\,b^{17}\,c^9\,d^9-141104\,a\,b^{17}\,c^7\,d^{11}+216576\,a\,b^{17}\,c^5\,d^{13}-131328\,a\,b^{17}\,c^3\,d^{15}+27648\,a\,b^{17}\,c\,d^{17}+400\,b^{18}\,c^{12}\,d^6+8440\,b^{18}\,c^{10}\,d^8+31081\,b^{18}\,c^8\,d^{10}-136032\,b^{18}\,c^6\,d^{12}+173664\,b^{18}\,c^4\,d^{14}-96768\,b^{18}\,c^2\,d^{16}+20736\,b^{18}\,d^{18}\right)\,\left(16\,a^{30}\,c^{10}\,d^{20}-80\,a^{30}\,c^8\,d^{22}+160\,a^{30}\,c^6\,d^{24}-160\,a^{30}\,c^4\,d^{26}+80\,a^{30}\,c^2\,d^{28}-16\,a^{30}\,d^{30}-320\,a^{29}\,b\,c^{11}\,d^{19}+1600\,a^{29}\,b\,c^9\,d^{21}-3200\,a^{29}\,b\,c^7\,d^{23}+3200\,a^{29}\,b\,c^5\,d^{25}-1600\,a^{29}\,b\,c^3\,d^{27}+320\,a^{29}\,b\,c\,d^{29}+3040\,a^{28}\,b^2\,c^{12}\,d^{18}-15280\,a^{28}\,b^2\,c^{10}\,d^{20}+30800\,a^{28}\,b^2\,c^8\,d^{22}-31200\,a^{28}\,b^2\,c^6\,d^{24}+16000\,a^{28}\,b^2\,c^4\,d^{26}-3440\,a^{28}\,b^2\,c^2\,d^{28}+80\,a^{28}\,b^2\,d^{30}-18240\,a^{27}\,b^3\,c^{13}\,d^{17}+92800\,a^{27}\,b^3\,c^{11}\,d^{19}-190400\,a^{27}\,b^3\,c^9\,d^{21}+198400\,a^{27}\,b^3\,c^7\,d^{23}-107200\,a^{27}\,b^3\,c^5\,d^{25}+26240\,a^{27}\,b^3\,c^3\,d^{27}-1600\,a^{27}\,b^3\,c\,d^{29}+77520\,a^{26}\,b^4\,c^{14}\,d^{16}-402800\,a^{26}\,b^4\,c^{12}\,d^{18}+851360\,a^{26}\,b^4\,c^{10}\,d^{20}-928000\,a^{26}\,b^4\,c^8\,d^{22}+541200\,a^{26}\,b^4\,c^6\,d^{24}-155120\,a^{26}\,b^4\,c^4\,d^{26}+16000\,a^{26}\,b^4\,c^2\,d^{28}-160\,a^{26}\,b^4\,d^{30}-248064\,a^{25}\,b^5\,c^{15}\,d^{15}+1331520\,a^{25}\,b^5\,c^{13}\,d^{17}-2939840\,a^{25}\,b^5\,c^{11}\,d^{19}+3408640\,a^{25}\,b^5\,c^9\,d^{21}-2184320\,a^{25}\,b^5\,c^7\,d^{23}+736064\,a^{25}\,b^5\,c^5\,d^{25}-107200\,a^{25}\,b^5\,c^3\,d^{27}+3200\,a^{25}\,b^5\,c\,d^{29}+620160\,a^{24}\,b^6\,c^{16}\,d^{14}-3488400\,a^{24}\,b^6\,c^{14}\,d^{16}+8170000\,a^{24}\,b^6\,c^{12}\,d^{18}-10229760\,a^{24}\,b^6\,c^{10}\,d^{20}+7281600\,a^{24}\,b^6\,c^8\,d^{22}-2863760\,a^{24}\,b^6\,c^6\,d^{24}+541200\,a^{24}\,b^6\,c^4\,d^{26}-31200\,a^{24}\,b^6\,c^2\,d^{28}+160\,a^{24}\,b^6\,d^{30}-1240320\,a^{23}\,b^7\,c^{17}\,d^{13}+7441920\,a^{23}\,b^7\,c^{15}\,d^{15}-18787200\,a^{23}\,b^7\,c^{13}\,d^{17}+25721600\,a^{23}\,b^7\,c^{11}\,d^{19}-20444800\,a^{23}\,b^7\,c^9\,d^{21}+9297920\,a^{23}\,b^7\,c^7\,d^{23}-2184320\,a^{23}\,b^7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,a\,b^{23}\,c^9\,d^{15}+4\,b^{24}\,c^{24}+76\,b^{24}\,c^{22}\,d^2+136\,b^{24}\,c^{20}\,d^4-3560\,b^{24}\,c^{18}\,d^6+9460\,b^{24}\,c^{16}\,d^8-10568\,b^{24}\,c^{14}\,d^{10}+5568\,b^{24}\,c^{12}\,d^{12}-1152\,b^{24}\,c^{10}\,d^{14}\right)}^2}{4}-\left(1600\,a^{12}\,b^6\,c^4\,d^{14}+1600\,a^{12}\,b^6\,c^2\,d^{16}+400\,a^{12}\,b^6\,d^{18}-17600\,a^{11}\,b^7\,c^5\,d^{13}-3200\,a^{11}\,b^7\,c^3\,d^{15}+2800\,a^{11}\,b^7\,c\,d^{17}+88720\,a^{10}\,b^8\,c^6\,d^{12}-64720\,a^{10}\,b^8\,c^4\,d^{14}-5260\,a^{10}\,b^8\,c^2\,d^{16}+8440\,a^{10}\,b^8\,d^{18}-239360\,a^9\,b^9\,c^7\,d^{11}+406880\,a^9\,b^9\,c^5\,d^{13}-182200\,a^9\,b^9\,c^3\,d^{15}+20260\,a^9\,b^9\,c\,d^{17}+354016\,a^8\,b^{10}\,c^8\,d^{10}-1026928\,a^8\,b^{10}\,c^6\,d^{12}+900624\,a^8\,b^{10}\,c^4\,d^{14}-308392\,a^8\,b^{10}\,c^2\,d^{16}+31081\,a^8\,b^{10}\,d^{18}-239360\,a^7\,b^{11}\,c^9\,d^9+1206848\,a^7\,b^{11}\,c^7\,d^{11}-1641528\,a^7\,b^{11}\,c^5\,d^{13}+838256\,a^7\,b^{11}\,c^3\,d^{15}-141104\,a^7\,b^{11}\,c\,d^{17}+88720\,a^6\,b^{12}\,c^{10}\,d^8-1026928\,a^6\,b^{12}\,c^8\,d^{10}+2430936\,a^6\,b^{12}\,c^6\,d^{12}-2218576\,a^6\,b^{12}\,c^4\,d^{14}+901948\,a^6\,b^{12}\,c^2\,d^{16}-136032\,a^6\,b^{12}\,d^{18}-17600\,a^5\,b^{13}\,c^{11}\,d^7+406880\,a^5\,b^{13}\,c^9\,d^9-1641528\,a^5\,b^{13}\,c^7\,d^{11}+2158808\,a^5\,b^{13}\,c^5\,d^{13}-1158992\,a^5\,b^{13}\,c^3\,d^{15}+216576\,a^5\,b^{13}\,c\,d^{17}+1600\,a^4\,b^{14}\,c^{12}\,d^6-64720\,a^4\,b^{14}\,c^{10}\,d^8+900624\,a^4\,b^{14}\,c^8\,d^{10}-2218576\,a^4\,b^{14}\,c^6\,d^{12}+2185654\,a^4\,b^{14}\,c^4\,d^{14}-989856\,a^4\,b^{14}\,c^2\,d^{16}+173664\,a^4\,b^{14}\,d^{18}-3200\,a^3\,b^{15}\,c^{11}\,d^7-182200\,a^3\,b^{15}\,c^9\,d^9+838256\,a^3\,b^{15}\,c^7\,d^{11}-1158992\,a^3\,b^{15}\,c^5\,d^{13}+657408\,a^3\,b^{15}\,c^3\,d^{15}-131328\,a^3\,b^{15}\,c\,d^{17}+1600\,a^2\,b^{16}\,c^{12}\,d^6-5260\,a^2\,b^{16}\,c^{10}\,d^8-308392\,a^2\,b^{16}\,c^8\,d^{10}+901948\,a^2\,b^{16}\,c^6\,d^{12}-989856\,a^2\,b^{16}\,c^4\,d^{14}+495936\,a^2\,b^{16}\,c^2\,d^{16}-96768\,a^2\,b^{16}\,d^{18}+2800\,a\,b^{17}\,c^{11}\,d^7+20260\,a\,b^{17}\,c^9\,d^9-141104\,a\,b^{17}\,c^7\,d^{11}+216576\,a\,b^{17}\,c^5\,d^{13}-131328\,a\,b^{17}\,c^3\,d^{15}+27648\,a\,b^{17}\,c\,d^{17}+400\,b^{18}\,c^{12}\,d^6+8440\,b^{18}\,c^{10}\,d^8+31081\,b^{18}\,c^8\,d^{10}-136032\,b^{18}\,c^6\,d^{12}+173664\,b^{18}\,c^4\,d^{14}-96768\,b^{18}\,c^2\,d^{16}+20736\,b^{18}\,d^{18}\right)\,\left(16\,a^{30}\,c^{10}\,d^{20}-80\,a^{30}\,c^8\,d^{22}+160\,a^{30}\,c^6\,d^{24}-160\,a^{30}\,c^4\,d^{26}+80\,a^{30}\,c^2\,d^{28}-16\,a^{30}\,d^{30}-320\,a^{29}\,b\,c^{11}\,d^{19}+1600\,a^{29}\,b\,c^9\,d^{21}-3200\,a^{29}\,b\,c^7\,d^{23}+3200\,a^{29}\,b\,c^5\,d^{25}-1600\,a^{29}\,b\,c^3\,d^{27}+320\,a^{29}\,b\,c\,d^{29}+3040\,a^{28}\,b^2\,c^{12}\,d^{18}-15280\,a^{28}\,b^2\,c^{10}\,d^{20}+30800\,a^{28}\,b^2\,c^8\,d^{22}-31200\,a^{28}\,b^2\,c^6\,d^{24}+16000\,a^{28}\,b^2\,c^4\,d^{26}-3440\,a^{28}\,b^2\,c^2\,d^{28}+80\,a^{28}\,b^2\,d^{30}-18240\,a^{27}\,b^3\,c^{13}\,d^{17}+92800\,a^{27}\,b^3\,c^{11}\,d^{19}-190400\,a^{27}\,b^3\,c^9\,d^{21}+198400\,a^{27}\,b^3\,c^7\,d^{23}-107200\,a^{27}\,b^3\,c^5\,d^{25}+26240\,a^{27}\,b^3\,c^3\,d^{27}-1600\,a^{27}\,b^3\,c\,d^{29}+77520\,a^{26}\,b^4\,c^{14}\,d^{16}-402800\,a^{26}\,b^4\,c^{12}\,d^{18}+851360\,a^{26}\,b^4\,c^{10}\,d^{20}-928000\,a^{26}\,b^4\,c^8\,d^{22}+541200\,a^{26}\,b^4\,c^6\,d^{24}-155120\,a^{26}\,b^4\,c^4\,d^{26}+16000\,a^{26}\,b^4\,c^2\,d^{28}-160\,a^{26}\,b^4\,d^{30}-248064\,a^{25}\,b^5\,c^{15}\,d^{15}+1331520\,a^{25}\,b^5\,c^{13}\,d^{17}-2939840\,a^{25}\,b^5\,c^{11}\,d^{19}+3408640\,a^{25}\,b^5\,c^9\,d^{21}-2184320\,a^{25}\,b^5\,c^7\,d^{23}+736064\,a^{25}\,b^5\,c^5\,d^{25}-107200\,a^{25}\,b^5\,c^3\,d^{27}+3200\,a^{25}\,b^5\,c\,d^{29}+620160\,a^{24}\,b^6\,c^{16}\,d^{14}-3488400\,a^{24}\,b^6\,c^{14}\,d^{16}+8170000\,a^{24}\,b^6\,c^{12}\,d^{18}-10229760\,a^{24}\,b^6\,c^{10}\,d^{20}+7281600\,a^{24}\,b^6\,c^8\,d^{22}-2863760\,a^{24}\,b^6\,c^6\,d^{24}+541200\,a^{24}\,b^6\,c^4\,d^{26}-31200\,a^{24}\,b^6\,c^2\,d^{28}+160\,a^{24}\,b^6\,d^{30}-1240320\,a^{23}\,b^7\,c^{17}\,d^{13}+7441920\,a^{23}\,b^7\,c^{15}\,d^{15}-18787200\,a^{23}\,b^7\,c^{13}\,d^{17}+25721600\,a^{23}\,b^7\,c^{11}\,d^{19}-20444800\,a^{23}\,b^7\,c^9\,d^{21}+9297920\,a^{23}\,b^7\,c^7\,d^{23}-2184320\,a^{23}\,b^7\,c^5\,d^{25}+198400\,a^{23}\,b^7\,c^3\,d^{27}-3200\,a^{23}\,b^7\,c\,d^{29}+2015520\,a^{22}\,b^8\,c^{18}\,d^{12}-13178400\,a^{22}\,b^8\,c^{16}\,d^{14}+36434400\,a^{22}\,b^8\,c^{14}\,d^{16}-55069600\,a^{22}\,b^8\,c^{12}\,d^{18}+48989680\,a^{22}\,b^8\,c^{10}\,d^{20}-25575920\,a^{22}\,b^8\,c^8\,d^{22}+7281600\,a^{22}\,b^8\,c^6\,d^{24}-928000\,a^{22}\,b^8\,c^4\,d^{26}+30800\,a^{22}\,b^8\,c^2\,d^{28}-80\,a^{22}\,b^8\,d^{30}-2687360\,a^{21}\,b^9\,c^{19}\,d^{11}+19638400\,a^{21}\,b^9\,c^{17}\,d^{13}-60362240\,a^{21}\,b^9\,c^{15}\,d^{15}+101475200\,a^{21}\,b^9\,c^{13}\,d^{17}-101172800\,a^{21}\,b^9\,c^{11}\,d^{19}+60333760\,a^{21}\,b^9\,c^9\,d^{21}-20444800\,a^{21}\,b^9\,c^7\,d^{23}+3408640\,a^{21}\,b^9\,c^5\,d^{25}-190400\,a^{21}\,b^9\,c^3\,d^{27}+1600\,a^{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9}\,c^{15}\,d^9+10875200\,a^5\,b^{19}\,c^{13}\,d^{11}-11781560\,a^5\,b^{19}\,c^{11}\,d^{13}+7078256\,a^5\,b^{19}\,c^9\,d^{15}-2232576\,a^5\,b^{19}\,c^7\,d^{17}+290304\,a^5\,b^{19}\,c^5\,d^{19}+16\,a^4\,b^{20}\,c^{24}+176\,a^4\,b^{20}\,c^{22}\,d^2+21124\,a^4\,b^{20}\,c^{20}\,d^4-276020\,a^4\,b^{20}\,c^{18}\,d^6+1586920\,a^4\,b^{20}\,c^{16}\,d^8-4147952\,a^4\,b^{20}\,c^{14}\,d^{10}+5501328\,a^4\,b^{20}\,c^{12}\,d^{12}-3975688\,a^4\,b^{20}\,c^{10}\,d^{14}+1512000\,a^4\,b^{20}\,c^8\,d^{16}-241920\,a^4\,b^{20}\,c^6\,d^{18}-176\,a^3\,b^{21}\,c^{23}\,d-288\,a^3\,b^{21}\,c^{21}\,d^3+37680\,a^3\,b^{21}\,c^{19}\,d^5-335040\,a^3\,b^{21}\,c^{17}\,d^7+1210560\,a^3\,b^{21}\,c^{15}\,d^9-2002728\,a^3\,b^{21}\,c^{13}\,d^{11}+1720736\,a^3\,b^{21}\,c^{11}\,d^{13}-758400\,a^3\,b^{21}\,c^9\,d^{15}+138240\,a^3\,b^{21}\,c^7\,d^{17}+16\,a^2\,b^{22}\,c^{24}-196\,a^2\,b^{22}\,c^{22}\,d^2-1564\,a^2\,b^{22}\,c^{20}\,d^4+44120\,a^2\,b^{22}\,c^{18}\,d^6-263320\,a^2\,b^{22}\,c^{16}\,d^8+547088\,a^2\,b^{22}\,c^{14}\,d^{10}-541208\,a^2\,b^{22}\,c^{12}\,d^{12}+263808\,a^2\,b^{22}\,c^{10}\,d^{14}-51840\,a^2\,b^{22}\,c^8\,d^{16}-8\,a\,b^{23}\,c^{23}\,d-536\,a\,b^{23}\,c^{21}\,d^3-2960\,a\,b^{23}\,c^{19}\,d^5+40720\,a\,b^{23}\,c^{17}\,d^7-101240\,a\,b^{23}\,c^{15}\,d^9+109456\,a\,b^{23}\,c^{13}\,d^{11}-56448\,a\,b^{23}\,c^{11}\,d^{13}+11520\,a\,b^{23}\,c^9\,d^{15}+4\,b^{24}\,c^{24}+76\,b^{24}\,c^{22}\,d^2+136\,b^{24}\,c^{20}\,d^4-3560\,b^{24}\,c^{18}\,d^6+9460\,b^{24}\,c^{16}\,d^8-10568\,b^{24}\,c^{14}\,d^{10}+5568\,b^{24}\,c^{12}\,d^{12}-1152\,b^{24}\,c^{10}\,d^{14}\right)}^2}{4}-\left(1600\,a^{12}\,b^6\,c^4\,d^{14}+1600\,a^{12}\,b^6\,c^2\,d^{16}+400\,a^{12}\,b^6\,d^{18}-17600\,a^{11}\,b^7\,c^5\,d^{13}-3200\,a^{11}\,b^7\,c^3\,d^{15}+2800\,a^{11}\,b^7\,c\,d^{17}+88720\,a^{10}\,b^8\,c^6\,d^{12}-64720\,a^{10}\,b^8\,c^4\,d^{14}-5260\,a^{10}\,b^8\,c^2\,d^{16}+8440\,a^{10}\,b^8\,d^{18}-239360\,a^9\,b^9\,c^7\,d^{11}+406880\,a^9\,b^9\,c^5\,d^{13}-182200\,a^9\,b^9\,c^3\,d^{15}+20260\,a^9\,b^9\,c\,d^{17}+354016\,a^8\,b^{10}\,c^8\,d^{10}-1026928\,a^8\,b^{10}\,c^6\,d^{12}+900624\,a^8\,b^{10}\,c^4\,d^{14}-308392\,a^8\,b^{10}\,c^2\,d^{16}+31081\,a^8\,b^{10}\,d^{18}-239360\,a^7\,b^{11}\,c^9\,d^9+1206848\,a^7\,b^{11}\,c^7\,d^{11}-1641528\,a^7\,b^{11}\,c^5\,d^{13}+838256\,a^7\,b^{11}\,c^3\,d^{15}-141104\,a^7\,b^{11}\,c\,d^{17}+88720\,a^6\,b^{12}\,c^{10}\,d^8-1026928\,a^6\,b^{12}\,c^8\,d^{10}+2430936\,a^6\,b^{12}\,c^6\,d^{12}-2218576\,a^6\,b^{12}\,c^4\,d^{14}+901948\,a^6\,b^{12}\,c^2\,d^{16}-136032\,a^6\,b^{12}\,d^{18}-17600\,a^5\,b^{13}\,c^{11}\,d^7+406880\,a^5\,b^{13}\,c^9\,d^9-1641528\,a^5\,b^{13}\,c^7\,d^{11}+2158808\,a^5\,b^{13}\,c^5\,d^{13}-1158992\,a^5\,b^{13}\,c^3\,d^{15}+216576\,a^5\,b^{13}\,c\,d^{17}+1600\,a^4\,b^{14}\,c^{12}\,d^6-64720\,a^4\,b^{14}\,c^{10}\,d^8+900624\,a^4\,b^{14}\,c^8\,d^{10}-2218576\,a^4\,b^{14}\,c^6\,d^{12}+2185654\,a^4\,b^{14}\,c^4\,d^{14}-989856\,a^4\,b^{14}\,c^2\,d^{16}+173664\,a^4\,b^{14}\,d^{18}-3200\,a^3\,b^{15}\,c^{11}\,d^7-182200\,a^3\,b^{15}\,c^9\,d^9+838256\,a^3\,b^{15}\,c^7\,d^{11}-1158992\,a^3\,b^{15}\,c^5\,d^{13}+657408\,a^3\,b^{15}\,c^3\,d^{15}-131328\,a^3\,b^{15}\,c\,d^{17}+1600\,a^2\,b^{16}\,c^{12}\,d^6-5260\,a^2\,b^{16}\,c^{10}\,d^8-308392\,a^2\,b^{16}\,c^8\,d^{10}+901948\,a^2\,b^{16}\,c^6\,d^{12}-989856\,a^2\,b^{16}\,c^4\,d^{14}+495936\,a^2\,b^{16}\,c^2\,d^{16}-96768\,a^2\,b^{16}\,d^{18}+2800\,a\,b^{17}\,c^{11}\,d^7+20260\,a\,b^{17}\,c^9\,d^9-141104\,a\,b^{17}\,c^7\,d^{11}+216576\,a\,b^{17}\,c^5\,d^{13}-131328\,a\,b^{17}\,c^3\,d^{15}+27648\,a\,b^{17}\,c\,d^{17}+400\,b^{18}\,c^{12}\,d^6+8440\,b^{18}\,c^{10}\,d^8+31081\,b^{18}\,c^8\,d^{10}-136032\,b^{18}\,c^6\,d^{12}+173664\,b^{18}\,c^4\,d^{14}-96768\,b^{18}\,c^2\,d^{16}+20736\,b^{18}\,d^{18}\right)\,\left(16\,a^{30}\,c^{10}\,d^{20}-80\,a^{30}\,c^8\,d^{22}+160\,a^{30}\,c^6\,d^{24}-160\,a^{30}\,c^4\,d^{26}+80\,a^{30}\,c^2\,d^{28}-16\,a^{30}\,d^{30}-320\,a^{29}\,b\,c^{11}\,d^{19}+1600\,a^{29}\,b\,c^9\,d^{21}-3200\,a^{29}\,b\,c^7\,d^{23}+3200\,a^{29}\,b\,c^5\,d^{25}-1600\,a^{29}\,b\,c^3\,d^{27}+320\,a^{29}\,b\,c\,d^{29}+3040\,a^{28}\,b^2\,c^{12}\,d^{18}-15280\,a^{28}\,b^2\,c^{10}\,d^{20}+30800\,a^{28}\,b^2\,c^8\,d^{22}-31200\,a^{28}\,b^2\,c^6\,d^{24}+16000\,a^{28}\,b^2\,c^4\,d^{26}-3440\,a^{28}\,b^2\,c^2\,d^{28}+80\,a^{28}\,b^2\,d^{30}-18240\,a^{27}\,b^3\,c^{13}\,d^{17}+92800\,a^{27}\,b^3\,c^{11}\,d^{19}-190400\,a^{27}\,b^3\,c^9\,d^{21}+198400\,a^{27}\,b^3\,c^7\,d^{23}-107200\,a^{27}\,b^3\,c^5\,d^{25}+26240\,a^{27}\,b^3\,c^3\,d^{27}-1600\,a^{27}\,b^3\,c\,d^{29}+77520\,a^{26}\,b^4\,c^{14}\,d^{16}-402800\,a^{26}\,b^4\,c^{12}\,d^{18}+851360\,a^{26}\,b^4\,c^{10}\,d^{20}-928000\,a^{26}\,b^4\,c^8\,d^{22}+541200\,a^{26}\,b^4\,c^6\,d^{24}-155120\,a^{26}\,b^4\,c^4\,d^{26}+16000\,a^{26}\,b^4\,c^2\,d^{28}-160\,a^{26}\,b^4\,d^{30}-248064\,a^{25}\,b^5\,c^{15}\,d^{15}+1331520\,a^{25}\,b^5\,c^{13}\,d^{17}-2939840\,a^{25}\,b^5\,c^{11}\,d^{19}+3408640\,a^{25}\,b^5\,c^9\,d^{21}-2184320\,a^{25}\,b^5\,c^7\,d^{23}+736064\,a^{25}\,b^5\,c^5\,d^{25}-107200\,a^{25}\,b^5\,c^3\,d^{27}+3200\,a^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- 7408*a^19*b^6*c^4*d^21 + 11336*a^19*b^6*c^6*d^19 + 24904*a^19*b^6*c^8*d^17 - 85536*a^19*b^6*c^10*d^15 + 92512*a^19*b^6*c^12*d^13 - 44408*a^19*b^6*c^14*d^11 + 8008*a^19*b^6*c^16*d^9 + 2032*a^20*b^5*c^3*d^22 - 4008*a^20*b^5*c^5*d^20 - 11336*a^20*b^5*c^7*d^18 + 46464*a^20*b^5*c^9*d^16 - 60768*a^20*b^5*c^11*d^14 + 35672*a^20*b^5*c^13*d^12 - 8008*a^20*b^5*c^15*d^10 - 368*a^21*b^4*c^2*d^23 + 1192*a^21*b^4*c^4*d^21 + 4008*a^21*b^4*c^6*d^19 - 20592*a^21*b^4*c^8*d^17 + 31328*a^21*b^4*c^10*d^15 - 20664*a^21*b^4*c^12*d^13 + 5096*a^21*b^4*c^14*d^11 - 328*a^22*b^3*c^3*d^22 - 1192*a^22*b^3*c^5*d^20 + 7408*a^22*b^3*c^7*d^18 - 12272*a^22*b^3*c^9*d^16 + 8536*a^22*b^3*c^11*d^14 - 2184*a^22*b^3*c^13*d^12 + 72*a^23*b^2*c^2*d^23 + 328*a^23*b^2*c^4*d^21 - 2032*a^23*b^2*c^6*d^19 + 3408*a^23*b^2*c^8*d^17 - 2392*a^23*b^2*c^10*d^15 + 616*a^23*b^2*c^12*d^13 - 8*a*b^24*c^24*d - 8*a^24*b*c*d^24))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^22*c^25 - 12*a^25*c*d^24 - 12*a*b^24*c^25 - 104*a^5*b^20*c^25 + 96*a^7*b^18*c^25 - 44*a^9*b^16*c^25 + 8*a^11*b^14*c^25 + 56*a^25*c^3*d^22 - 104*a^25*c^5*d^20 + 96*a^25*c^7*d^18 - 44*a^25*c^9*d^16 + 8*a^25*c^11*d^14 + 16*a*b^24*c^15*d^10 - 76*a*b^24*c^17*d^8 + 144*a*b^24*c^19*d^6 - 136*a*b^24*c^21*d^4 + 64*a*b^24*c^23*d^2 + 168*a^2*b^23*c^24*d - 784*a^4*b^21*c^24*d + 1456*a^6*b^19*c^24*d - 1344*a^8*b^17*c^24*d + 616*a^10*b^15*c^24*d - 112*a^12*b^13*c^24*d + 16*a^15*b^10*c*d^24 - 76*a^17*b^8*c*d^24 + 144*a^19*b^6*c*d^24 - 136*a^21*b^4*c*d^24 + 64*a^23*b^2*c*d^24 + 168*a^24*b*c^2*d^23 - 784*a^24*b*c^4*d^21 + 1456*a^24*b*c^6*d^19 - 1344*a^24*b*c^8*d^17 + 616*a^24*b*c^10*d^15 - 112*a^24*b*c^12*d^13 - 224*a^2*b^23*c^14*d^11 + 1064*a^2*b^23*c^16*d^9 - 2016*a^2*b^23*c^18*d^7 + 1904*a^2*b^23*c^20*d^5 - 896*a^2*b^23*c^22*d^3 + 1456*a^3*b^22*c^13*d^12 - 6992*a^3*b^22*c^15*d^10 + 13464*a^3*b^22*c^17*d^8 - 13056*a^3*b^22*c^19*d^6 + 6464*a^3*b^22*c^21*d^4 - 1392*a^3*b^22*c^23*d^2 - 5824*a^4*b^21*c^12*d^13 + 28728*a^4*b^21*c^14*d^11 - 57456*a^4*b^21*c^16*d^9 + 59024*a^4*b^21*c^18*d^7 - 32256*a^4*b^21*c^20*d^5 + 8568*a^4*b^21*c^22*d^3 + 16016*a^5*b^20*c^11*d^14 - 82992*a^5*b^20*c^13*d^12 + 177048*a^5*b^20*c^15*d^10 - 198696*a^5*b^20*c^17*d^8 + 123584*a^5*b^20*c^19*d^6 - 40512*a^5*b^20*c^21*d^4 + 5656*a^5*b^20*c^23*d^2 - 32032*a^6*b^19*c^10*d^15 + 179816*a^6*b^19*c^12*d^13 - 421344*a^6*b^19*c^14*d^11 + 529312*a^6*b^19*c^16*d^9 - 379008*a^6*b^19*c^18*d^7 + 150024*a^6*b^19*c^20*d^5 - 28224*a^6*b^19*c^22*d^3 + 48048*a^7*b^18*c^9*d^16 - 304304*a^7*b^18*c^11*d^14 + 805896*a^7*b^18*c^13*d^12 - 1151104*a^7*b^18*c^15*d^10 + 949952*a^7*b^18*c^17*d^8 - 446736*a^7*b^18*c^19*d^6 + 108136*a^7*b^18*c^21*d^4 - 9984*a^7*b^18*c^23*d^2 - 54912*a^8*b^17*c^8*d^17 + 412984*a^8*b^17*c^10*d^15 - 1267344*a^8*b^17*c^12*d^13 + 2077536*a^8*b^17*c^14*d^11 - 1975808*a^8*b^17*c^16*d^9 + 1095384*a^8*b^17*c^18*d^7 - 331632*a^8*b^17*c^20*d^5 + 45136*a^8*b^17*c^22*d^3 + 48048*a^9*b^16*c^7*d^18 - 456456*a^9*b^16*c^9*d^16 + 1657656*a^9*b^16*c^11*d^14 - 3143504*a^9*b^16*c^13*d^12 + 3453696*a^9*b^16*c^15*d^10 - 2247636*a^9*b^16*c^17*d^8 + 831208*a^9*b^16*c^19*d^6 - 151944*a^9*b^16*c^21*d^4 + 8976*a^9*b^16*c^23*d^2 - 32032*a^10*b^15*c^6*d^19 + 412984*a^10*b^15*c^8*d^17 - 1812096*a^10*b^15*c^10*d^15 + 4016896*a^10*b^15*c^12*d^13 - 5121024*a^10*b^15*c^14*d^11 + 3897024*a^10*b^15*c^16*d^9 - 1728832*a^10*b^15*c^18*d^7 + 404768*a^10*b^15*c^20*d^5 - 38304*a^10*b^15*c^22*d^3 + 16016*a^11*b^14*c^5*d^20 - 304304*a^11*b^14*c^7*d^18 + 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34548*a^18*b^4*c^8*d^14 - 26952*a^18*b^4*c^10*d^12 + 8008*a^18*b^4*c^12*d^10 - 732*a^19*b^3*c^3*d^19 + 3308*a^19*b^3*c^5*d^17 - 7652*a^19*b^3*c^7*d^15 + 7908*a^19*b^3*c^9*d^13 - 2912*a^19*b^3*c^11*d^11 + 28*a^20*b^2*c^2*d^20 - 212*a^20*b^2*c^4*d^18 + 1068*a^20*b^2*c^6*d^16 - 1612*a^20*b^2*c^8*d^14 + 728*a^20*b^2*c^10*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 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17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) + (8*tan(e/2 + (f*x)/2)*(12*a^5*b^17*c^22 - 4*a^22*c*d^21 - 4*a*b^21*c^22 - 8*a^7*b^15*c^22 + 12*a^22*c^5*d^17 - 8*a^22*c^7*d^15 - 24*a*b^21*c^12*d^10 + 100*a*b^21*c^14*d^8 - 164*a*b^21*c^16*d^6 + 120*a*b^21*c^18*d^4 - 28*a*b^21*c^20*d^2 + 20*a^2*b^20*c^21*d + 72*a^4*b^18*c^21*d - 204*a^6*b^16*c^21*d + 112*a^8*b^14*c^21*d - 24*a^12*b^10*c*d^21 + 100*a^14*b^8*c*d^21 - 164*a^16*b^6*c*d^21 + 120*a^18*b^4*c*d^21 - 28*a^20*b^2*c*d^21 + 20*a^21*b*c^2*d^20 + 72*a^21*b*c^4*d^18 - 204*a^21*b*c^6*d^16 + 112*a^21*b*c^8*d^14 + 216*a^2*b^20*c^11*d^11 - 908*a^2*b^20*c^13*d^9 + 1540*a^2*b^20*c^15*d^7 - 1200*a^2*b^20*c^17*d^5 + 332*a^2*b^20*c^19*d^3 - 840*a^3*b^19*c^10*d^12 + 3672*a^3*b^19*c^12*d^10 - 6788*a^3*b^19*c^14*d^8 + 6132*a^3*b^19*c^16*d^6 - 2388*a^3*b^19*c^18*d^4 + 212*a^3*b^19*c^20*d^2 + 1800*a^4*b^18*c^9*d^13 - 8680*a^4*b^18*c^11*d^11 + 18852*a^4*b^18*c^13*d^9 - 21228*a^4*b^18*c^15*d^7 + 11692*a^4*b^18*c^17*d^5 - 2508*a^4*b^18*c^19*d^3 - 2160*a^5*b^17*c^8*d^14 + 13100*a^5*b^17*c^10*d^12 - 36820*a^5*b^17*c^12*d^10 + 53712*a^5*b^17*c^14*d^8 - 39608*a^5*b^17*c^16*d^6 + 12832*a^5*b^17*c^18*d^4 - 1068*a^5*b^17*c^20*d^2 + 1008*a^6*b^16*c^7*d^15 - 12420*a^6*b^16*c^9*d^13 + 51764*a^6*b^16*c^11*d^11 - 100128*a^6*b^16*c^13*d^9 + 96048*a^6*b^16*c^15*d^7 - 42920*a^6*b^16*c^17*d^5 + 6852*a^6*b^16*c^19*d^3 + 1008*a^7*b^15*c^6*d^16 + 5136*a^7*b^15*c^8*d^14 - 48820*a^7*b^15*c^10*d^12 + 134700*a^7*b^15*c^12*d^10 - 171472*a^7*b^15*c^14*d^8 + 103992*a^7*b^15*c^16*d^6 - 26148*a^7*b^15*c^18*d^4 + 1612*a^7*b^15*c^20*d^2 - 2160*a^8*b^14*c^5*d^17 + 5136*a^8*b^14*c^7*d^15 + 20436*a^8*b^14*c^9*d^13 - 121524*a^8*b^14*c^11*d^11 + 224888*a^8*b^14*c^13*d^9 - 186952*a^8*b^14*c^15*d^7 + 67572*a^8*b^14*c^17*d^5 - 7508*a^8*b^14*c^19*d^3 + 1800*a^9*b^13*c^4*d^18 - 12420*a^9*b^13*c^6*d^16 + 20436*a^9*b^13*c^8*d^14 + 49416*a^9*b^13*c^10*d^12 - 201552*a^9*b^13*c^12*d^10 + 245708*a^9*b^13*c^14*d^8 - 125412*a^9*b^13*c^16*d^6 + 22752*a^9*b^13*c^18*d^4 - 728*a^9*b^13*c^20*d^2 - 840*a^10*b^12*c^3*d^19 + 13100*a^10*b^12*c^5*d^17 - 48820*a^10*b^12*c^7*d^15 + 49416*a^10*b^12*c^9*d^13 + 82088*a^10*b^12*c^11*d^11 - 219092*a^10*b^12*c^13*d^9 + 168468*a^10*b^12*c^15*d^7 - 47152*a^10*b^12*c^17*d^5 + 2832*a^10*b^12*c^19*d^3 + 216*a^11*b^11*c^2*d^20 - 8680*a^11*b^11*c^4*d^18 + 51764*a^11*b^11*c^6*d^16 - 121524*a^11*b^11*c^8*d^14 + 82088*a^11*b^11*c^10*d^12 + 88712*a^11*b^11*c^12*d^10 - 153012*a^11*b^11*c^14*d^8 + 67604*a^11*b^11*c^16*d^6 - 7168*a^11*b^11*c^18*d^4 + 3672*a^12*b^10*c^3*d^19 - 36820*a^12*b^10*c^5*d^17 + 134700*a^12*b^10*c^7*d^15 - 201552*a^12*b^10*c^9*d^13 + 88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 12544*a^13*b^9*c^16*d^6 - 6788*a^14*b^8*c^3*d^19 + 53712*a^14*b^8*c^5*d^17 - 171472*a^14*b^8*c^7*d^15 + 245708*a^14*b^8*c^9*d^13 - 153012*a^14*b^8*c^11*d^11 + 26256*a^14*b^8*c^13*d^9 + 5496*a^14*b^8*c^15*d^7 + 1540*a^15*b^7*c^2*d^20 - 21228*a^15*b^7*c^4*d^18 + 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4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 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31328*a^21*b^4*c^10*d^15 - 20664*a^21*b^4*c^12*d^13 + 5096*a^21*b^4*c^14*d^11 - 328*a^22*b^3*c^3*d^22 - 1192*a^22*b^3*c^5*d^20 + 7408*a^22*b^3*c^7*d^18 - 12272*a^22*b^3*c^9*d^16 + 8536*a^22*b^3*c^11*d^14 - 2184*a^22*b^3*c^13*d^12 + 72*a^23*b^2*c^2*d^23 + 328*a^23*b^2*c^4*d^21 - 2032*a^23*b^2*c^6*d^19 + 3408*a^23*b^2*c^8*d^17 - 2392*a^23*b^2*c^10*d^15 + 616*a^23*b^2*c^12*d^13 - 8*a*b^24*c^24*d - 8*a^24*b*c*d^24))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 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5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 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4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 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21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19)) + (4*(288*a*b^18*c^6*d^13 - 1104*a*b^18*c^8*d^11 + 1538*a*b^18*c^10*d^9 - 872*a*b^18*c^12*d^7 + 108*a*b^18*c^14*d^5 + 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13080*a^11*b^8*c^10*d^9 + 4360*a^11*b^8*c^12*d^7 + 4944*a^12*b^7*c^3*d^16 - 20208*a^12*b^7*c^5*d^14 + 40296*a^12*b^7*c^7*d^12 - 30104*a^12*b^7*c^9*d^10 + 4360*a^12*b^7*c^11*d^8 - 304*a^13*b^6*c^2*d^17 + 6704*a^13*b^6*c^4*d^15 - 22728*a^13*b^6*c^6*d^13 + 27208*a^13*b^6*c^8*d^11 - 8720*a^13*b^6*c^10*d^9 - 1664*a^14*b^5*c^3*d^16 + 7404*a^14*b^5*c^5*d^14 - 12984*a^14*b^5*c^7*d^12 + 6488*a^14*b^5*c^9*d^10 - 32*a^15*b^4*c^2*d^17 - 744*a^15*b^4*c^4*d^15 + 3096*a^15*b^4*c^6*d^13 - 2752*a^15*b^4*c^8*d^11 - 72*a^16*b^3*c^3*d^16 - 264*a^16*b^3*c^5*d^14 + 728*a^16*b^3*c^7*d^12 + 8*a^17*b^2*c^2*d^17 - 40*a^17*b^2*c^4*d^15 - 112*a^17*b^2*c^6*d^13 + 2*a*b^18*c^18*d + 2*a^18*b*c*d^18))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^19 + a^19*c*d^18 + 4*a^3*b^16*c^19 + 4*a^5*b^14*c^19 + 4*a^19*c^3*d^16 + 4*a^19*c^5*d^14 - 576*a*b^18*c^5*d^14 + 2640*a*b^18*c^7*d^12 - 4732*a*b^18*c^9*d^10 + 3961*a*b^18*c^11*d^8 - 1344*a*b^18*c^13*d^6 + 14*a*b^18*c^15*d^4 + 18*a*b^18*c^17*d^2 + 4*a^2*b^17*c^18*d - 20*a^4*b^15*c^18*d - 576*a^5*b^14*c*d^18 - 56*a^6*b^13*c^18*d + 2640*a^7*b^12*c*d^18 - 4732*a^9*b^10*c*d^18 + 3961*a^11*b^8*c*d^18 - 1344*a^13*b^6*c*d^18 + 14*a^15*b^4*c*d^18 + 18*a^17*b^2*c*d^18 + 4*a^18*b*c^2*d^17 - 20*a^18*b*c^4*d^15 - 56*a^18*b*c^6*d^13 + 2304*a^2*b^17*c^4*d^15 - 10944*a^2*b^17*c^6*d^13 + 20720*a^2*b^17*c^8*d^11 - 18788*a^2*b^17*c^10*d^9 + 7392*a^2*b^17*c^12*d^7 - 520*a^2*b^17*c^14*d^5 - 24*a^2*b^17*c^16*d^3 - 3456*a^3*b^16*c^3*d^16 + 20016*a^3*b^16*c^5*d^14 - 48112*a^3*b^16*c^7*d^12 + 58925*a^3*b^16*c^9*d^10 - 36732*a^3*b^16*c^11*d^8 + 9736*a^3*b^16*c^13*d^6 - 760*a^3*b^16*c^15*d^4 - 44*a^3*b^16*c^17*d^2 + 2304*a^4*b^15*c^2*d^17 - 23424*a^4*b^15*c^4*d^15 + 81680*a^4*b^15*c^6*d^13 - 135520*a^4*b^15*c^8*d^11 + 114144*a^4*b^15*c^10*d^9 - 44168*a^4*b^15*c^12*d^7 + 5696*a^4*b^15*c^14*d^5 - 332*a^4*b^15*c^16*d^3 + 20016*a^5*b^14*c^3*d^16 - 99112*a^5*b^14*c^5*d^14 + 213338*a^5*b^14*c^7*d^12 - 235152*a^5*b^14*c^9*d^10 + 130428*a^5*b^14*c^11*d^8 - 31908*a^5*b^14*c^13*d^6 + 3966*a^5*b^14*c^15*d^4 - 140*a^5*b^14*c^17*d^2 - 10944*a^6*b^13*c^2*d^17 + 81680*a^6*b^13*c^4*d^15 - 243832*a^6*b^13*c^6*d^13 + 364608*a^6*b^13*c^8*d^11 - 281736*a^6*b^13*c^10*d^9 + 103104*a^6*b^13*c^12*d^7 - 16860*a^6*b^13*c^14*d^5 + 1660*a^6*b^13*c^16*d^3 - 48112*a^7*b^12*c^3*d^16 + 213338*a^7*b^12*c^5*d^14 - 425832*a^7*b^12*c^7*d^12 + 434414*a^7*b^12*c^9*d^10 - 219064*a^7*b^12*c^11*d^8 + 50732*a^7*b^12*c^13*d^6 - 7220*a^7*b^12*c^15*d^4 + 364*a^7*b^12*c^17*d^2 + 20720*a^8*b^11*c^2*d^17 - 135520*a^8*b^11*c^4*d^15 + 364608*a^8*b^11*c^6*d^13 - 496336*a^8*b^11*c^8*d^11 + 343832*a^8*b^11*c^10*d^9 - 111220*a^8*b^11*c^12*d^7 + 17956*a^8*b^11*c^14*d^5 - 1376*a^8*b^11*c^16*d^3 + 58925*a^9*b^10*c^3*d^16 - 235152*a^9*b^10*c^5*d^14 + 434414*a^9*b^10*c^7*d^12 - 401788*a^9*b^10*c^9*d^10 + 172673*a^9*b^10*c^11*d^8 - 31940*a^9*b^10*c^13*d^6 + 3244*a^9*b^10*c^15*d^4 - 18788*a^10*b^9*c^2*d^17 + 114144*a^10*b^9*c^4*d^15 - 281736*a^10*b^9*c^6*d^13 + 343832*a^10*b^9*c^8*d^11 - 197840*a^10*b^9*c^10*d^9 + 45940*a^10*b^9*c^12*d^7 - 4760*a^10*b^9*c^14*d^5 - 36732*a^11*b^8*c^3*d^16 + 130428*a^11*b^8*c^5*d^14 - 219064*a^11*b^8*c^7*d^12 + 172673*a^11*b^8*c^9*d^10 - 52480*a^11*b^8*c^11*d^8 + 4580*a^11*b^8*c^13*d^6 + 7392*a^12*b^7*c^2*d^17 - 44168*a^12*b^7*c^4*d^15 + 103104*a^12*b^7*c^6*d^13 - 111220*a^12*b^7*c^8*d^11 + 45940*a^12*b^7*c^10*d^9 - 4000*a^12*b^7*c^12*d^7 + 9736*a^13*b^6*c^3*d^16 - 31908*a^13*b^6*c^5*d^14 + 50732*a^13*b^6*c^7*d^12 - 31940*a^13*b^6*c^9*d^10 + 4580*a^13*b^6*c^11*d^8 - 520*a^14*b^5*c^2*d^17 + 5696*a^14*b^5*c^4*d^15 - 16860*a^14*b^5*c^6*d^13 + 17956*a^14*b^5*c^8*d^11 - 4760*a^14*b^5*c^10*d^9 - 760*a^15*b^4*c^3*d^16 + 3966*a^15*b^4*c^5*d^14 - 7220*a^15*b^4*c^7*d^12 + 3244*a^15*b^4*c^9*d^10 - 24*a^16*b^3*c^2*d^17 - 332*a^16*b^3*c^4*d^15 + 1660*a^16*b^3*c^6*d^13 - 1376*a^16*b^3*c^8*d^11 - 44*a^17*b^2*c^3*d^16 - 140*a^17*b^2*c^5*d^14 + 364*a^17*b^2*c^7*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 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59264*a^10*b^15*c^17*d^8 - 85536*a^10*b^15*c^19*d^6 + 31328*a^10*b^15*c^21*d^4 - 2392*a^10*b^15*c^23*d^2 + 8008*a^11*b^14*c^6*d^19 - 37752*a^11*b^14*c^8*d^17 + 36608*a^11*b^14*c^10*d^15 + 43264*a^11*b^14*c^12*d^13 - 56256*a^11*b^14*c^14*d^11 - 67008*a^11*b^14*c^16*d^9 + 125472*a^11*b^14*c^18*d^7 - 60768*a^11*b^14*c^20*d^5 + 8536*a^11*b^14*c^22*d^3 - 5096*a^12*b^13*c^5*d^20 + 44408*a^12*b^13*c^7*d^18 - 92352*a^12*b^13*c^9*d^16 + 43264*a^12*b^13*c^11*d^14 + 22464*a^12*b^13*c^13*d^12 + 56256*a^12*b^13*c^15*d^10 - 141408*a^12*b^13*c^17*d^8 + 92512*a^12*b^13*c^19*d^6 - 20664*a^12*b^13*c^21*d^4 + 616*a^12*b^13*c^23*d^2 + 2184*a^13*b^12*c^4*d^21 - 35672*a^13*b^12*c^6*d^19 + 109408*a^13*b^12*c^8*d^17 - 113152*a^13*b^12*c^10*d^15 + 22464*a^13*b^12*c^12*d^13 - 22464*a^13*b^12*c^14*d^11 + 113152*a^13*b^12*c^16*d^9 - 109408*a^13*b^12*c^18*d^7 + 35672*a^13*b^12*c^20*d^5 - 2184*a^13*b^12*c^22*d^3 - 616*a^14*b^11*c^3*d^22 + 20664*a^14*b^11*c^5*d^20 - 92512*a^14*b^11*c^7*d^18 + 141408*a^14*b^11*c^9*d^16 - 56256*a^14*b^11*c^11*d^14 - 22464*a^14*b^11*c^13*d^12 - 43264*a^14*b^11*c^15*d^10 + 92352*a^14*b^11*c^17*d^8 - 44408*a^14*b^11*c^19*d^6 + 5096*a^14*b^11*c^21*d^4 + 104*a^15*b^10*c^2*d^23 - 8536*a^15*b^10*c^4*d^21 + 60768*a^15*b^10*c^6*d^19 - 125472*a^15*b^10*c^8*d^17 + 67008*a^15*b^10*c^10*d^15 + 56256*a^15*b^10*c^12*d^13 - 43264*a^15*b^10*c^14*d^11 - 36608*a^15*b^10*c^16*d^9 + 37752*a^15*b^10*c^18*d^7 - 8008*a^15*b^10*c^20*d^5 + 2392*a^16*b^9*c^3*d^22 - 31328*a^16*b^9*c^5*d^20 + 85536*a^16*b^9*c^7*d^18 - 59264*a^16*b^9*c^9*d^16 - 67008*a^16*b^9*c^11*d^14 + 113152*a^16*b^9*c^13*d^12 - 36608*a^16*b^9*c^15*d^10 - 14872*a^16*b^9*c^17*d^8 + 8008*a^16*b^9*c^19*d^6 - 408*a^17*b^8*c^2*d^23 + 12272*a^17*b^8*c^4*d^21 - 46464*a^17*b^8*c^6*d^19 + 42696*a^17*b^8*c^8*d^17 + 59264*a^17*b^8*c^10*d^15 - 141408*a^17*b^8*c^12*d^13 + 92352*a^17*b^8*c^14*d^11 - 14872*a^17*b^8*c^16*d^9 - 3432*a^17*b^8*c^18*d^7 - 3408*a^18*b^7*c^3*d^22 + 20592*a^18*b^7*c^5*d^20 - 24904*a^18*b^7*c^7*d^18 - 42696*a^18*b^7*c^9*d^16 + 125472*a^18*b^7*c^11*d^14 - 109408*a^18*b^7*c^13*d^12 + 37752*a^18*b^7*c^15*d^10 - 3432*a^18*b^7*c^17*d^8 + 592*a^19*b^6*c^2*d^23 - 7408*a^19*b^6*c^4*d^21 + 11336*a^19*b^6*c^6*d^19 + 24904*a^19*b^6*c^8*d^17 - 85536*a^19*b^6*c^10*d^15 + 92512*a^19*b^6*c^12*d^13 - 44408*a^19*b^6*c^14*d^11 + 8008*a^19*b^6*c^16*d^9 + 2032*a^20*b^5*c^3*d^22 - 4008*a^20*b^5*c^5*d^20 - 11336*a^20*b^5*c^7*d^18 + 46464*a^20*b^5*c^9*d^16 - 60768*a^20*b^5*c^11*d^14 + 35672*a^20*b^5*c^13*d^12 - 8008*a^20*b^5*c^15*d^10 - 368*a^21*b^4*c^2*d^23 + 1192*a^21*b^4*c^4*d^21 + 4008*a^21*b^4*c^6*d^19 - 20592*a^21*b^4*c^8*d^17 + 31328*a^21*b^4*c^10*d^15 - 20664*a^21*b^4*c^12*d^13 + 5096*a^21*b^4*c^14*d^11 - 328*a^22*b^3*c^3*d^22 - 1192*a^22*b^3*c^5*d^20 + 7408*a^22*b^3*c^7*d^18 - 12272*a^22*b^3*c^9*d^16 + 8536*a^22*b^3*c^11*d^14 - 2184*a^22*b^3*c^13*d^12 + 72*a^23*b^2*c^2*d^23 + 328*a^23*b^2*c^4*d^21 - 2032*a^23*b^2*c^6*d^19 + 3408*a^23*b^2*c^8*d^17 - 2392*a^23*b^2*c^10*d^15 + 616*a^23*b^2*c^12*d^13 - 8*a*b^24*c^24*d - 8*a^24*b*c*d^24))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^22*c^25 - 12*a^25*c*d^24 - 12*a*b^24*c^25 - 104*a^5*b^20*c^25 + 96*a^7*b^18*c^25 - 44*a^9*b^16*c^25 + 8*a^11*b^14*c^25 + 56*a^25*c^3*d^22 - 104*a^25*c^5*d^20 + 96*a^25*c^7*d^18 - 44*a^25*c^9*d^16 + 8*a^25*c^11*d^14 + 16*a*b^24*c^15*d^10 - 76*a*b^24*c^17*d^8 + 144*a*b^24*c^19*d^6 - 136*a*b^24*c^21*d^4 + 64*a*b^24*c^23*d^2 + 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24024*a^16*b^6*c^14*d^8 + 6588*a^17*b^5*c^3*d^19 - 34492*a^17*b^5*c^5*d^17 + 85760*a^17*b^5*c^7*d^15 - 109032*a^17*b^5*c^9*d^13 + 67468*a^17*b^5*c^11*d^11 - 16016*a^17*b^5*c^13*d^9 - 960*a^18*b^4*c^2*d^20 + 6588*a^18*b^4*c^4*d^18 - 21232*a^18*b^4*c^6*d^16 + 34548*a^18*b^4*c^8*d^14 - 26952*a^18*b^4*c^10*d^12 + 8008*a^18*b^4*c^12*d^10 - 732*a^19*b^3*c^3*d^19 + 3308*a^19*b^3*c^5*d^17 - 7652*a^19*b^3*c^7*d^15 + 7908*a^19*b^3*c^9*d^13 - 2912*a^19*b^3*c^11*d^11 + 28*a^20*b^2*c^2*d^20 - 212*a^20*b^2*c^4*d^18 + 1068*a^20*b^2*c^6*d^16 - 1612*a^20*b^2*c^8*d^14 + 728*a^20*b^2*c^10*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 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21228*a^4*b^18*c^15*d^7 + 11692*a^4*b^18*c^17*d^5 - 2508*a^4*b^18*c^19*d^3 - 2160*a^5*b^17*c^8*d^14 + 13100*a^5*b^17*c^10*d^12 - 36820*a^5*b^17*c^12*d^10 + 53712*a^5*b^17*c^14*d^8 - 39608*a^5*b^17*c^16*d^6 + 12832*a^5*b^17*c^18*d^4 - 1068*a^5*b^17*c^20*d^2 + 1008*a^6*b^16*c^7*d^15 - 12420*a^6*b^16*c^9*d^13 + 51764*a^6*b^16*c^11*d^11 - 100128*a^6*b^16*c^13*d^9 + 96048*a^6*b^16*c^15*d^7 - 42920*a^6*b^16*c^17*d^5 + 6852*a^6*b^16*c^19*d^3 + 1008*a^7*b^15*c^6*d^16 + 5136*a^7*b^15*c^8*d^14 - 48820*a^7*b^15*c^10*d^12 + 134700*a^7*b^15*c^12*d^10 - 171472*a^7*b^15*c^14*d^8 + 103992*a^7*b^15*c^16*d^6 - 26148*a^7*b^15*c^18*d^4 + 1612*a^7*b^15*c^20*d^2 - 2160*a^8*b^14*c^5*d^17 + 5136*a^8*b^14*c^7*d^15 + 20436*a^8*b^14*c^9*d^13 - 121524*a^8*b^14*c^11*d^11 + 224888*a^8*b^14*c^13*d^9 - 186952*a^8*b^14*c^15*d^7 + 67572*a^8*b^14*c^17*d^5 - 7508*a^8*b^14*c^19*d^3 + 1800*a^9*b^13*c^4*d^18 - 12420*a^9*b^13*c^6*d^16 + 20436*a^9*b^13*c^8*d^14 + 49416*a^9*b^13*c^10*d^12 - 201552*a^9*b^13*c^12*d^10 + 245708*a^9*b^13*c^14*d^8 - 125412*a^9*b^13*c^16*d^6 + 22752*a^9*b^13*c^18*d^4 - 728*a^9*b^13*c^20*d^2 - 840*a^10*b^12*c^3*d^19 + 13100*a^10*b^12*c^5*d^17 - 48820*a^10*b^12*c^7*d^15 + 49416*a^10*b^12*c^9*d^13 + 82088*a^10*b^12*c^11*d^11 - 219092*a^10*b^12*c^13*d^9 + 168468*a^10*b^12*c^15*d^7 - 47152*a^10*b^12*c^17*d^5 + 2832*a^10*b^12*c^19*d^3 + 216*a^11*b^11*c^2*d^20 - 8680*a^11*b^11*c^4*d^18 + 51764*a^11*b^11*c^6*d^16 - 121524*a^11*b^11*c^8*d^14 + 82088*a^11*b^11*c^10*d^12 + 88712*a^11*b^11*c^12*d^10 - 153012*a^11*b^11*c^14*d^8 + 67604*a^11*b^11*c^16*d^6 - 7168*a^11*b^11*c^18*d^4 + 3672*a^12*b^10*c^3*d^19 - 36820*a^12*b^10*c^5*d^17 + 134700*a^12*b^10*c^7*d^15 - 201552*a^12*b^10*c^9*d^13 + 88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 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1068*a^20*b^2*c^5*d^17 + 1612*a^20*b^2*c^7*d^15 - 728*a^20*b^2*c^9*d^13))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19)) + (4*(288*a*b^18*c^6*d^13 - 1104*a*b^18*c^8*d^11 + 1538*a*b^18*c^10*d^9 - 872*a*b^18*c^12*d^7 + 108*a*b^18*c^14*d^5 + 40*a*b^18*c^16*d^3 + 8*a^3*b^16*c^18*d + 8*a^5*b^14*c^18*d + 288*a^6*b^13*c*d^18 - 1104*a^8*b^11*c*d^18 + 1538*a^10*b^9*c*d^18 - 872*a^12*b^7*c*d^18 + 108*a^14*b^5*c*d^18 + 40*a^16*b^3*c*d^18 + 8*a^18*b*c^3*d^16 + 8*a^18*b*c^5*d^14 - 864*a^2*b^17*c^5*d^14 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5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 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268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^22*c^25 - 12*a^25*c*d^24 - 12*a*b^24*c^25 - 104*a^5*b^20*c^25 + 96*a^7*b^18*c^25 - 44*a^9*b^16*c^25 + 8*a^11*b^14*c^25 + 56*a^25*c^3*d^22 - 104*a^25*c^5*d^20 + 96*a^25*c^7*d^18 - 44*a^25*c^9*d^16 + 8*a^25*c^11*d^14 + 16*a*b^24*c^15*d^10 - 76*a*b^24*c^17*d^8 + 144*a*b^24*c^19*d^6 - 136*a*b^24*c^21*d^4 + 64*a*b^24*c^23*d^2 + 168*a^2*b^23*c^24*d - 784*a^4*b^21*c^24*d + 1456*a^6*b^19*c^24*d - 1344*a^8*b^17*c^24*d + 616*a^10*b^15*c^24*d - 112*a^12*b^13*c^24*d + 16*a^15*b^10*c*d^24 - 76*a^17*b^8*c*d^24 + 144*a^19*b^6*c*d^24 - 136*a^21*b^4*c*d^24 + 64*a^23*b^2*c*d^24 + 168*a^24*b*c^2*d^23 - 784*a^24*b*c^4*d^21 + 1456*a^24*b*c^6*d^19 - 1344*a^24*b*c^8*d^17 + 616*a^24*b*c^10*d^15 - 112*a^24*b*c^12*d^13 - 224*a^2*b^23*c^14*d^11 + 1064*a^2*b^23*c^16*d^9 - 2016*a^2*b^23*c^18*d^7 + 1904*a^2*b^23*c^20*d^5 - 896*a^2*b^23*c^22*d^3 + 1456*a^3*b^22*c^13*d^12 - 6992*a^3*b^22*c^15*d^10 + 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1095384*a^8*b^17*c^18*d^7 - 331632*a^8*b^17*c^20*d^5 + 45136*a^8*b^17*c^22*d^3 + 48048*a^9*b^16*c^7*d^18 - 456456*a^9*b^16*c^9*d^16 + 1657656*a^9*b^16*c^11*d^14 - 3143504*a^9*b^16*c^13*d^12 + 3453696*a^9*b^16*c^15*d^10 - 2247636*a^9*b^16*c^17*d^8 + 831208*a^9*b^16*c^19*d^6 - 151944*a^9*b^16*c^21*d^4 + 8976*a^9*b^16*c^23*d^2 - 32032*a^10*b^15*c^6*d^19 + 412984*a^10*b^15*c^8*d^17 - 1812096*a^10*b^15*c^10*d^15 + 4016896*a^10*b^15*c^12*d^13 - 5121024*a^10*b^15*c^14*d^11 + 3897024*a^10*b^15*c^16*d^9 - 1728832*a^10*b^15*c^18*d^7 + 404768*a^10*b^15*c^20*d^5 - 38304*a^10*b^15*c^22*d^3 + 16016*a^11*b^14*c^5*d^20 - 304304*a^11*b^14*c^7*d^18 + 1657656*a^11*b^14*c^9*d^16 - 4356352*a^11*b^14*c^11*d^14 + 6476288*a^11*b^14*c^13*d^12 - 5745024*a^11*b^14*c^15*d^10 + 3021984*a^11*b^14*c^17*d^8 - 880256*a^11*b^14*c^19*d^6 + 118032*a^11*b^14*c^21*d^4 - 4048*a^11*b^14*c^23*d^2 - 5824*a^12*b^13*c^4*d^21 + 179816*a^12*b^13*c^6*d^19 - 1267344*a^12*b^13*c^8*d^17 + 4016896*a^12*b^13*c^10*d^15 - 7002112*a^12*b^13*c^12*d^13 + 7235136*a^12*b^13*c^14*d^11 - 4480896*a^12*b^13*c^16*d^9 + 1588704*a^12*b^13*c^18*d^7 - 280896*a^12*b^13*c^20*d^5 + 16632*a^12*b^13*c^22*d^3 + 1456*a^13*b^12*c^3*d^22 - 82992*a^13*b^12*c^5*d^20 + 805896*a^13*b^12*c^7*d^18 - 3143504*a^13*b^12*c^9*d^16 + 6476288*a^13*b^12*c^11*d^14 - 7809984*a^13*b^12*c^13*d^12 + 5666752*a^13*b^12*c^15*d^10 - 2403856*a^13*b^12*c^17*d^8 + 537264*a^13*b^12*c^19*d^6 - 48048*a^13*b^12*c^21*d^4 + 728*a^13*b^12*c^23*d^2 - 224*a^14*b^11*c^2*d^23 + 28728*a^14*b^11*c^4*d^21 - 421344*a^14*b^11*c^6*d^19 + 2077536*a^14*b^11*c^8*d^17 - 5121024*a^14*b^11*c^10*d^15 + 7235136*a^14*b^11*c^12*d^13 - 6126848*a^14*b^11*c^14*d^11 + 3071744*a^14*b^11*c^16*d^9 - 844896*a^14*b^11*c^18*d^7 + 104104*a^14*b^11*c^20*d^5 - 2912*a^14*b^11*c^22*d^3 - 6992*a^15*b^10*c^3*d^22 + 177048*a^15*b^10*c^5*d^20 - 1151104*a^15*b^10*c^7*d^18 + 3453696*a^15*b^10*c^9*d^16 - 5745024*a^15*b^10*c^11*d^14 + 5666752*a^15*b^10*c^13*d^12 - 3331328*a^15*b^10*c^15*d^10 + 1105104*a^15*b^10*c^17*d^8 - 176176*a^15*b^10*c^19*d^6 + 8008*a^15*b^10*c^21*d^4 + 1064*a^16*b^9*c^2*d^23 - 57456*a^16*b^9*c^4*d^21 + 529312*a^16*b^9*c^6*d^19 - 1975808*a^16*b^9*c^8*d^17 + 3897024*a^16*b^9*c^10*d^15 - 4480896*a^16*b^9*c^12*d^13 + 3071744*a^16*b^9*c^14*d^11 - 1208064*a^16*b^9*c^16*d^9 + 239096*a^16*b^9*c^18*d^7 - 16016*a^16*b^9*c^20*d^5 + 13464*a^17*b^8*c^3*d^22 - 198696*a^17*b^8*c^5*d^20 + 949952*a^17*b^8*c^7*d^18 - 2247636*a^17*b^8*c^9*d^16 + 3021984*a^17*b^8*c^11*d^14 - 2403856*a^17*b^8*c^13*d^12 + 1105104*a^17*b^8*c^15*d^10 - 264264*a^17*b^8*c^17*d^8 + 24024*a^17*b^8*c^19*d^6 - 2016*a^18*b^7*c^2*d^23 + 59024*a^18*b^7*c^4*d^21 - 379008*a^18*b^7*c^6*d^19 + 1095384*a^18*b^7*c^8*d^17 - 1728832*a^18*b^7*c^10*d^15 + 1588704*a^18*b^7*c^12*d^13 - 844896*a^18*b^7*c^14*d^11 + 239096*a^18*b^7*c^16*d^9 - 27456*a^18*b^7*c^18*d^7 - 13056*a^19*b^6*c^3*d^22 + 123584*a^19*b^6*c^5*d^20 - 446736*a^19*b^6*c^7*d^18 + 831208*a^19*b^6*c^9*d^16 - 880256*a^19*b^6*c^11*d^14 + 537264*a^19*b^6*c^13*d^12 - 176176*a^19*b^6*c^15*d^10 + 24024*a^19*b^6*c^17*d^8 + 1904*a^20*b^5*c^2*d^23 - 32256*a^20*b^5*c^4*d^21 + 150024*a^20*b^5*c^6*d^19 - 331632*a^20*b^5*c^8*d^17 + 404768*a^20*b^5*c^10*d^15 - 280896*a^20*b^5*c^12*d^13 + 104104*a^20*b^5*c^14*d^11 - 16016*a^20*b^5*c^16*d^9 + 6464*a^21*b^4*c^3*d^22 - 40512*a^21*b^4*c^5*d^20 + 108136*a^21*b^4*c^7*d^18 - 151944*a^21*b^4*c^9*d^16 + 118032*a^21*b^4*c^11*d^14 - 48048*a^21*b^4*c^13*d^12 + 8008*a^21*b^4*c^15*d^10 - 896*a^22*b^3*c^2*d^23 + 8568*a^22*b^3*c^4*d^21 - 28224*a^22*b^3*c^6*d^19 + 45136*a^22*b^3*c^8*d^17 - 38304*a^22*b^3*c^10*d^15 + 16632*a^22*b^3*c^12*d^13 - 2912*a^22*b^3*c^14*d^11 - 1392*a^23*b^2*c^3*d^22 + 5656*a^23*b^2*c^5*d^20 - 9984*a^23*b^2*c^7*d^18 + 8976*a^23*b^2*c^9*d^16 - 4048*a^23*b^2*c^11*d^14 + 728*a^23*b^2*c^13*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 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67604*a^11*b^11*c^16*d^6 - 7168*a^11*b^11*c^18*d^4 + 3672*a^12*b^10*c^3*d^19 - 36820*a^12*b^10*c^5*d^17 + 134700*a^12*b^10*c^7*d^15 - 201552*a^12*b^10*c^9*d^13 + 88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 12544*a^13*b^9*c^16*d^6 - 6788*a^14*b^8*c^3*d^19 + 53712*a^14*b^8*c^5*d^17 - 171472*a^14*b^8*c^7*d^15 + 245708*a^14*b^8*c^9*d^13 - 153012*a^14*b^8*c^11*d^11 + 26256*a^14*b^8*c^13*d^9 + 5496*a^14*b^8*c^15*d^7 + 1540*a^15*b^7*c^2*d^20 - 21228*a^15*b^7*c^4*d^18 + 96048*a^15*b^7*c^6*d^16 - 186952*a^15*b^7*c^8*d^14 + 168468*a^15*b^7*c^10*d^12 - 63372*a^15*b^7*c^12*d^10 + 5496*a^15*b^7*c^14*d^8 + 6132*a^16*b^6*c^3*d^19 - 39608*a^16*b^6*c^5*d^17 + 103992*a^16*b^6*c^7*d^15 - 125412*a^16*b^6*c^9*d^13 + 67604*a^16*b^6*c^11*d^11 - 12544*a^16*b^6*c^13*d^9 - 1200*a^17*b^5*c^2*d^20 + 11692*a^17*b^5*c^4*d^18 - 42920*a^17*b^5*c^6*d^16 + 67572*a^17*b^5*c^8*d^14 - 47152*a^17*b^5*c^10*d^12 + 12008*a^17*b^5*c^12*d^10 - 2388*a^18*b^4*c^3*d^19 + 12832*a^18*b^4*c^5*d^17 - 26148*a^18*b^4*c^7*d^15 + 22752*a^18*b^4*c^9*d^13 - 7168*a^18*b^4*c^11*d^11 + 332*a^19*b^3*c^2*d^20 - 2508*a^19*b^3*c^4*d^18 + 6852*a^19*b^3*c^6*d^16 - 7508*a^19*b^3*c^8*d^14 + 2832*a^19*b^3*c^10*d^12 + 212*a^20*b^2*c^3*d^19 - 1068*a^20*b^2*c^5*d^17 + 1612*a^20*b^2*c^7*d^15 - 728*a^20*b^2*c^9*d^13))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 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288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(a*b^18*c^19 + a^19*c*d^18 + 4*a^3*b^16*c^19 + 4*a^5*b^14*c^19 + 4*a^19*c^3*d^16 + 4*a^19*c^5*d^14 - 576*a*b^18*c^5*d^14 + 2640*a*b^18*c^7*d^12 - 4732*a*b^18*c^9*d^10 + 3961*a*b^18*c^11*d^8 - 1344*a*b^18*c^13*d^6 + 14*a*b^18*c^15*d^4 + 18*a*b^18*c^17*d^2 + 4*a^2*b^17*c^18*d - 20*a^4*b^15*c^18*d - 576*a^5*b^14*c*d^18 - 56*a^6*b^13*c^18*d + 2640*a^7*b^12*c*d^18 - 4732*a^9*b^10*c*d^18 + 3961*a^11*b^8*c*d^18 - 1344*a^13*b^6*c*d^18 + 14*a^15*b^4*c*d^18 + 18*a^17*b^2*c*d^18 + 4*a^18*b*c^2*d^17 - 20*a^18*b*c^4*d^15 - 56*a^18*b*c^6*d^13 + 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6342200*a^21*b^9*c^13*d^17 - 3772640*a^21*b^9*c^15*d^15 + 1227400*a^21*b^9*c^17*d^13 - 167960*a^21*b^9*c^19*d^11 + 1925*a^22*b^8*c^2*d^28 - 58000*a^22*b^8*c^4*d^26 + 455100*a^22*b^8*c^6*d^24 - 1598495*a^22*b^8*c^8*d^22 + 3061855*a^22*b^8*c^10*d^20 - 3441850*a^22*b^8*c^12*d^18 + 2277150*a^22*b^8*c^14*d^16 - 823650*a^22*b^8*c^16*d^14 + 125970*a^22*b^8*c^18*d^12 + 12400*a^23*b^7*c^3*d^27 - 136520*a^23*b^7*c^5*d^25 + 581120*a^23*b^7*c^7*d^23 - 1277800*a^23*b^7*c^9*d^21 + 1607600*a^23*b^7*c^11*d^19 - 1174200*a^23*b^7*c^13*d^17 + 465120*a^23*b^7*c^15*d^15 - 77520*a^23*b^7*c^17*d^13 - 1950*a^24*b^6*c^2*d^28 + 33825*a^24*b^6*c^4*d^26 - 178985*a^24*b^6*c^6*d^24 + 455100*a^24*b^6*c^8*d^22 - 639360*a^24*b^6*c^10*d^20 + 510625*a^24*b^6*c^12*d^18 - 218025*a^24*b^6*c^14*d^16 + 38760*a^24*b^6*c^16*d^14 - 6700*a^25*b^5*c^3*d^27 + 46004*a^25*b^5*c^5*d^25 - 136520*a^25*b^5*c^7*d^23 + 213040*a^25*b^5*c^9*d^21 - 183740*a^25*b^5*c^11*d^19 + 83220*a^25*b^5*c^13*d^17 - 15504*a^25*b^5*c^15*d^15 + 1000*a^26*b^4*c^2*d^28 - 9695*a^26*b^4*c^4*d^26 + 33825*a^26*b^4*c^6*d^24 - 58000*a^26*b^4*c^8*d^22 + 53210*a^26*b^4*c^10*d^20 - 25175*a^26*b^4*c^12*d^18 + 4845*a^26*b^4*c^14*d^16 + 1640*a^27*b^3*c^3*d^27 - 6700*a^27*b^3*c^5*d^25 + 12400*a^27*b^3*c^7*d^23 - 11900*a^27*b^3*c^9*d^21 + 5800*a^27*b^3*c^11*d^19 - 1140*a^27*b^3*c^13*d^17 - 215*a^28*b^2*c^2*d^28 + 1000*a^28*b^2*c^4*d^26 - 1950*a^28*b^2*c^6*d^24 + 1925*a^28*b^2*c^8*d^22 - 955*a^28*b^2*c^10*d^20 + 190*a^28*b^2*c^12*d^18 + 20*a*b^29*c^29*d + 20*a^29*b*c*d^29)))^(1/2)*2i)/f - ((a^7*d^7 + b^7*c^7 - 4*a^2*b^5*c^7 + a^3*b^4*d^7 - 2*a^5*b^2*d^7 - 4*a^7*c^2*d^5 + b^7*c^3*d^4 - 2*b^7*c^5*d^2 - 7*a*b^6*c^2*d^5 + 14*a*b^6*c^4*d^3 - 7*a^2*b^5*c*d^6 + 10*a^3*b^4*c^6*d + 14*a^4*b^3*c*d^6 + 10*a^6*b*c^3*d^4 + 6*a^2*b^5*c^3*d^4 + 8*a^2*b^5*c^5*d^2 + 6*a^3*b^4*c^2*d^5 - 20*a^3*b^4*c^4*d^3 - 20*a^4*b^3*c^3*d^4 + 8*a^5*b^2*c^2*d^5 - 7*a*b^6*c^6*d - 7*a^6*b*c*d^6)/((a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) - (tan(e/2 + (f*x)/2)*(11*a^2*b^6*c^8 - 2*b^8*c^8 - 2*a^8*d^8 - 2*a^4*b^4*d^8 + 4*a^6*b^2*d^8 + 11*a^8*c^2*d^6 - 2*b^8*c^4*d^4 + 4*b^8*c^6*d^2 + 16*a*b^7*c^3*d^5 - 32*a*b^7*c^5*d^3 + 16*a^3*b^5*c*d^7 - 13*a^3*b^5*c^7*d - 32*a^5*b^3*c*d^7 - 13*a^7*b*c^3*d^5 + 56*a^2*b^6*c^2*d^6 - 85*a^2*b^6*c^4*d^4 + 6*a^2*b^6*c^6*d^2 - 26*a^3*b^5*c^3*d^5 + 26*a^3*b^5*c^5*d^3 - 85*a^4*b^4*c^2*d^6 + 160*a^4*b^4*c^4*d^4 - 40*a^4*b^4*c^6*d^2 + 26*a^5*b^3*c^3*d^5 + 6*a^6*b^2*c^2*d^6 - 40*a^6*b^2*c^4*d^4 + 16*a*b^7*c^7*d + 16*a^7*b*c*d^7))/(a*c*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^5*(6*a*b^8*c^9 + 8*a^8*b*d^9 + 6*a^9*c*d^8 + 8*b^9*c^8*d - 21*a^3*b^6*c^9 + 8*a^4*b^5*d^9 - 16*a^6*b^3*d^9 - 21*a^9*c^3*d^6 + 8*b^9*c^4*d^5 - 16*b^9*c^6*d^3 - 48*a*b^8*c^3*d^6 + 102*a*b^8*c^5*d^4 - 60*a*b^8*c^7*d^2 - 64*a^2*b^7*c^8*d - 48*a^3*b^6*c*d^8 + 35*a^4*b^5*c^8*d + 102*a^5*b^4*c*d^8 - 60*a^7*b^2*c*d^8 - 64*a^8*b*c^2*d^7 + 35*a^8*b*c^4*d^5 - 64*a^2*b^7*c^2*d^7 + 44*a^2*b^7*c^4*d^5 + 96*a^2*b^7*c^6*d^3 + 64*a^3*b^6*c^3*d^6 - 45*a^3*b^6*c^5*d^4 + 74*a^3*b^6*c^7*d^2 + 44*a^4*b^5*c^2*d^7 - 106*a^4*b^5*c^4*d^5 - 26*a^4*b^5*c^6*d^3 - 45*a^5*b^4*c^3*d^6 - 160*a^5*b^4*c^5*d^4 + 40*a^5*b^4*c^7*d^2 + 96*a^6*b^3*c^2*d^7 - 26*a^6*b^3*c^4*d^5 + 74*a^7*b^2*c^3*d^6 + 40*a^7*b^2*c^5*d^4))/(a^2*c^2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^3*(6*a*b^8*c^9 + 8*a^8*b*d^9 + 6*a^9*c*d^8 + 8*b^9*c^8*d - 27*a^3*b^6*c^9 + 8*a^4*b^5*d^9 - 16*a^6*b^3*d^9 - 27*a^9*c^3*d^6 + 8*b^9*c^4*d^5 - 16*b^9*c^6*d^3 - 48*a*b^8*c^3*d^6 + 102*a*b^8*c^5*d^4 - 60*a*b^8*c^7*d^2 - 72*a^2*b^7*c^8*d - 48*a^3*b^6*c*d^8 + 37*a^4*b^5*c^8*d + 102*a^5*b^4*c*d^8 - 60*a^7*b^2*c*d^8 - 72*a^8*b*c^2*d^7 + 37*a^8*b*c^4*d^5 - 160*a^2*b^7*c^2*d^7 + 204*a^2*b^7*c^4*d^5 + 64*a^2*b^7*c^6*d^3 - 40*a^3*b^6*c^3*d^6 + 93*a^3*b^6*c^5*d^4 + 34*a^3*b^6*c^7*d^2 + 204*a^4*b^5*c^2*d^7 - 390*a^4*b^5*c^4*d^5 + 42*a^4*b^5*c^6*d^3 + 93*a^5*b^4*c^3*d^6 - 320*a^5*b^4*c^5*d^4 + 80*a^5*b^4*c^7*d^2 + 64*a^6*b^3*c^2*d^7 + 42*a^6*b^3*c^4*d^5 + 34*a^7*b^2*c^3*d^6 + 80*a^7*b^2*c^5*d^4))/(a^2*c^2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) - (tan(e/2 + (f*x)/2)^6*(7*a^2*b^7*c^9 - 2*b^9*c^9 - 2*a^9*d^9 + 4*a^4*b^5*c^9 - 2*a^5*b^4*d^9 + 4*a^7*b^2*d^9 + 7*a^9*c^2*d^7 + 4*a^9*c^4*d^5 - 2*b^9*c^5*d^4 + 4*b^9*c^7*d^2 + 6*a*b^8*c^4*d^5 - 12*a*b^8*c^6*d^3 + 7*a^3*b^6*c^8*d + 6*a^4*b^5*c*d^8 - 10*a^5*b^4*c^8*d - 12*a^6*b^3*c*d^8 + 7*a^8*b*c^3*d^6 - 10*a^8*b*c^5*d^4 + 32*a^2*b^7*c^3*d^6 - 57*a^2*b^7*c^5*d^4 + 18*a^2*b^7*c^7*d^2 + 32*a^3*b^6*c^2*d^7 - 37*a^3*b^6*c^4*d^5 - 14*a^3*b^6*c^6*d^3 - 37*a^4*b^5*c^3*d^6 + 82*a^4*b^5*c^5*d^4 - 52*a^4*b^5*c^7*d^2 - 57*a^5*b^4*c^2*d^7 + 82*a^5*b^4*c^4*d^5 + 20*a^5*b^4*c^6*d^3 - 14*a^6*b^3*c^3*d^6 + 20*a^6*b^3*c^5*d^4 + 18*a^7*b^2*c^2*d^7 - 52*a^7*b^2*c^4*d^5 + 6*a*b^8*c^8*d + 6*a^8*b*c*d^8))/(a^2*c^2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) - (tan(e/2 + (f*x)/2)^2*(5*a^2*b^7*c^9 - 2*b^9*c^9 - 2*a^9*d^9 + 12*a^4*b^5*c^9 - 2*a^5*b^4*d^9 + 4*a^7*b^2*d^9 + 5*a^9*c^2*d^7 + 12*a^9*c^4*d^5 - 2*b^9*c^5*d^4 + 4*b^9*c^7*d^2 + 6*a*b^8*c^4*d^5 - 12*a*b^8*c^6*d^3 + 45*a^3*b^6*c^8*d + 6*a^4*b^5*c*d^8 - 30*a^5*b^4*c^8*d - 12*a^6*b^3*c*d^8 + 45*a^8*b*c^3*d^6 - 30*a^8*b*c^5*d^4 + 104*a^2*b^7*c^3*d^6 - 187*a^2*b^7*c^5*d^4 + 66*a^2*b^7*c^7*d^2 + 104*a^3*b^6*c^2*d^7 - 111*a^3*b^6*c^4*d^5 - 62*a^3*b^6*c^6*d^3 - 111*a^4*b^5*c^3*d^6 + 262*a^4*b^5*c^5*d^4 - 124*a^4*b^5*c^7*d^2 - 187*a^5*b^4*c^2*d^7 + 262*a^5*b^4*c^4*d^5 + 20*a^5*b^4*c^6*d^3 - 62*a^6*b^3*c^3*d^6 + 20*a^6*b^3*c^5*d^4 + 66*a^7*b^2*c^2*d^7 - 124*a^7*b^2*c^4*d^5 + 6*a*b^8*c^8*d + 6*a^8*b*c*d^8))/(a^2*c^2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) - (tan(e/2 + (f*x)/2)^7*(5*a^2*b^6*c^8 - 2*b^8*c^8 - 2*a^8*d^8 - 2*a^4*b^4*d^8 + 4*a^6*b^2*d^8 + 5*a^8*c^2*d^6 - 2*b^8*c^4*d^4 + 4*b^8*c^6*d^2 + 8*a*b^7*c^3*d^5 - 16*a*b^7*c^5*d^3 + 8*a^3*b^5*c*d^7 - 11*a^3*b^5*c^7*d - 16*a^5*b^3*c*d^7 - 11*a^7*b*c^3*d^5 + 5*a^2*b^6*c^4*d^4 - 10*a^2*b^6*c^6*d^2 - 22*a^3*b^5*c^3*d^5 + 22*a^3*b^5*c^5*d^3 + 5*a^4*b^4*c^2*d^6 + 22*a^5*b^3*c^3*d^5 - 10*a^6*b^2*c^2*d^6 + 8*a*b^7*c^7*d + 8*a^7*b*c*d^7))/(a*c*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)) + (tan(e/2 + (f*x)/2)^4*(3*a^2*c^2 + 4*a^2*d^2 + 4*b^2*c^2 + 8*b^2*d^2 + 16*a*b*c*d)*(a^7*d^7 + b^7*c^7 - 4*a^2*b^5*c^7 + a^3*b^4*d^7 - 2*a^5*b^2*d^7 - 4*a^7*c^2*d^5 + b^7*c^3*d^4 - 2*b^7*c^5*d^2 - 7*a*b^6*c^2*d^5 + 14*a*b^6*c^4*d^3 - 7*a^2*b^5*c*d^6 + 10*a^3*b^4*c^6*d + 14*a^4*b^3*c*d^6 + 10*a^6*b*c^3*d^4 + 6*a^2*b^5*c^3*d^4 + 8*a^2*b^5*c^5*d^2 + 6*a^3*b^4*c^2*d^5 - 20*a^3*b^4*c^4*d^3 - 20*a^4*b^3*c^3*d^4 + 8*a^5*b^2*c^2*d^5 - 7*a*b^6*c^6*d - 7*a^6*b*c*d^6))/(a^2*c^2*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3)*(a^4*c^4 + a^4*d^4 + b^4*c^4 + b^4*d^4 - 2*a^2*b^2*c^4 - 2*a^2*b^2*d^4 - 2*a^4*c^2*d^2 - 2*b^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)*(4*a*b*c^2 + 4*a^2*c*d) + tan(e/2 + (f*x)/2)^4*(6*a^2*c^2 + 8*a^2*d^2 + 8*b^2*c^2 + 16*b^2*d^2 + 32*a*b*c*d) + tan(e/2 + (f*x)/2)^2*(4*a^2*c^2 + 4*a^2*d^2 + 4*b^2*c^2 + 16*a*b*c*d) + tan(e/2 + (f*x)/2)^6*(4*a^2*c^2 + 4*a^2*d^2 + 4*b^2*c^2 + 16*a*b*c*d) + tan(e/2 + (f*x)/2)^3*(12*a*b*c^2 + 16*a*b*d^2 + 12*a^2*c*d + 16*b^2*c*d) + tan(e/2 + (f*x)/2)^5*(12*a*b*c^2 + 16*a*b*d^2 + 12*a^2*c*d + 16*b^2*c*d) + tan(e/2 + (f*x)/2)^7*(4*a*b*c^2 + 4*a^2*c*d) + a^2*c^2 + a^2*c^2*tan(e/2 + (f*x)/2)^8)) + (atan(((-(((4*a^24*d^24 + 4*b^24*c^24 + 16*a^2*b^22*c^24 + 16*a^4*b^20*c^24 - 1152*a^10*b^14*d^24 + 5568*a^12*b^12*d^24 - 10568*a^14*b^10*d^24 + 9460*a^16*b^8*d^24 - 3560*a^18*b^6*d^24 + 136*a^20*b^4*d^24 + 76*a^22*b^2*d^24 + 16*a^24*c^2*d^22 + 16*a^24*c^4*d^20 - 1152*b^24*c^10*d^14 + 5568*b^24*c^12*d^12 - 10568*b^24*c^14*d^10 + 9460*b^24*c^16*d^8 - 3560*b^24*c^18*d^6 + 136*b^24*c^20*d^4 + 76*b^24*c^22*d^2 + 11520*a*b^23*c^9*d^15 - 56448*a*b^23*c^11*d^13 + 109456*a*b^23*c^13*d^11 - 101240*a*b^23*c^15*d^9 + 40720*a*b^23*c^17*d^7 - 2960*a*b^23*c^19*d^5 - 536*a*b^23*c^21*d^3 - 176*a^3*b^21*c^23*d - 320*a^5*b^19*c^23*d + 11520*a^9*b^15*c*d^23 - 56448*a^11*b^13*c*d^23 + 109456*a^13*b^11*c*d^23 - 101240*a^15*b^9*c*d^23 + 40720*a^17*b^7*c*d^23 - 2960*a^19*b^5*c*d^23 - 536*a^21*b^3*c*d^23 - 176*a^23*b*c^3*d^21 - 320*a^23*b*c^5*d^19 - 51840*a^2*b^22*c^8*d^16 + 263808*a^2*b^22*c^10*d^14 - 541208*a^2*b^22*c^12*d^12 + 547088*a^2*b^22*c^14*d^10 - 263320*a^2*b^22*c^16*d^8 + 44120*a^2*b^22*c^18*d^6 - 1564*a^2*b^22*c^20*d^4 - 196*a^2*b^22*c^22*d^2 + 138240*a^3*b^21*c^7*d^17 - 758400*a^3*b^21*c^9*d^15 + 1720736*a^3*b^21*c^11*d^13 - 2002728*a^3*b^21*c^13*d^11 + 1210560*a^3*b^21*c^15*d^9 - 335040*a^3*b^21*c^17*d^7 + 37680*a^3*b^21*c^19*d^5 - 288*a^3*b^21*c^21*d^3 - 241920*a^4*b^20*c^6*d^18 + 1512000*a^4*b^20*c^8*d^16 - 3975688*a^4*b^20*c^10*d^14 + 5501328*a^4*b^20*c^12*d^12 - 4147952*a^4*b^20*c^14*d^10 + 1586920*a^4*b^20*c^16*d^8 - 276020*a^4*b^20*c^18*d^6 + 21124*a^4*b^20*c^20*d^4 + 176*a^4*b^20*c^22*d^2 + 290304*a^5*b^19*c^5*d^19 - 2232576*a^5*b^19*c^7*d^17 + 7078256*a^5*b^19*c^9*d^15 - 11781560*a^5*b^19*c^11*d^13 + 10875200*a^5*b^19*c^13*d^11 - 5365072*a^5*b^19*c^15*d^9 + 1310168*a^5*b^19*c^17*d^7 - 170968*a^5*b^19*c^19*d^5 + 8160*a^5*b^19*c^21*d^3 - 241920*a^6*b^18*c^4*d^20 + 2532096*a^6*b^18*c^6*d^18 - 9955992*a^6*b^18*c^8*d^16 + 20019440*a^6*b^18*c^10*d^14 - 22419600*a^6*b^18*c^12*d^12 + 13887520*a^6*b^18*c^14*d^10 - 4506428*a^6*b^18*c^16*d^8 + 793756*a^6*b^18*c^18*d^6 - 72240*a^6*b^18*c^20*d^4 + 3040*a^6*b^18*c^22*d^2 + 138240*a^7*b^17*c^3*d^21 - 2232576*a^7*b^17*c^5*d^19 + 11150016*a^7*b^17*c^7*d^17 - 27336616*a^7*b^17*c^9*d^15 + 37153600*a^7*b^17*c^11*d^13 - 28461040*a^7*b^17*c^13*d^11 + 11779808*a^7*b^17*c^15*d^9 - 2621008*a^7*b^17*c^17*d^7 + 336688*a^7*b^17*c^19*d^5 - 17920*a^7*b^17*c^21*d^3 - 51840*a^8*b^16*c^2*d^22 + 1512000*a^8*b^16*c^4*d^20 - 9955992*a^8*b^16*c^6*d^18 + 30289656*a^8*b^16*c^8*d^16 - 50137600*a^8*b^16*c^10*d^14 + 46972560*a^8*b^16*c^12*d^12 - 24199280*a^8*b^16*c^14*d^10 + 6661036*a^8*b^16*c^16*d^8 - 1058448*a^8*b^16*c^18*d^6 + 72560*a^8*b^16*c^20*d^4 - 758400*a^9*b^15*c^3*d^21 + 7078256*a^9*b^15*c^5*d^19 - 27336616*a^9*b^15*c^7*d^17 + 55383904*a^9*b^15*c^9*d^15 - 63124080*a^9*b^15*c^11*d^13 + 39987520*a^9*b^15*c^13*d^11 - 13462088*a^9*b^15*c^15*d^9 + 2478528*a^9*b^15*c^17*d^7 - 212032*a^9*b^15*c^19*d^5 + 263808*a^10*b^14*c^2*d^22 - 3975688*a^10*b^14*c^4*d^20 + 20019440*a^10*b^14*c^6*d^18 - 50137600*a^10*b^14*c^8*d^16 + 69593872*a^10*b^14*c^10*d^14 - 53854288*a^10*b^14*c^12*d^12 + 21989928*a^10*b^14*c^14*d^10 - 4591360*a^10*b^14*c^16*d^8 + 460480*a^10*b^14*c^18*d^6 + 1720736*a^11*b^13*c^3*d^21 - 11781560*a^11*b^13*c^5*d^19 + 37153600*a^11*b^13*c^7*d^17 - 63124080*a^11*b^13*c^9*d^15 + 59445728*a^11*b^13*c^11*d^13 - 29358696*a^11*b^13*c^13*d^11 + 6995840*a^11*b^13*c^15*d^9 - 762560*a^11*b^13*c^17*d^7 - 541208*a^12*b^12*c^2*d^22 + 5501328*a^12*b^12*c^4*d^20 - 22419600*a^12*b^12*c^6*d^18 + 46972560*a^12*b^12*c^8*d^16 - 53854288*a^12*b^12*c^10*d^14 + 32294808*a^12*b^12*c^12*d^12 - 8958208*a^12*b^12*c^14*d^10 + 999040*a^12*b^12*c^16*d^8 - 2002728*a^13*b^11*c^3*d^21 + 10875200*a^13*b^11*c^5*d^19 - 28461040*a^13*b^11*c^7*d^17 + 39987520*a^13*b^11*c^9*d^15 - 29358696*a^13*b^11*c^11*d^13 + 9722048*a^13*b^11*c^13*d^11 - 1104320*a^13*b^11*c^15*d^9 + 547088*a^14*b^10*c^2*d^22 - 4147952*a^14*b^10*c^4*d^20 + 13887520*a^14*b^10*c^6*d^18 - 24199280*a^14*b^10*c^8*d^16 + 21989928*a^14*b^10*c^10*d^14 - 8958208*a^14*b^10*c^12*d^12 + 1124032*a^14*b^10*c^14*d^10 + 1210560*a^15*b^9*c^3*d^21 - 5365072*a^15*b^9*c^5*d^19 + 11779808*a^15*b^9*c^7*d^17 - 13462088*a^15*b^9*c^9*d^15 + 6995840*a^15*b^9*c^11*d^13 - 1104320*a^15*b^9*c^13*d^11 - 263320*a^16*b^8*c^2*d^22 + 1586920*a^16*b^8*c^4*d^20 - 4506428*a^16*b^8*c^6*d^18 + 6661036*a^16*b^8*c^8*d^16 - 4591360*a^16*b^8*c^10*d^14 + 999040*a^16*b^8*c^12*d^12 - 335040*a^17*b^7*c^3*d^21 + 1310168*a^17*b^7*c^5*d^19 - 2621008*a^17*b^7*c^7*d^17 + 2478528*a^17*b^7*c^9*d^15 - 762560*a^17*b^7*c^11*d^13 + 44120*a^18*b^6*c^2*d^22 - 276020*a^18*b^6*c^4*d^20 + 793756*a^18*b^6*c^6*d^18 - 1058448*a^18*b^6*c^8*d^16 + 460480*a^18*b^6*c^10*d^14 + 37680*a^19*b^5*c^3*d^21 - 170968*a^19*b^5*c^5*d^19 + 336688*a^19*b^5*c^7*d^17 - 212032*a^19*b^5*c^9*d^15 - 1564*a^20*b^4*c^2*d^22 + 21124*a^20*b^4*c^4*d^20 - 72240*a^20*b^4*c^6*d^18 + 72560*a^20*b^4*c^8*d^16 - 288*a^21*b^3*c^3*d^21 + 8160*a^21*b^3*c^5*d^19 - 17920*a^21*b^3*c^7*d^17 - 196*a^22*b^2*c^2*d^22 + 176*a^22*b^2*c^4*d^20 + 3040*a^22*b^2*c^6*d^18 - 8*a*b^23*c^23*d - 8*a^23*b*c*d^23)^2/4 - (20736*b^18*d^18 - 96768*a^2*b^16*d^18 + 173664*a^4*b^14*d^18 - 136032*a^6*b^12*d^18 + 31081*a^8*b^10*d^18 + 8440*a^10*b^8*d^18 + 400*a^12*b^6*d^18 - 96768*b^18*c^2*d^16 + 173664*b^18*c^4*d^14 - 136032*b^18*c^6*d^12 + 31081*b^18*c^8*d^10 + 8440*b^18*c^10*d^8 + 400*b^18*c^12*d^6 - 131328*a*b^17*c^3*d^15 + 216576*a*b^17*c^5*d^13 - 141104*a*b^17*c^7*d^11 + 20260*a*b^17*c^9*d^9 + 2800*a*b^17*c^11*d^7 - 131328*a^3*b^15*c*d^17 + 216576*a^5*b^13*c*d^17 - 141104*a^7*b^11*c*d^17 + 20260*a^9*b^9*c*d^17 + 2800*a^11*b^7*c*d^17 + 495936*a^2*b^16*c^2*d^16 - 989856*a^2*b^16*c^4*d^14 + 901948*a^2*b^16*c^6*d^12 - 308392*a^2*b^16*c^8*d^10 - 5260*a^2*b^16*c^10*d^8 + 1600*a^2*b^16*c^12*d^6 + 657408*a^3*b^15*c^3*d^15 - 1158992*a^3*b^15*c^5*d^13 + 838256*a^3*b^15*c^7*d^11 - 182200*a^3*b^15*c^9*d^9 - 3200*a^3*b^15*c^11*d^7 - 989856*a^4*b^14*c^2*d^16 + 2185654*a^4*b^14*c^4*d^14 - 2218576*a^4*b^14*c^6*d^12 + 900624*a^4*b^14*c^8*d^10 - 64720*a^4*b^14*c^10*d^8 + 1600*a^4*b^14*c^12*d^6 - 1158992*a^5*b^13*c^3*d^15 + 2158808*a^5*b^13*c^5*d^13 - 1641528*a^5*b^13*c^7*d^11 + 406880*a^5*b^13*c^9*d^9 - 17600*a^5*b^13*c^11*d^7 + 901948*a^6*b^12*c^2*d^16 - 2218576*a^6*b^12*c^4*d^14 + 2430936*a^6*b^12*c^6*d^12 - 1026928*a^6*b^12*c^8*d^10 + 88720*a^6*b^12*c^10*d^8 + 838256*a^7*b^11*c^3*d^15 - 1641528*a^7*b^11*c^5*d^13 + 1206848*a^7*b^11*c^7*d^11 - 239360*a^7*b^11*c^9*d^9 - 308392*a^8*b^10*c^2*d^16 + 900624*a^8*b^10*c^4*d^14 - 1026928*a^8*b^10*c^6*d^12 + 354016*a^8*b^10*c^8*d^10 - 182200*a^9*b^9*c^3*d^15 + 406880*a^9*b^9*c^5*d^13 - 239360*a^9*b^9*c^7*d^11 - 5260*a^10*b^8*c^2*d^16 - 64720*a^10*b^8*c^4*d^14 + 88720*a^10*b^8*c^6*d^12 - 3200*a^11*b^7*c^3*d^15 - 17600*a^11*b^7*c^5*d^13 + 1600*a^12*b^6*c^2*d^16 + 1600*a^12*b^6*c^4*d^14 + 27648*a*b^17*c*d^17)*(80*a^2*b^28*c^30 - 16*b^30*c^30 - 16*a^30*d^30 - 160*a^4*b^26*c^30 + 160*a^6*b^24*c^30 - 80*a^8*b^22*c^30 + 16*a^10*b^20*c^30 + 16*a^20*b^10*d^30 - 80*a^22*b^8*d^30 + 160*a^24*b^6*d^30 - 160*a^26*b^4*d^30 + 80*a^28*b^2*d^30 + 80*a^30*c^2*d^28 - 160*a^30*c^4*d^26 + 160*a^30*c^6*d^24 - 80*a^30*c^8*d^22 + 16*a^30*c^10*d^20 + 16*b^30*c^20*d^10 - 80*b^30*c^22*d^8 + 160*b^30*c^24*d^6 - 160*b^30*c^26*d^4 + 80*b^30*c^28*d^2 - 320*a*b^29*c^19*d^11 + 1600*a*b^29*c^21*d^9 - 3200*a*b^29*c^23*d^7 + 3200*a*b^29*c^25*d^5 - 1600*a*b^29*c^27*d^3 - 1600*a^3*b^27*c^29*d + 3200*a^5*b^25*c^29*d - 3200*a^7*b^23*c^29*d + 1600*a^9*b^21*c^29*d - 320*a^11*b^19*c^29*d - 320*a^19*b^11*c*d^29 + 1600*a^21*b^9*c*d^29 - 3200*a^23*b^7*c*d^29 + 3200*a^25*b^5*c*d^29 - 1600*a^27*b^3*c*d^29 - 1600*a^29*b*c^3*d^27 + 3200*a^29*b*c^5*d^25 - 3200*a^29*b*c^7*d^23 + 1600*a^29*b*c^9*d^21 - 320*a^29*b*c^11*d^19 + 3040*a^2*b^28*c^18*d^12 - 15280*a^2*b^28*c^20*d^10 + 30800*a^2*b^28*c^22*d^8 - 31200*a^2*b^28*c^24*d^6 + 16000*a^2*b^28*c^26*d^4 - 3440*a^2*b^28*c^28*d^2 - 18240*a^3*b^27*c^17*d^13 + 92800*a^3*b^27*c^19*d^11 - 190400*a^3*b^27*c^21*d^9 + 198400*a^3*b^27*c^23*d^7 - 107200*a^3*b^27*c^25*d^5 + 26240*a^3*b^27*c^27*d^3 + 77520*a^4*b^26*c^16*d^14 - 402800*a^4*b^26*c^18*d^12 + 851360*a^4*b^26*c^20*d^10 - 928000*a^4*b^26*c^22*d^8 + 541200*a^4*b^26*c^24*d^6 - 155120*a^4*b^26*c^26*d^4 + 16000*a^4*b^26*c^28*d^2 - 248064*a^5*b^25*c^15*d^15 + 1331520*a^5*b^25*c^17*d^13 - 2939840*a^5*b^25*c^19*d^11 + 3408640*a^5*b^25*c^21*d^9 - 2184320*a^5*b^25*c^23*d^7 + 736064*a^5*b^25*c^25*d^5 - 107200*a^5*b^25*c^27*d^3 + 620160*a^6*b^24*c^14*d^16 - 3488400*a^6*b^24*c^16*d^14 + 8170000*a^6*b^24*c^18*d^12 - 10229760*a^6*b^24*c^20*d^10 + 7281600*a^6*b^24*c^22*d^8 - 2863760*a^6*b^24*c^24*d^6 + 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72*a^23*b^2*c^2*d^23 + 328*a^23*b^2*c^4*d^21 - 2032*a^23*b^2*c^6*d^19 + 3408*a^23*b^2*c^8*d^17 - 2392*a^23*b^2*c^10*d^15 + 616*a^23*b^2*c^12*d^13 - 8*a*b^24*c^24*d - 8*a^24*b*c*d^24))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 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198696*a^5*b^20*c^17*d^8 + 123584*a^5*b^20*c^19*d^6 - 40512*a^5*b^20*c^21*d^4 + 5656*a^5*b^20*c^23*d^2 - 32032*a^6*b^19*c^10*d^15 + 179816*a^6*b^19*c^12*d^13 - 421344*a^6*b^19*c^14*d^11 + 529312*a^6*b^19*c^16*d^9 - 379008*a^6*b^19*c^18*d^7 + 150024*a^6*b^19*c^20*d^5 - 28224*a^6*b^19*c^22*d^3 + 48048*a^7*b^18*c^9*d^16 - 304304*a^7*b^18*c^11*d^14 + 805896*a^7*b^18*c^13*d^12 - 1151104*a^7*b^18*c^15*d^10 + 949952*a^7*b^18*c^17*d^8 - 446736*a^7*b^18*c^19*d^6 + 108136*a^7*b^18*c^21*d^4 - 9984*a^7*b^18*c^23*d^2 - 54912*a^8*b^17*c^8*d^17 + 412984*a^8*b^17*c^10*d^15 - 1267344*a^8*b^17*c^12*d^13 + 2077536*a^8*b^17*c^14*d^11 - 1975808*a^8*b^17*c^16*d^9 + 1095384*a^8*b^17*c^18*d^7 - 331632*a^8*b^17*c^20*d^5 + 45136*a^8*b^17*c^22*d^3 + 48048*a^9*b^16*c^7*d^18 - 456456*a^9*b^16*c^9*d^16 + 1657656*a^9*b^16*c^11*d^14 - 3143504*a^9*b^16*c^13*d^12 + 3453696*a^9*b^16*c^15*d^10 - 2247636*a^9*b^16*c^17*d^8 + 831208*a^9*b^16*c^19*d^6 - 151944*a^9*b^16*c^21*d^4 + 8976*a^9*b^16*c^23*d^2 - 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53210*a^4*b^26*c^20*d^10 - 58000*a^4*b^26*c^22*d^8 + 33825*a^4*b^26*c^24*d^6 - 9695*a^4*b^26*c^26*d^4 + 1000*a^4*b^26*c^28*d^2 - 15504*a^5*b^25*c^15*d^15 + 83220*a^5*b^25*c^17*d^13 - 183740*a^5*b^25*c^19*d^11 + 213040*a^5*b^25*c^21*d^9 - 136520*a^5*b^25*c^23*d^7 + 46004*a^5*b^25*c^25*d^5 - 6700*a^5*b^25*c^27*d^3 + 38760*a^6*b^24*c^14*d^16 - 218025*a^6*b^24*c^16*d^14 + 510625*a^6*b^24*c^18*d^12 - 639360*a^6*b^24*c^20*d^10 + 455100*a^6*b^24*c^22*d^8 - 178985*a^6*b^24*c^24*d^6 + 33825*a^6*b^24*c^26*d^4 - 1950*a^6*b^24*c^28*d^2 - 77520*a^7*b^23*c^13*d^17 + 465120*a^7*b^23*c^15*d^15 - 1174200*a^7*b^23*c^17*d^13 + 1607600*a^7*b^23*c^19*d^11 - 1277800*a^7*b^23*c^21*d^9 + 581120*a^7*b^23*c^23*d^7 - 136520*a^7*b^23*c^25*d^5 + 12400*a^7*b^23*c^27*d^3 + 125970*a^8*b^22*c^12*d^18 - 823650*a^8*b^22*c^14*d^16 + 2277150*a^8*b^22*c^16*d^14 - 3441850*a^8*b^22*c^18*d^12 + 3061855*a^8*b^22*c^20*d^10 - 1598495*a^8*b^22*c^22*d^8 + 455100*a^8*b^22*c^24*d^6 - 58000*a^8*b^22*c^26*d^4 + 1925*a^8*b^22*c^28*d^2 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21339185*a^12*b^18*c^18*d^12 + 11341480*a^12*b^18*c^20*d^10 - 3441850*a^12*b^18*c^22*d^8 + 510625*a^12*b^18*c^24*d^6 - 25175*a^12*b^18*c^26*d^4 + 190*a^12*b^18*c^28*d^2 - 77520*a^13*b^17*c^7*d^23 + 1227400*a^13*b^17*c^9*d^21 - 6653800*a^13*b^17*c^11*d^19 + 18346400*a^13*b^17*c^13*d^17 - 29535120*a^13*b^17*c^15*d^15 + 29213260*a^13*b^17*c^17*d^13 - 17770700*a^13*b^17*c^19*d^11 + 6342200*a^13*b^17*c^21*d^9 - 1174200*a^13*b^17*c^23*d^7 + 83220*a^13*b^17*c^25*d^5 - 1140*a^13*b^17*c^27*d^3 + 38760*a^14*b^16*c^6*d^24 - 823650*a^14*b^16*c^8*d^22 + 5384410*a^14*b^16*c^10*d^20 - 17183600*a^14*b^16*c^12*d^18 + 31460200*a^14*b^16*c^14*d^16 - 35234455*a^14*b^16*c^16*d^14 + 24426875*a^14*b^16*c^18*d^12 - 10132510*a^14*b^16*c^20*d^10 + 2277150*a^14*b^16*c^22*d^8 - 218025*a^14*b^16*c^24*d^6 + 4845*a^14*b^16*c^26*d^4 - 15504*a^15*b^15*c^5*d^25 + 465120*a^15*b^15*c^7*d^23 - 3772640*a^15*b^15*c^9*d^21 + 14108640*a^15*b^15*c^11*d^19 - 29535120*a^15*b^15*c^13*d^17 + 37499008*a^15*b^15*c^15*d^15 - 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3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 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212*a^3*b^19*c^20*d^2 + 1800*a^4*b^18*c^9*d^13 - 8680*a^4*b^18*c^11*d^11 + 18852*a^4*b^18*c^13*d^9 - 21228*a^4*b^18*c^15*d^7 + 11692*a^4*b^18*c^17*d^5 - 2508*a^4*b^18*c^19*d^3 - 2160*a^5*b^17*c^8*d^14 + 13100*a^5*b^17*c^10*d^12 - 36820*a^5*b^17*c^12*d^10 + 53712*a^5*b^17*c^14*d^8 - 39608*a^5*b^17*c^16*d^6 + 12832*a^5*b^17*c^18*d^4 - 1068*a^5*b^17*c^20*d^2 + 1008*a^6*b^16*c^7*d^15 - 12420*a^6*b^16*c^9*d^13 + 51764*a^6*b^16*c^11*d^11 - 100128*a^6*b^16*c^13*d^9 + 96048*a^6*b^16*c^15*d^7 - 42920*a^6*b^16*c^17*d^5 + 6852*a^6*b^16*c^19*d^3 + 1008*a^7*b^15*c^6*d^16 + 5136*a^7*b^15*c^8*d^14 - 48820*a^7*b^15*c^10*d^12 + 134700*a^7*b^15*c^12*d^10 - 171472*a^7*b^15*c^14*d^8 + 103992*a^7*b^15*c^16*d^6 - 26148*a^7*b^15*c^18*d^4 + 1612*a^7*b^15*c^20*d^2 - 2160*a^8*b^14*c^5*d^17 + 5136*a^8*b^14*c^7*d^15 + 20436*a^8*b^14*c^9*d^13 - 121524*a^8*b^14*c^11*d^11 + 224888*a^8*b^14*c^13*d^9 - 186952*a^8*b^14*c^15*d^7 + 67572*a^8*b^14*c^17*d^5 - 7508*a^8*b^14*c^19*d^3 + 1800*a^9*b^13*c^4*d^18 - 12420*a^9*b^13*c^6*d^16 + 20436*a^9*b^13*c^8*d^14 + 49416*a^9*b^13*c^10*d^12 - 201552*a^9*b^13*c^12*d^10 + 245708*a^9*b^13*c^14*d^8 - 125412*a^9*b^13*c^16*d^6 + 22752*a^9*b^13*c^18*d^4 - 728*a^9*b^13*c^20*d^2 - 840*a^10*b^12*c^3*d^19 + 13100*a^10*b^12*c^5*d^17 - 48820*a^10*b^12*c^7*d^15 + 49416*a^10*b^12*c^9*d^13 + 82088*a^10*b^12*c^11*d^11 - 219092*a^10*b^12*c^13*d^9 + 168468*a^10*b^12*c^15*d^7 - 47152*a^10*b^12*c^17*d^5 + 2832*a^10*b^12*c^19*d^3 + 216*a^11*b^11*c^2*d^20 - 8680*a^11*b^11*c^4*d^18 + 51764*a^11*b^11*c^6*d^16 - 121524*a^11*b^11*c^8*d^14 + 82088*a^11*b^11*c^10*d^12 + 88712*a^11*b^11*c^12*d^10 - 153012*a^11*b^11*c^14*d^8 + 67604*a^11*b^11*c^16*d^6 - 7168*a^11*b^11*c^18*d^4 + 3672*a^12*b^10*c^3*d^19 - 36820*a^12*b^10*c^5*d^17 + 134700*a^12*b^10*c^7*d^15 - 201552*a^12*b^10*c^9*d^13 + 88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 12544*a^13*b^9*c^16*d^6 - 6788*a^14*b^8*c^3*d^19 + 53712*a^14*b^8*c^5*d^17 - 171472*a^14*b^8*c^7*d^15 + 245708*a^14*b^8*c^9*d^13 - 153012*a^14*b^8*c^11*d^11 + 26256*a^14*b^8*c^13*d^9 + 5496*a^14*b^8*c^15*d^7 + 1540*a^15*b^7*c^2*d^20 - 21228*a^15*b^7*c^4*d^18 + 96048*a^15*b^7*c^6*d^16 - 186952*a^15*b^7*c^8*d^14 + 168468*a^15*b^7*c^10*d^12 - 63372*a^15*b^7*c^12*d^10 + 5496*a^15*b^7*c^14*d^8 + 6132*a^16*b^6*c^3*d^19 - 39608*a^16*b^6*c^5*d^17 + 103992*a^16*b^6*c^7*d^15 - 125412*a^16*b^6*c^9*d^13 + 67604*a^16*b^6*c^11*d^11 - 12544*a^16*b^6*c^13*d^9 - 1200*a^17*b^5*c^2*d^20 + 11692*a^17*b^5*c^4*d^18 - 42920*a^17*b^5*c^6*d^16 + 67572*a^17*b^5*c^8*d^14 - 47152*a^17*b^5*c^10*d^12 + 12008*a^17*b^5*c^12*d^10 - 2388*a^18*b^4*c^3*d^19 + 12832*a^18*b^4*c^5*d^17 - 26148*a^18*b^4*c^7*d^15 + 22752*a^18*b^4*c^9*d^13 - 7168*a^18*b^4*c^11*d^11 + 332*a^19*b^3*c^2*d^20 - 2508*a^19*b^3*c^4*d^18 + 6852*a^19*b^3*c^6*d^16 - 7508*a^19*b^3*c^8*d^14 + 2832*a^19*b^3*c^10*d^12 + 212*a^20*b^2*c^3*d^19 - 1068*a^20*b^2*c^5*d^17 + 1612*a^20*b^2*c^7*d^15 - 728*a^20*b^2*c^9*d^13))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19)) + (4*(288*a*b^18*c^6*d^13 - 1104*a*b^18*c^8*d^11 + 1538*a*b^18*c^10*d^9 - 872*a*b^18*c^12*d^7 + 108*a*b^18*c^14*d^5 + 40*a*b^18*c^16*d^3 + 8*a^3*b^16*c^18*d + 8*a^5*b^14*c^18*d + 288*a^6*b^13*c*d^18 - 1104*a^8*b^11*c*d^18 + 1538*a^10*b^9*c*d^18 - 872*a^12*b^7*c*d^18 + 108*a^14*b^5*c*d^18 + 40*a^16*b^3*c*d^18 + 8*a^18*b*c^3*d^16 + 8*a^18*b*c^5*d^14 - 864*a^2*b^17*c^5*d^14 + 3216*a^2*b^17*c^7*d^12 - 4262*a^2*b^17*c^9*d^10 + 2256*a^2*b^17*c^11*d^8 - 304*a^2*b^17*c^13*d^6 - 32*a^2*b^17*c^15*d^4 + 8*a^2*b^17*c^17*d^2 + 576*a^3*b^16*c^4*d^15 - 3024*a^3*b^16*c^6*d^13 + 6304*a^3*b^16*c^8*d^11 - 7216*a^3*b^16*c^10*d^9 + 4944*a^3*b^16*c^12*d^7 - 1664*a^3*b^16*c^14*d^5 - 72*a^3*b^16*c^16*d^3 + 576*a^4*b^15*c^3*d^16 + 912*a^4*b^15*c^5*d^14 - 8720*a^4*b^15*c^7*d^12 + 16632*a^4*b^15*c^9*d^10 - 14888*a^4*b^15*c^11*d^8 + 6704*a^4*b^15*c^13*d^6 - 744*a^4*b^15*c^15*d^4 - 40*a^4*b^15*c^17*d^2 - 864*a^5*b^14*c^2*d^17 + 912*a^5*b^14*c^4*d^15 + 5140*a^5*b^14*c^6*d^13 - 16080*a^5*b^14*c^8*d^11 + 23520*a^5*b^14*c^10*d^9 - 20208*a^5*b^14*c^12*d^7 + 7404*a^5*b^14*c^14*d^5 - 264*a^5*b^14*c^16*d^3 - 3024*a^6*b^13*c^3*d^16 + 5140*a^6*b^13*c^5*d^14 + 5280*a^6*b^13*c^7*d^12 - 28380*a^6*b^13*c^9*d^10 + 39792*a^6*b^13*c^11*d^8 - 22728*a^6*b^13*c^13*d^6 + 3096*a^6*b^13*c^15*d^4 - 112*a^6*b^13*c^17*d^2 + 3216*a^7*b^12*c^2*d^17 - 8720*a^7*b^12*c^4*d^15 + 5280*a^7*b^12*c^6*d^13 + 15000*a^7*b^12*c^8*d^11 - 40656*a^7*b^12*c^10*d^9 + 40296*a^7*b^12*c^12*d^7 - 12984*a^7*b^12*c^14*d^5 + 728*a^7*b^12*c^16*d^3 + 6304*a^8*b^11*c^3*d^16 - 16080*a^8*b^11*c^5*d^14 + 15000*a^8*b^11*c^7*d^12 + 16024*a^8*b^11*c^9*d^10 - 46184*a^8*b^11*c^11*d^8 + 27208*a^8*b^11*c^13*d^6 - 2752*a^8*b^11*c^15*d^4 - 4262*a^9*b^10*c^2*d^17 + 16632*a^9*b^10*c^4*d^15 - 28380*a^9*b^10*c^6*d^13 + 16024*a^9*b^10*c^8*d^11 + 22018*a^9*b^10*c^10*d^9 - 30104*a^9*b^10*c^12*d^7 + 6488*a^9*b^10*c^14*d^5 - 7216*a^10*b^9*c^3*d^16 + 23520*a^10*b^9*c^5*d^14 - 40656*a^10*b^9*c^7*d^12 + 22018*a^10*b^9*c^9*d^10 + 13080*a^10*b^9*c^11*d^8 - 8720*a^10*b^9*c^13*d^6 + 2256*a^11*b^8*c^2*d^17 - 14888*a^11*b^8*c^4*d^15 + 39792*a^11*b^8*c^6*d^13 - 46184*a^11*b^8*c^8*d^11 + 13080*a^11*b^8*c^10*d^9 + 4360*a^11*b^8*c^12*d^7 + 4944*a^12*b^7*c^3*d^16 - 20208*a^12*b^7*c^5*d^14 + 40296*a^12*b^7*c^7*d^12 - 30104*a^12*b^7*c^9*d^10 + 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12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 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760*a^15*b^4*c^3*d^16 + 3966*a^15*b^4*c^5*d^14 - 7220*a^15*b^4*c^7*d^12 + 3244*a^15*b^4*c^9*d^10 - 24*a^16*b^3*c^2*d^17 - 332*a^16*b^3*c^4*d^15 + 1660*a^16*b^3*c^6*d^13 - 1376*a^16*b^3*c^8*d^11 - 44*a^17*b^2*c^3*d^16 - 140*a^17*b^2*c^5*d^14 + 364*a^17*b^2*c^7*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 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1904*a^2*b^23*c^20*d^5 - 896*a^2*b^23*c^22*d^3 + 1456*a^3*b^22*c^13*d^12 - 6992*a^3*b^22*c^15*d^10 + 13464*a^3*b^22*c^17*d^8 - 13056*a^3*b^22*c^19*d^6 + 6464*a^3*b^22*c^21*d^4 - 1392*a^3*b^22*c^23*d^2 - 5824*a^4*b^21*c^12*d^13 + 28728*a^4*b^21*c^14*d^11 - 57456*a^4*b^21*c^16*d^9 + 59024*a^4*b^21*c^18*d^7 - 32256*a^4*b^21*c^20*d^5 + 8568*a^4*b^21*c^22*d^3 + 16016*a^5*b^20*c^11*d^14 - 82992*a^5*b^20*c^13*d^12 + 177048*a^5*b^20*c^15*d^10 - 198696*a^5*b^20*c^17*d^8 + 123584*a^5*b^20*c^19*d^6 - 40512*a^5*b^20*c^21*d^4 + 5656*a^5*b^20*c^23*d^2 - 32032*a^6*b^19*c^10*d^15 + 179816*a^6*b^19*c^12*d^13 - 421344*a^6*b^19*c^14*d^11 + 529312*a^6*b^19*c^16*d^9 - 379008*a^6*b^19*c^18*d^7 + 150024*a^6*b^19*c^20*d^5 - 28224*a^6*b^19*c^22*d^3 + 48048*a^7*b^18*c^9*d^16 - 304304*a^7*b^18*c^11*d^14 + 805896*a^7*b^18*c^13*d^12 - 1151104*a^7*b^18*c^15*d^10 + 949952*a^7*b^18*c^17*d^8 - 446736*a^7*b^18*c^19*d^6 + 108136*a^7*b^18*c^21*d^4 - 9984*a^7*b^18*c^23*d^2 - 54912*a^8*b^17*c^8*d^17 + 412984*a^8*b^17*c^10*d^15 - 1267344*a^8*b^17*c^12*d^13 + 2077536*a^8*b^17*c^14*d^11 - 1975808*a^8*b^17*c^16*d^9 + 1095384*a^8*b^17*c^18*d^7 - 331632*a^8*b^17*c^20*d^5 + 45136*a^8*b^17*c^22*d^3 + 48048*a^9*b^16*c^7*d^18 - 456456*a^9*b^16*c^9*d^16 + 1657656*a^9*b^16*c^11*d^14 - 3143504*a^9*b^16*c^13*d^12 + 3453696*a^9*b^16*c^15*d^10 - 2247636*a^9*b^16*c^17*d^8 + 831208*a^9*b^16*c^19*d^6 - 151944*a^9*b^16*c^21*d^4 + 8976*a^9*b^16*c^23*d^2 - 32032*a^10*b^15*c^6*d^19 + 412984*a^10*b^15*c^8*d^17 - 1812096*a^10*b^15*c^10*d^15 + 4016896*a^10*b^15*c^12*d^13 - 5121024*a^10*b^15*c^14*d^11 + 3897024*a^10*b^15*c^16*d^9 - 1728832*a^10*b^15*c^18*d^7 + 404768*a^10*b^15*c^20*d^5 - 38304*a^10*b^15*c^22*d^3 + 16016*a^11*b^14*c^5*d^20 - 304304*a^11*b^14*c^7*d^18 + 1657656*a^11*b^14*c^9*d^16 - 4356352*a^11*b^14*c^11*d^14 + 6476288*a^11*b^14*c^13*d^12 - 5745024*a^11*b^14*c^15*d^10 + 3021984*a^11*b^14*c^17*d^8 - 880256*a^11*b^14*c^19*d^6 + 118032*a^11*b^14*c^21*d^4 - 4048*a^11*b^14*c^23*d^2 - 5824*a^12*b^13*c^4*d^21 + 179816*a^12*b^13*c^6*d^19 - 1267344*a^12*b^13*c^8*d^17 + 4016896*a^12*b^13*c^10*d^15 - 7002112*a^12*b^13*c^12*d^13 + 7235136*a^12*b^13*c^14*d^11 - 4480896*a^12*b^13*c^16*d^9 + 1588704*a^12*b^13*c^18*d^7 - 280896*a^12*b^13*c^20*d^5 + 16632*a^12*b^13*c^22*d^3 + 1456*a^13*b^12*c^3*d^22 - 82992*a^13*b^12*c^5*d^20 + 805896*a^13*b^12*c^7*d^18 - 3143504*a^13*b^12*c^9*d^16 + 6476288*a^13*b^12*c^11*d^14 - 7809984*a^13*b^12*c^13*d^12 + 5666752*a^13*b^12*c^15*d^10 - 2403856*a^13*b^12*c^17*d^8 + 537264*a^13*b^12*c^19*d^6 - 48048*a^13*b^12*c^21*d^4 + 728*a^13*b^12*c^23*d^2 - 224*a^14*b^11*c^2*d^23 + 28728*a^14*b^11*c^4*d^21 - 421344*a^14*b^11*c^6*d^19 + 2077536*a^14*b^11*c^8*d^17 - 5121024*a^14*b^11*c^10*d^15 + 7235136*a^14*b^11*c^12*d^13 - 6126848*a^14*b^11*c^14*d^11 + 3071744*a^14*b^11*c^16*d^9 - 844896*a^14*b^11*c^18*d^7 + 104104*a^14*b^11*c^20*d^5 - 2912*a^14*b^11*c^22*d^3 - 6992*a^15*b^10*c^3*d^22 + 177048*a^15*b^10*c^5*d^20 - 1151104*a^15*b^10*c^7*d^18 + 3453696*a^15*b^10*c^9*d^16 - 5745024*a^15*b^10*c^11*d^14 + 5666752*a^15*b^10*c^13*d^12 - 3331328*a^15*b^10*c^15*d^10 + 1105104*a^15*b^10*c^17*d^8 - 176176*a^15*b^10*c^19*d^6 + 8008*a^15*b^10*c^21*d^4 + 1064*a^16*b^9*c^2*d^23 - 57456*a^16*b^9*c^4*d^21 + 529312*a^16*b^9*c^6*d^19 - 1975808*a^16*b^9*c^8*d^17 + 3897024*a^16*b^9*c^10*d^15 - 4480896*a^16*b^9*c^12*d^13 + 3071744*a^16*b^9*c^14*d^11 - 1208064*a^16*b^9*c^16*d^9 + 239096*a^16*b^9*c^18*d^7 - 16016*a^16*b^9*c^20*d^5 + 13464*a^17*b^8*c^3*d^22 - 198696*a^17*b^8*c^5*d^20 + 949952*a^17*b^8*c^7*d^18 - 2247636*a^17*b^8*c^9*d^16 + 3021984*a^17*b^8*c^11*d^14 - 2403856*a^17*b^8*c^13*d^12 + 1105104*a^17*b^8*c^15*d^10 - 264264*a^17*b^8*c^17*d^8 + 24024*a^17*b^8*c^19*d^6 - 2016*a^18*b^7*c^2*d^23 + 59024*a^18*b^7*c^4*d^21 - 379008*a^18*b^7*c^6*d^19 + 1095384*a^18*b^7*c^8*d^17 - 1728832*a^18*b^7*c^10*d^15 + 1588704*a^18*b^7*c^12*d^13 - 844896*a^18*b^7*c^14*d^11 + 239096*a^18*b^7*c^16*d^9 - 27456*a^18*b^7*c^18*d^7 - 13056*a^19*b^6*c^3*d^22 + 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3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(12*a^5*b^17*c^22 - 4*a^22*c*d^21 - 4*a*b^21*c^22 - 8*a^7*b^15*c^22 + 12*a^22*c^5*d^17 - 8*a^22*c^7*d^15 - 24*a*b^21*c^12*d^10 + 100*a*b^21*c^14*d^8 - 164*a*b^21*c^16*d^6 + 120*a*b^21*c^18*d^4 - 28*a*b^21*c^20*d^2 + 20*a^2*b^20*c^21*d + 72*a^4*b^18*c^21*d - 204*a^6*b^16*c^21*d + 112*a^8*b^14*c^21*d - 24*a^12*b^10*c*d^21 + 100*a^14*b^8*c*d^21 - 164*a^16*b^6*c*d^21 + 120*a^18*b^4*c*d^21 - 28*a^20*b^2*c*d^21 + 20*a^21*b*c^2*d^20 + 72*a^21*b*c^4*d^18 - 204*a^21*b*c^6*d^16 + 112*a^21*b*c^8*d^14 + 216*a^2*b^20*c^11*d^11 - 908*a^2*b^20*c^13*d^9 + 1540*a^2*b^20*c^15*d^7 - 1200*a^2*b^20*c^17*d^5 + 332*a^2*b^20*c^19*d^3 - 840*a^3*b^19*c^10*d^12 + 3672*a^3*b^19*c^12*d^10 - 6788*a^3*b^19*c^14*d^8 + 6132*a^3*b^19*c^16*d^6 - 2388*a^3*b^19*c^18*d^4 + 212*a^3*b^19*c^20*d^2 + 1800*a^4*b^18*c^9*d^13 - 8680*a^4*b^18*c^11*d^11 + 18852*a^4*b^18*c^13*d^9 - 21228*a^4*b^18*c^15*d^7 + 11692*a^4*b^18*c^17*d^5 - 2508*a^4*b^18*c^19*d^3 - 2160*a^5*b^17*c^8*d^14 + 13100*a^5*b^17*c^10*d^12 - 36820*a^5*b^17*c^12*d^10 + 53712*a^5*b^17*c^14*d^8 - 39608*a^5*b^17*c^16*d^6 + 12832*a^5*b^17*c^18*d^4 - 1068*a^5*b^17*c^20*d^2 + 1008*a^6*b^16*c^7*d^15 - 12420*a^6*b^16*c^9*d^13 + 51764*a^6*b^16*c^11*d^11 - 100128*a^6*b^16*c^13*d^9 + 96048*a^6*b^16*c^15*d^7 - 42920*a^6*b^16*c^17*d^5 + 6852*a^6*b^16*c^19*d^3 + 1008*a^7*b^15*c^6*d^16 + 5136*a^7*b^15*c^8*d^14 - 48820*a^7*b^15*c^10*d^12 + 134700*a^7*b^15*c^12*d^10 - 171472*a^7*b^15*c^14*d^8 + 103992*a^7*b^15*c^16*d^6 - 26148*a^7*b^15*c^18*d^4 + 1612*a^7*b^15*c^20*d^2 - 2160*a^8*b^14*c^5*d^17 + 5136*a^8*b^14*c^7*d^15 + 20436*a^8*b^14*c^9*d^13 - 121524*a^8*b^14*c^11*d^11 + 224888*a^8*b^14*c^13*d^9 - 186952*a^8*b^14*c^15*d^7 + 67572*a^8*b^14*c^17*d^5 - 7508*a^8*b^14*c^19*d^3 + 1800*a^9*b^13*c^4*d^18 - 12420*a^9*b^13*c^6*d^16 + 20436*a^9*b^13*c^8*d^14 + 49416*a^9*b^13*c^10*d^12 - 201552*a^9*b^13*c^12*d^10 + 245708*a^9*b^13*c^14*d^8 - 125412*a^9*b^13*c^16*d^6 + 22752*a^9*b^13*c^18*d^4 - 728*a^9*b^13*c^20*d^2 - 840*a^10*b^12*c^3*d^19 + 13100*a^10*b^12*c^5*d^17 - 48820*a^10*b^12*c^7*d^15 + 49416*a^10*b^12*c^9*d^13 + 82088*a^10*b^12*c^11*d^11 - 219092*a^10*b^12*c^13*d^9 + 168468*a^10*b^12*c^15*d^7 - 47152*a^10*b^12*c^17*d^5 + 2832*a^10*b^12*c^19*d^3 + 216*a^11*b^11*c^2*d^20 - 8680*a^11*b^11*c^4*d^18 + 51764*a^11*b^11*c^6*d^16 - 121524*a^11*b^11*c^8*d^14 + 82088*a^11*b^11*c^10*d^12 + 88712*a^11*b^11*c^12*d^10 - 153012*a^11*b^11*c^14*d^8 + 67604*a^11*b^11*c^16*d^6 - 7168*a^11*b^11*c^18*d^4 + 3672*a^12*b^10*c^3*d^19 - 36820*a^12*b^10*c^5*d^17 + 134700*a^12*b^10*c^7*d^15 - 201552*a^12*b^10*c^9*d^13 + 88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 12544*a^13*b^9*c^16*d^6 - 6788*a^14*b^8*c^3*d^19 + 53712*a^14*b^8*c^5*d^17 - 171472*a^14*b^8*c^7*d^15 + 245708*a^14*b^8*c^9*d^13 - 153012*a^14*b^8*c^11*d^11 + 26256*a^14*b^8*c^13*d^9 + 5496*a^14*b^8*c^15*d^7 + 1540*a^15*b^7*c^2*d^20 - 21228*a^15*b^7*c^4*d^18 + 96048*a^15*b^7*c^6*d^16 - 186952*a^15*b^7*c^8*d^14 + 168468*a^15*b^7*c^10*d^12 - 63372*a^15*b^7*c^12*d^10 + 5496*a^15*b^7*c^14*d^8 + 6132*a^16*b^6*c^3*d^19 - 39608*a^16*b^6*c^5*d^17 + 103992*a^16*b^6*c^7*d^15 - 125412*a^16*b^6*c^9*d^13 + 67604*a^16*b^6*c^11*d^11 - 12544*a^16*b^6*c^13*d^9 - 1200*a^17*b^5*c^2*d^20 + 11692*a^17*b^5*c^4*d^18 - 42920*a^17*b^5*c^6*d^16 + 67572*a^17*b^5*c^8*d^14 - 47152*a^17*b^5*c^10*d^12 + 12008*a^17*b^5*c^12*d^10 - 2388*a^18*b^4*c^3*d^19 + 12832*a^18*b^4*c^5*d^17 - 26148*a^18*b^4*c^7*d^15 + 22752*a^18*b^4*c^9*d^13 - 7168*a^18*b^4*c^11*d^11 + 332*a^19*b^3*c^2*d^20 - 2508*a^19*b^3*c^4*d^18 + 6852*a^19*b^3*c^6*d^16 - 7508*a^19*b^3*c^8*d^14 + 2832*a^19*b^3*c^10*d^12 + 212*a^20*b^2*c^3*d^19 - 1068*a^20*b^2*c^5*d^17 + 1612*a^20*b^2*c^7*d^15 - 728*a^20*b^2*c^9*d^13))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19)) + (4*(288*a*b^18*c^6*d^13 - 1104*a*b^18*c^8*d^11 + 1538*a*b^18*c^10*d^9 - 872*a*b^18*c^12*d^7 + 108*a*b^18*c^14*d^5 + 40*a*b^18*c^16*d^3 + 8*a^3*b^16*c^18*d + 8*a^5*b^14*c^18*d + 288*a^6*b^13*c*d^18 - 1104*a^8*b^11*c*d^18 + 1538*a^10*b^9*c*d^18 - 872*a^12*b^7*c*d^18 + 108*a^14*b^5*c*d^18 + 40*a^16*b^3*c*d^18 + 8*a^18*b*c^3*d^16 + 8*a^18*b*c^5*d^14 - 864*a^2*b^17*c^5*d^14 + 3216*a^2*b^17*c^7*d^12 - 4262*a^2*b^17*c^9*d^10 + 2256*a^2*b^17*c^11*d^8 - 304*a^2*b^17*c^13*d^6 - 32*a^2*b^17*c^15*d^4 + 8*a^2*b^17*c^17*d^2 + 576*a^3*b^16*c^4*d^15 - 3024*a^3*b^16*c^6*d^13 + 6304*a^3*b^16*c^8*d^11 - 7216*a^3*b^16*c^10*d^9 + 4944*a^3*b^16*c^12*d^7 - 1664*a^3*b^16*c^14*d^5 - 72*a^3*b^16*c^16*d^3 + 576*a^4*b^15*c^3*d^16 + 912*a^4*b^15*c^5*d^14 - 8720*a^4*b^15*c^7*d^12 + 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16024*a^9*b^10*c^8*d^11 + 22018*a^9*b^10*c^10*d^9 - 30104*a^9*b^10*c^12*d^7 + 6488*a^9*b^10*c^14*d^5 - 7216*a^10*b^9*c^3*d^16 + 23520*a^10*b^9*c^5*d^14 - 40656*a^10*b^9*c^7*d^12 + 22018*a^10*b^9*c^9*d^10 + 13080*a^10*b^9*c^11*d^8 - 8720*a^10*b^9*c^13*d^6 + 2256*a^11*b^8*c^2*d^17 - 14888*a^11*b^8*c^4*d^15 + 39792*a^11*b^8*c^6*d^13 - 46184*a^11*b^8*c^8*d^11 + 13080*a^11*b^8*c^10*d^9 + 4360*a^11*b^8*c^12*d^7 + 4944*a^12*b^7*c^3*d^16 - 20208*a^12*b^7*c^5*d^14 + 40296*a^12*b^7*c^7*d^12 - 30104*a^12*b^7*c^9*d^10 + 4360*a^12*b^7*c^11*d^8 - 304*a^13*b^6*c^2*d^17 + 6704*a^13*b^6*c^4*d^15 - 22728*a^13*b^6*c^6*d^13 + 27208*a^13*b^6*c^8*d^11 - 8720*a^13*b^6*c^10*d^9 - 1664*a^14*b^5*c^3*d^16 + 7404*a^14*b^5*c^5*d^14 - 12984*a^14*b^5*c^7*d^12 + 6488*a^14*b^5*c^9*d^10 - 32*a^15*b^4*c^2*d^17 - 744*a^15*b^4*c^4*d^15 + 3096*a^15*b^4*c^6*d^13 - 2752*a^15*b^4*c^8*d^11 - 72*a^16*b^3*c^3*d^16 - 264*a^16*b^3*c^5*d^14 + 728*a^16*b^3*c^7*d^12 + 8*a^17*b^2*c^2*d^17 - 40*a^17*b^2*c^4*d^15 - 112*a^17*b^2*c^6*d^13 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3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 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12*a^25*c*d^24 - 12*a*b^24*c^25 - 104*a^5*b^20*c^25 + 96*a^7*b^18*c^25 - 44*a^9*b^16*c^25 + 8*a^11*b^14*c^25 + 56*a^25*c^3*d^22 - 104*a^25*c^5*d^20 + 96*a^25*c^7*d^18 - 44*a^25*c^9*d^16 + 8*a^25*c^11*d^14 + 16*a*b^24*c^15*d^10 - 76*a*b^24*c^17*d^8 + 144*a*b^24*c^19*d^6 - 136*a*b^24*c^21*d^4 + 64*a*b^24*c^23*d^2 + 168*a^2*b^23*c^24*d - 784*a^4*b^21*c^24*d + 1456*a^6*b^19*c^24*d - 1344*a^8*b^17*c^24*d + 616*a^10*b^15*c^24*d - 112*a^12*b^13*c^24*d + 16*a^15*b^10*c*d^24 - 76*a^17*b^8*c*d^24 + 144*a^19*b^6*c*d^24 - 136*a^21*b^4*c*d^24 + 64*a^23*b^2*c*d^24 + 168*a^24*b*c^2*d^23 - 784*a^24*b*c^4*d^21 + 1456*a^24*b*c^6*d^19 - 1344*a^24*b*c^8*d^17 + 616*a^24*b*c^10*d^15 - 112*a^24*b*c^12*d^13 - 224*a^2*b^23*c^14*d^11 + 1064*a^2*b^23*c^16*d^9 - 2016*a^2*b^23*c^18*d^7 + 1904*a^2*b^23*c^20*d^5 - 896*a^2*b^23*c^22*d^3 + 1456*a^3*b^22*c^13*d^12 - 6992*a^3*b^22*c^15*d^10 + 13464*a^3*b^22*c^17*d^8 - 13056*a^3*b^22*c^19*d^6 + 6464*a^3*b^22*c^21*d^4 - 1392*a^3*b^22*c^23*d^2 - 5824*a^4*b^21*c^12*d^13 + 28728*a^4*b^21*c^14*d^11 - 57456*a^4*b^21*c^16*d^9 + 59024*a^4*b^21*c^18*d^7 - 32256*a^4*b^21*c^20*d^5 + 8568*a^4*b^21*c^22*d^3 + 16016*a^5*b^20*c^11*d^14 - 82992*a^5*b^20*c^13*d^12 + 177048*a^5*b^20*c^15*d^10 - 198696*a^5*b^20*c^17*d^8 + 123584*a^5*b^20*c^19*d^6 - 40512*a^5*b^20*c^21*d^4 + 5656*a^5*b^20*c^23*d^2 - 32032*a^6*b^19*c^10*d^15 + 179816*a^6*b^19*c^12*d^13 - 421344*a^6*b^19*c^14*d^11 + 529312*a^6*b^19*c^16*d^9 - 379008*a^6*b^19*c^18*d^7 + 150024*a^6*b^19*c^20*d^5 - 28224*a^6*b^19*c^22*d^3 + 48048*a^7*b^18*c^9*d^16 - 304304*a^7*b^18*c^11*d^14 + 805896*a^7*b^18*c^13*d^12 - 1151104*a^7*b^18*c^15*d^10 + 949952*a^7*b^18*c^17*d^8 - 446736*a^7*b^18*c^19*d^6 + 108136*a^7*b^18*c^21*d^4 - 9984*a^7*b^18*c^23*d^2 - 54912*a^8*b^17*c^8*d^17 + 412984*a^8*b^17*c^10*d^15 - 1267344*a^8*b^17*c^12*d^13 + 2077536*a^8*b^17*c^14*d^11 - 1975808*a^8*b^17*c^16*d^9 + 1095384*a^8*b^17*c^18*d^7 - 331632*a^8*b^17*c^20*d^5 + 45136*a^8*b^17*c^22*d^3 + 48048*a^9*b^16*c^7*d^18 - 456456*a^9*b^16*c^9*d^16 + 1657656*a^9*b^16*c^11*d^14 - 3143504*a^9*b^16*c^13*d^12 + 3453696*a^9*b^16*c^15*d^10 - 2247636*a^9*b^16*c^17*d^8 + 831208*a^9*b^16*c^19*d^6 - 151944*a^9*b^16*c^21*d^4 + 8976*a^9*b^16*c^23*d^2 - 32032*a^10*b^15*c^6*d^19 + 412984*a^10*b^15*c^8*d^17 - 1812096*a^10*b^15*c^10*d^15 + 4016896*a^10*b^15*c^12*d^13 - 5121024*a^10*b^15*c^14*d^11 + 3897024*a^10*b^15*c^16*d^9 - 1728832*a^10*b^15*c^18*d^7 + 404768*a^10*b^15*c^20*d^5 - 38304*a^10*b^15*c^22*d^3 + 16016*a^11*b^14*c^5*d^20 - 304304*a^11*b^14*c^7*d^18 + 1657656*a^11*b^14*c^9*d^16 - 4356352*a^11*b^14*c^11*d^14 + 6476288*a^11*b^14*c^13*d^12 - 5745024*a^11*b^14*c^15*d^10 + 3021984*a^11*b^14*c^17*d^8 - 880256*a^11*b^14*c^19*d^6 + 118032*a^11*b^14*c^21*d^4 - 4048*a^11*b^14*c^23*d^2 - 5824*a^12*b^13*c^4*d^21 + 179816*a^12*b^13*c^6*d^19 - 1267344*a^12*b^13*c^8*d^17 + 4016896*a^12*b^13*c^10*d^15 - 7002112*a^12*b^13*c^12*d^13 + 7235136*a^12*b^13*c^14*d^11 - 4480896*a^12*b^13*c^16*d^9 + 1588704*a^12*b^13*c^18*d^7 - 280896*a^12*b^13*c^20*d^5 + 16632*a^12*b^13*c^22*d^3 + 1456*a^13*b^12*c^3*d^22 - 82992*a^13*b^12*c^5*d^20 + 805896*a^13*b^12*c^7*d^18 - 3143504*a^13*b^12*c^9*d^16 + 6476288*a^13*b^12*c^11*d^14 - 7809984*a^13*b^12*c^13*d^12 + 5666752*a^13*b^12*c^15*d^10 - 2403856*a^13*b^12*c^17*d^8 + 537264*a^13*b^12*c^19*d^6 - 48048*a^13*b^12*c^21*d^4 + 728*a^13*b^12*c^23*d^2 - 224*a^14*b^11*c^2*d^23 + 28728*a^14*b^11*c^4*d^21 - 421344*a^14*b^11*c^6*d^19 + 2077536*a^14*b^11*c^8*d^17 - 5121024*a^14*b^11*c^10*d^15 + 7235136*a^14*b^11*c^12*d^13 - 6126848*a^14*b^11*c^14*d^11 + 3071744*a^14*b^11*c^16*d^9 - 844896*a^14*b^11*c^18*d^7 + 104104*a^14*b^11*c^20*d^5 - 2912*a^14*b^11*c^22*d^3 - 6992*a^15*b^10*c^3*d^22 + 177048*a^15*b^10*c^5*d^20 - 1151104*a^15*b^10*c^7*d^18 + 3453696*a^15*b^10*c^9*d^16 - 5745024*a^15*b^10*c^11*d^14 + 5666752*a^15*b^10*c^13*d^12 - 3331328*a^15*b^10*c^15*d^10 + 1105104*a^15*b^10*c^17*d^8 - 176176*a^15*b^10*c^19*d^6 + 8008*a^15*b^10*c^21*d^4 + 1064*a^16*b^9*c^2*d^23 - 57456*a^16*b^9*c^4*d^21 + 529312*a^16*b^9*c^6*d^19 - 1975808*a^16*b^9*c^8*d^17 + 3897024*a^16*b^9*c^10*d^15 - 4480896*a^16*b^9*c^12*d^13 + 3071744*a^16*b^9*c^14*d^11 - 1208064*a^16*b^9*c^16*d^9 + 239096*a^16*b^9*c^18*d^7 - 16016*a^16*b^9*c^20*d^5 + 13464*a^17*b^8*c^3*d^22 - 198696*a^17*b^8*c^5*d^20 + 949952*a^17*b^8*c^7*d^18 - 2247636*a^17*b^8*c^9*d^16 + 3021984*a^17*b^8*c^11*d^14 - 2403856*a^17*b^8*c^13*d^12 + 1105104*a^17*b^8*c^15*d^10 - 264264*a^17*b^8*c^17*d^8 + 24024*a^17*b^8*c^19*d^6 - 2016*a^18*b^7*c^2*d^23 + 59024*a^18*b^7*c^4*d^21 - 379008*a^18*b^7*c^6*d^19 + 1095384*a^18*b^7*c^8*d^17 - 1728832*a^18*b^7*c^10*d^15 + 1588704*a^18*b^7*c^12*d^13 - 844896*a^18*b^7*c^14*d^11 + 239096*a^18*b^7*c^16*d^9 - 27456*a^18*b^7*c^18*d^7 - 13056*a^19*b^6*c^3*d^22 + 123584*a^19*b^6*c^5*d^20 - 446736*a^19*b^6*c^7*d^18 + 831208*a^19*b^6*c^9*d^16 - 880256*a^19*b^6*c^11*d^14 + 537264*a^19*b^6*c^13*d^12 - 176176*a^19*b^6*c^15*d^10 + 24024*a^19*b^6*c^17*d^8 + 1904*a^20*b^5*c^2*d^23 - 32256*a^20*b^5*c^4*d^21 + 150024*a^20*b^5*c^6*d^19 - 331632*a^20*b^5*c^8*d^17 + 404768*a^20*b^5*c^10*d^15 - 280896*a^20*b^5*c^12*d^13 + 104104*a^20*b^5*c^14*d^11 - 16016*a^20*b^5*c^16*d^9 + 6464*a^21*b^4*c^3*d^22 - 40512*a^21*b^4*c^5*d^20 + 108136*a^21*b^4*c^7*d^18 - 151944*a^21*b^4*c^9*d^16 + 118032*a^21*b^4*c^11*d^14 - 48048*a^21*b^4*c^13*d^12 + 8008*a^21*b^4*c^15*d^10 - 896*a^22*b^3*c^2*d^23 + 8568*a^22*b^3*c^4*d^21 - 28224*a^22*b^3*c^6*d^19 + 45136*a^22*b^3*c^8*d^17 - 38304*a^22*b^3*c^10*d^15 + 16632*a^22*b^3*c^12*d^13 - 2912*a^22*b^3*c^14*d^11 - 1392*a^23*b^2*c^3*d^22 + 5656*a^23*b^2*c^5*d^20 - 9984*a^23*b^2*c^7*d^18 + 8976*a^23*b^2*c^9*d^16 - 4048*a^23*b^2*c^11*d^14 + 728*a^23*b^2*c^13*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 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8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 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288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) + (8*tan(e/2 + (f*x)/2)*(12*a^5*b^17*c^22 - 4*a^22*c*d^21 - 4*a*b^21*c^22 - 8*a^7*b^15*c^22 + 12*a^22*c^5*d^17 - 8*a^22*c^7*d^15 - 24*a*b^21*c^12*d^10 + 100*a*b^21*c^14*d^8 - 164*a*b^21*c^16*d^6 + 120*a*b^21*c^18*d^4 - 28*a*b^21*c^20*d^2 + 20*a^2*b^20*c^21*d + 72*a^4*b^18*c^21*d - 204*a^6*b^16*c^21*d + 112*a^8*b^14*c^21*d - 24*a^12*b^10*c*d^21 + 100*a^14*b^8*c*d^21 - 164*a^16*b^6*c*d^21 + 120*a^18*b^4*c*d^21 - 28*a^20*b^2*c*d^21 + 20*a^21*b*c^2*d^20 + 72*a^21*b*c^4*d^18 - 204*a^21*b*c^6*d^16 + 112*a^21*b*c^8*d^14 + 216*a^2*b^20*c^11*d^11 - 908*a^2*b^20*c^13*d^9 + 1540*a^2*b^20*c^15*d^7 - 1200*a^2*b^20*c^17*d^5 + 332*a^2*b^20*c^19*d^3 - 840*a^3*b^19*c^10*d^12 + 3672*a^3*b^19*c^12*d^10 - 6788*a^3*b^19*c^14*d^8 + 6132*a^3*b^19*c^16*d^6 - 2388*a^3*b^19*c^18*d^4 + 212*a^3*b^19*c^20*d^2 + 1800*a^4*b^18*c^9*d^13 - 8680*a^4*b^18*c^11*d^11 + 18852*a^4*b^18*c^13*d^9 - 21228*a^4*b^18*c^15*d^7 + 11692*a^4*b^18*c^17*d^5 - 2508*a^4*b^18*c^19*d^3 - 2160*a^5*b^17*c^8*d^14 + 13100*a^5*b^17*c^10*d^12 - 36820*a^5*b^17*c^12*d^10 + 53712*a^5*b^17*c^14*d^8 - 39608*a^5*b^17*c^16*d^6 + 12832*a^5*b^17*c^18*d^4 - 1068*a^5*b^17*c^20*d^2 + 1008*a^6*b^16*c^7*d^15 - 12420*a^6*b^16*c^9*d^13 + 51764*a^6*b^16*c^11*d^11 - 100128*a^6*b^16*c^13*d^9 + 96048*a^6*b^16*c^15*d^7 - 42920*a^6*b^16*c^17*d^5 + 6852*a^6*b^16*c^19*d^3 + 1008*a^7*b^15*c^6*d^16 + 5136*a^7*b^15*c^8*d^14 - 48820*a^7*b^15*c^10*d^12 + 134700*a^7*b^15*c^12*d^10 - 171472*a^7*b^15*c^14*d^8 + 103992*a^7*b^15*c^16*d^6 - 26148*a^7*b^15*c^18*d^4 + 1612*a^7*b^15*c^20*d^2 - 2160*a^8*b^14*c^5*d^17 + 5136*a^8*b^14*c^7*d^15 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88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 12544*a^13*b^9*c^16*d^6 - 6788*a^14*b^8*c^3*d^19 + 53712*a^14*b^8*c^5*d^17 - 171472*a^14*b^8*c^7*d^15 + 245708*a^14*b^8*c^9*d^13 - 153012*a^14*b^8*c^11*d^11 + 26256*a^14*b^8*c^13*d^9 + 5496*a^14*b^8*c^15*d^7 + 1540*a^15*b^7*c^2*d^20 - 21228*a^15*b^7*c^4*d^18 + 96048*a^15*b^7*c^6*d^16 - 186952*a^15*b^7*c^8*d^14 + 168468*a^15*b^7*c^10*d^12 - 63372*a^15*b^7*c^12*d^10 + 5496*a^15*b^7*c^14*d^8 + 6132*a^16*b^6*c^3*d^19 - 39608*a^16*b^6*c^5*d^17 + 103992*a^16*b^6*c^7*d^15 - 125412*a^16*b^6*c^9*d^13 + 67604*a^16*b^6*c^11*d^11 - 12544*a^16*b^6*c^13*d^9 - 1200*a^17*b^5*c^2*d^20 + 11692*a^17*b^5*c^4*d^18 - 42920*a^17*b^5*c^6*d^16 + 67572*a^17*b^5*c^8*d^14 - 47152*a^17*b^5*c^10*d^12 + 12008*a^17*b^5*c^12*d^10 - 2388*a^18*b^4*c^3*d^19 + 12832*a^18*b^4*c^5*d^17 - 26148*a^18*b^4*c^7*d^15 + 22752*a^18*b^4*c^9*d^13 - 7168*a^18*b^4*c^11*d^11 + 332*a^19*b^3*c^2*d^20 - 2508*a^19*b^3*c^4*d^18 + 6852*a^19*b^3*c^6*d^16 - 7508*a^19*b^3*c^8*d^14 + 2832*a^19*b^3*c^10*d^12 + 212*a^20*b^2*c^3*d^19 - 1068*a^20*b^2*c^5*d^17 + 1612*a^20*b^2*c^7*d^15 - 728*a^20*b^2*c^9*d^13))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 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21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19)) + (4*(288*a*b^18*c^6*d^13 - 1104*a*b^18*c^8*d^11 + 1538*a*b^18*c^10*d^9 - 872*a*b^18*c^12*d^7 + 108*a*b^18*c^14*d^5 + 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5140*a^6*b^13*c^5*d^14 + 5280*a^6*b^13*c^7*d^12 - 28380*a^6*b^13*c^9*d^10 + 39792*a^6*b^13*c^11*d^8 - 22728*a^6*b^13*c^13*d^6 + 3096*a^6*b^13*c^15*d^4 - 112*a^6*b^13*c^17*d^2 + 3216*a^7*b^12*c^2*d^17 - 8720*a^7*b^12*c^4*d^15 + 5280*a^7*b^12*c^6*d^13 + 15000*a^7*b^12*c^8*d^11 - 40656*a^7*b^12*c^10*d^9 + 40296*a^7*b^12*c^12*d^7 - 12984*a^7*b^12*c^14*d^5 + 728*a^7*b^12*c^16*d^3 + 6304*a^8*b^11*c^3*d^16 - 16080*a^8*b^11*c^5*d^14 + 15000*a^8*b^11*c^7*d^12 + 16024*a^8*b^11*c^9*d^10 - 46184*a^8*b^11*c^11*d^8 + 27208*a^8*b^11*c^13*d^6 - 2752*a^8*b^11*c^15*d^4 - 4262*a^9*b^10*c^2*d^17 + 16632*a^9*b^10*c^4*d^15 - 28380*a^9*b^10*c^6*d^13 + 16024*a^9*b^10*c^8*d^11 + 22018*a^9*b^10*c^10*d^9 - 30104*a^9*b^10*c^12*d^7 + 6488*a^9*b^10*c^14*d^5 - 7216*a^10*b^9*c^3*d^16 + 23520*a^10*b^9*c^5*d^14 - 40656*a^10*b^9*c^7*d^12 + 22018*a^10*b^9*c^9*d^10 + 13080*a^10*b^9*c^11*d^8 - 8720*a^10*b^9*c^13*d^6 + 2256*a^11*b^8*c^2*d^17 - 14888*a^11*b^8*c^4*d^15 + 39792*a^11*b^8*c^6*d^13 - 46184*a^11*b^8*c^8*d^11 + 13080*a^11*b^8*c^10*d^9 + 4360*a^11*b^8*c^12*d^7 + 4944*a^12*b^7*c^3*d^16 - 20208*a^12*b^7*c^5*d^14 + 40296*a^12*b^7*c^7*d^12 - 30104*a^12*b^7*c^9*d^10 + 4360*a^12*b^7*c^11*d^8 - 304*a^13*b^6*c^2*d^17 + 6704*a^13*b^6*c^4*d^15 - 22728*a^13*b^6*c^6*d^13 + 27208*a^13*b^6*c^8*d^11 - 8720*a^13*b^6*c^10*d^9 - 1664*a^14*b^5*c^3*d^16 + 7404*a^14*b^5*c^5*d^14 - 12984*a^14*b^5*c^7*d^12 + 6488*a^14*b^5*c^9*d^10 - 32*a^15*b^4*c^2*d^17 - 744*a^15*b^4*c^4*d^15 + 3096*a^15*b^4*c^6*d^13 - 2752*a^15*b^4*c^8*d^11 - 72*a^16*b^3*c^3*d^16 - 264*a^16*b^3*c^5*d^14 + 728*a^16*b^3*c^7*d^12 + 8*a^17*b^2*c^2*d^17 - 40*a^17*b^2*c^4*d^15 - 112*a^17*b^2*c^6*d^13 + 2*a*b^18*c^18*d + 2*a^18*b*c*d^18))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 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- 7408*a^19*b^6*c^4*d^21 + 11336*a^19*b^6*c^6*d^19 + 24904*a^19*b^6*c^8*d^17 - 85536*a^19*b^6*c^10*d^15 + 92512*a^19*b^6*c^12*d^13 - 44408*a^19*b^6*c^14*d^11 + 8008*a^19*b^6*c^16*d^9 + 2032*a^20*b^5*c^3*d^22 - 4008*a^20*b^5*c^5*d^20 - 11336*a^20*b^5*c^7*d^18 + 46464*a^20*b^5*c^9*d^16 - 60768*a^20*b^5*c^11*d^14 + 35672*a^20*b^5*c^13*d^12 - 8008*a^20*b^5*c^15*d^10 - 368*a^21*b^4*c^2*d^23 + 1192*a^21*b^4*c^4*d^21 + 4008*a^21*b^4*c^6*d^19 - 20592*a^21*b^4*c^8*d^17 + 31328*a^21*b^4*c^10*d^15 - 20664*a^21*b^4*c^12*d^13 + 5096*a^21*b^4*c^14*d^11 - 328*a^22*b^3*c^3*d^22 - 1192*a^22*b^3*c^5*d^20 + 7408*a^22*b^3*c^7*d^18 - 12272*a^22*b^3*c^9*d^16 + 8536*a^22*b^3*c^11*d^14 - 2184*a^22*b^3*c^13*d^12 + 72*a^23*b^2*c^2*d^23 + 328*a^23*b^2*c^4*d^21 - 2032*a^23*b^2*c^6*d^19 + 3408*a^23*b^2*c^8*d^17 - 2392*a^23*b^2*c^10*d^15 + 616*a^23*b^2*c^12*d^13 - 8*a*b^24*c^24*d - 8*a^24*b*c*d^24))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(56*a^3*b^22*c^25 - 12*a^25*c*d^24 - 12*a*b^24*c^25 - 104*a^5*b^20*c^25 + 96*a^7*b^18*c^25 - 44*a^9*b^16*c^25 + 8*a^11*b^14*c^25 + 56*a^25*c^3*d^22 - 104*a^25*c^5*d^20 + 96*a^25*c^7*d^18 - 44*a^25*c^9*d^16 + 8*a^25*c^11*d^14 + 16*a*b^24*c^15*d^10 - 76*a*b^24*c^17*d^8 + 144*a*b^24*c^19*d^6 - 136*a*b^24*c^21*d^4 + 64*a*b^24*c^23*d^2 + 168*a^2*b^23*c^24*d - 784*a^4*b^21*c^24*d + 1456*a^6*b^19*c^24*d - 1344*a^8*b^17*c^24*d + 616*a^10*b^15*c^24*d - 112*a^12*b^13*c^24*d + 16*a^15*b^10*c*d^24 - 76*a^17*b^8*c*d^24 + 144*a^19*b^6*c*d^24 - 136*a^21*b^4*c*d^24 + 64*a^23*b^2*c*d^24 + 168*a^24*b*c^2*d^23 - 784*a^24*b*c^4*d^21 + 1456*a^24*b*c^6*d^19 - 1344*a^24*b*c^8*d^17 + 616*a^24*b*c^10*d^15 - 112*a^24*b*c^12*d^13 - 224*a^2*b^23*c^14*d^11 + 1064*a^2*b^23*c^16*d^9 - 2016*a^2*b^23*c^18*d^7 + 1904*a^2*b^23*c^20*d^5 - 896*a^2*b^23*c^22*d^3 + 1456*a^3*b^22*c^13*d^12 - 6992*a^3*b^22*c^15*d^10 + 13464*a^3*b^22*c^17*d^8 - 13056*a^3*b^22*c^19*d^6 + 6464*a^3*b^22*c^21*d^4 - 1392*a^3*b^22*c^23*d^2 - 5824*a^4*b^21*c^12*d^13 + 28728*a^4*b^21*c^14*d^11 - 57456*a^4*b^21*c^16*d^9 + 59024*a^4*b^21*c^18*d^7 - 32256*a^4*b^21*c^20*d^5 + 8568*a^4*b^21*c^22*d^3 + 16016*a^5*b^20*c^11*d^14 - 82992*a^5*b^20*c^13*d^12 + 177048*a^5*b^20*c^15*d^10 - 198696*a^5*b^20*c^17*d^8 + 123584*a^5*b^20*c^19*d^6 - 40512*a^5*b^20*c^21*d^4 + 5656*a^5*b^20*c^23*d^2 - 32032*a^6*b^19*c^10*d^15 + 179816*a^6*b^19*c^12*d^13 - 421344*a^6*b^19*c^14*d^11 + 529312*a^6*b^19*c^16*d^9 - 379008*a^6*b^19*c^18*d^7 + 150024*a^6*b^19*c^20*d^5 - 28224*a^6*b^19*c^22*d^3 + 48048*a^7*b^18*c^9*d^16 - 304304*a^7*b^18*c^11*d^14 + 805896*a^7*b^18*c^13*d^12 - 1151104*a^7*b^18*c^15*d^10 + 949952*a^7*b^18*c^17*d^8 - 446736*a^7*b^18*c^19*d^6 + 108136*a^7*b^18*c^21*d^4 - 9984*a^7*b^18*c^23*d^2 - 54912*a^8*b^17*c^8*d^17 + 412984*a^8*b^17*c^10*d^15 - 1267344*a^8*b^17*c^12*d^13 + 2077536*a^8*b^17*c^14*d^11 - 1975808*a^8*b^17*c^16*d^9 + 1095384*a^8*b^17*c^18*d^7 - 331632*a^8*b^17*c^20*d^5 + 45136*a^8*b^17*c^22*d^3 + 48048*a^9*b^16*c^7*d^18 - 456456*a^9*b^16*c^9*d^16 + 1657656*a^9*b^16*c^11*d^14 - 3143504*a^9*b^16*c^13*d^12 + 3453696*a^9*b^16*c^15*d^10 - 2247636*a^9*b^16*c^17*d^8 + 831208*a^9*b^16*c^19*d^6 - 151944*a^9*b^16*c^21*d^4 + 8976*a^9*b^16*c^23*d^2 - 32032*a^10*b^15*c^6*d^19 + 412984*a^10*b^15*c^8*d^17 - 1812096*a^10*b^15*c^10*d^15 + 4016896*a^10*b^15*c^12*d^13 - 5121024*a^10*b^15*c^14*d^11 + 3897024*a^10*b^15*c^16*d^9 - 1728832*a^10*b^15*c^18*d^7 + 404768*a^10*b^15*c^20*d^5 - 38304*a^10*b^15*c^22*d^3 + 16016*a^11*b^14*c^5*d^20 - 304304*a^11*b^14*c^7*d^18 + 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34548*a^18*b^4*c^8*d^14 - 26952*a^18*b^4*c^10*d^12 + 8008*a^18*b^4*c^12*d^10 - 732*a^19*b^3*c^3*d^19 + 3308*a^19*b^3*c^5*d^17 - 7652*a^19*b^3*c^7*d^15 + 7908*a^19*b^3*c^9*d^13 - 2912*a^19*b^3*c^11*d^11 + 28*a^20*b^2*c^2*d^20 - 212*a^20*b^2*c^4*d^18 + 1068*a^20*b^2*c^6*d^16 - 1612*a^20*b^2*c^8*d^14 + 728*a^20*b^2*c^10*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 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17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 792*a^15*b^5*c^13*d^7 - 288*a^16*b^4*c^2*d^18 + 1587*a^16*b^4*c^4*d^16 - 3588*a^16*b^4*c^6*d^14 + 4032*a^16*b^4*c^8*d^12 - 2244*a^16*b^4*c^10*d^10 + 495*a^16*b^4*c^12*d^8 - 412*a^17*b^3*c^3*d^17 + 1168*a^17*b^3*c^5*d^15 - 1512*a^17*b^3*c^7*d^13 + 928*a^17*b^3*c^9*d^11 - 220*a^17*b^3*c^11*d^9 + 82*a^18*b^2*c^2*d^18 - 288*a^18*b^2*c^4*d^16 + 412*a^18*b^2*c^6*d^14 - 268*a^18*b^2*c^8*d^12 + 66*a^18*b^2*c^10*d^10 - 12*a*b^19*c^19*d - 12*a^19*b*c*d^19) - (8*tan(e/2 + (f*x)/2)*(12*a^5*b^17*c^22 - 4*a^22*c*d^21 - 4*a*b^21*c^22 - 8*a^7*b^15*c^22 + 12*a^22*c^5*d^17 - 8*a^22*c^7*d^15 - 24*a*b^21*c^12*d^10 + 100*a*b^21*c^14*d^8 - 164*a*b^21*c^16*d^6 + 120*a*b^21*c^18*d^4 - 28*a*b^21*c^20*d^2 + 20*a^2*b^20*c^21*d + 72*a^4*b^18*c^21*d - 204*a^6*b^16*c^21*d + 112*a^8*b^14*c^21*d - 24*a^12*b^10*c*d^21 + 100*a^14*b^8*c*d^21 - 164*a^16*b^6*c*d^21 + 120*a^18*b^4*c*d^21 - 28*a^20*b^2*c*d^21 + 20*a^21*b*c^2*d^20 + 72*a^21*b*c^4*d^18 - 204*a^21*b*c^6*d^16 + 112*a^21*b*c^8*d^14 + 216*a^2*b^20*c^11*d^11 - 908*a^2*b^20*c^13*d^9 + 1540*a^2*b^20*c^15*d^7 - 1200*a^2*b^20*c^17*d^5 + 332*a^2*b^20*c^19*d^3 - 840*a^3*b^19*c^10*d^12 + 3672*a^3*b^19*c^12*d^10 - 6788*a^3*b^19*c^14*d^8 + 6132*a^3*b^19*c^16*d^6 - 2388*a^3*b^19*c^18*d^4 + 212*a^3*b^19*c^20*d^2 + 1800*a^4*b^18*c^9*d^13 - 8680*a^4*b^18*c^11*d^11 + 18852*a^4*b^18*c^13*d^9 - 21228*a^4*b^18*c^15*d^7 + 11692*a^4*b^18*c^17*d^5 - 2508*a^4*b^18*c^19*d^3 - 2160*a^5*b^17*c^8*d^14 + 13100*a^5*b^17*c^10*d^12 - 36820*a^5*b^17*c^12*d^10 + 53712*a^5*b^17*c^14*d^8 - 39608*a^5*b^17*c^16*d^6 + 12832*a^5*b^17*c^18*d^4 - 1068*a^5*b^17*c^20*d^2 + 1008*a^6*b^16*c^7*d^15 - 12420*a^6*b^16*c^9*d^13 + 51764*a^6*b^16*c^11*d^11 - 100128*a^6*b^16*c^13*d^9 + 96048*a^6*b^16*c^15*d^7 - 42920*a^6*b^16*c^17*d^5 + 6852*a^6*b^16*c^19*d^3 + 1008*a^7*b^15*c^6*d^16 + 5136*a^7*b^15*c^8*d^14 - 48820*a^7*b^15*c^10*d^12 + 134700*a^7*b^15*c^12*d^10 - 171472*a^7*b^15*c^14*d^8 + 103992*a^7*b^15*c^16*d^6 - 26148*a^7*b^15*c^18*d^4 + 1612*a^7*b^15*c^20*d^2 - 2160*a^8*b^14*c^5*d^17 + 5136*a^8*b^14*c^7*d^15 + 20436*a^8*b^14*c^9*d^13 - 121524*a^8*b^14*c^11*d^11 + 224888*a^8*b^14*c^13*d^9 - 186952*a^8*b^14*c^15*d^7 + 67572*a^8*b^14*c^17*d^5 - 7508*a^8*b^14*c^19*d^3 + 1800*a^9*b^13*c^4*d^18 - 12420*a^9*b^13*c^6*d^16 + 20436*a^9*b^13*c^8*d^14 + 49416*a^9*b^13*c^10*d^12 - 201552*a^9*b^13*c^12*d^10 + 245708*a^9*b^13*c^14*d^8 - 125412*a^9*b^13*c^16*d^6 + 22752*a^9*b^13*c^18*d^4 - 728*a^9*b^13*c^20*d^2 - 840*a^10*b^12*c^3*d^19 + 13100*a^10*b^12*c^5*d^17 - 48820*a^10*b^12*c^7*d^15 + 49416*a^10*b^12*c^9*d^13 + 82088*a^10*b^12*c^11*d^11 - 219092*a^10*b^12*c^13*d^9 + 168468*a^10*b^12*c^15*d^7 - 47152*a^10*b^12*c^17*d^5 + 2832*a^10*b^12*c^19*d^3 + 216*a^11*b^11*c^2*d^20 - 8680*a^11*b^11*c^4*d^18 + 51764*a^11*b^11*c^6*d^16 - 121524*a^11*b^11*c^8*d^14 + 82088*a^11*b^11*c^10*d^12 + 88712*a^11*b^11*c^12*d^10 - 153012*a^11*b^11*c^14*d^8 + 67604*a^11*b^11*c^16*d^6 - 7168*a^11*b^11*c^18*d^4 + 3672*a^12*b^10*c^3*d^19 - 36820*a^12*b^10*c^5*d^17 + 134700*a^12*b^10*c^7*d^15 - 201552*a^12*b^10*c^9*d^13 + 88712*a^12*b^10*c^11*d^11 + 62676*a^12*b^10*c^13*d^9 - 63372*a^12*b^10*c^15*d^7 + 12008*a^12*b^10*c^17*d^5 - 908*a^13*b^9*c^2*d^20 + 18852*a^13*b^9*c^4*d^18 - 100128*a^13*b^9*c^6*d^16 + 224888*a^13*b^9*c^8*d^14 - 219092*a^13*b^9*c^10*d^12 + 62676*a^13*b^9*c^12*d^10 + 26256*a^13*b^9*c^14*d^8 - 12544*a^13*b^9*c^16*d^6 - 6788*a^14*b^8*c^3*d^19 + 53712*a^14*b^8*c^5*d^17 - 171472*a^14*b^8*c^7*d^15 + 245708*a^14*b^8*c^9*d^13 - 153012*a^14*b^8*c^11*d^11 + 26256*a^14*b^8*c^13*d^9 + 5496*a^14*b^8*c^15*d^7 + 1540*a^15*b^7*c^2*d^20 - 21228*a^15*b^7*c^4*d^18 + 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4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 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4*a^2*b^17*c^18*d - 20*a^4*b^15*c^18*d - 576*a^5*b^14*c*d^18 - 56*a^6*b^13*c^18*d + 2640*a^7*b^12*c*d^18 - 4732*a^9*b^10*c*d^18 + 3961*a^11*b^8*c*d^18 - 1344*a^13*b^6*c*d^18 + 14*a^15*b^4*c*d^18 + 18*a^17*b^2*c*d^18 + 4*a^18*b*c^2*d^17 - 20*a^18*b*c^4*d^15 - 56*a^18*b*c^6*d^13 + 2304*a^2*b^17*c^4*d^15 - 10944*a^2*b^17*c^6*d^13 + 20720*a^2*b^17*c^8*d^11 - 18788*a^2*b^17*c^10*d^9 + 7392*a^2*b^17*c^12*d^7 - 520*a^2*b^17*c^14*d^5 - 24*a^2*b^17*c^16*d^3 - 3456*a^3*b^16*c^3*d^16 + 20016*a^3*b^16*c^5*d^14 - 48112*a^3*b^16*c^7*d^12 + 58925*a^3*b^16*c^9*d^10 - 36732*a^3*b^16*c^11*d^8 + 9736*a^3*b^16*c^13*d^6 - 760*a^3*b^16*c^15*d^4 - 44*a^3*b^16*c^17*d^2 + 2304*a^4*b^15*c^2*d^17 - 23424*a^4*b^15*c^4*d^15 + 81680*a^4*b^15*c^6*d^13 - 135520*a^4*b^15*c^8*d^11 + 114144*a^4*b^15*c^10*d^9 - 44168*a^4*b^15*c^12*d^7 + 5696*a^4*b^15*c^14*d^5 - 332*a^4*b^15*c^16*d^3 + 20016*a^5*b^14*c^3*d^16 - 99112*a^5*b^14*c^5*d^14 + 213338*a^5*b^14*c^7*d^12 - 235152*a^5*b^14*c^9*d^10 + 130428*a^5*b^14*c^11*d^8 - 31908*a^5*b^14*c^13*d^6 + 3966*a^5*b^14*c^15*d^4 - 140*a^5*b^14*c^17*d^2 - 10944*a^6*b^13*c^2*d^17 + 81680*a^6*b^13*c^4*d^15 - 243832*a^6*b^13*c^6*d^13 + 364608*a^6*b^13*c^8*d^11 - 281736*a^6*b^13*c^10*d^9 + 103104*a^6*b^13*c^12*d^7 - 16860*a^6*b^13*c^14*d^5 + 1660*a^6*b^13*c^16*d^3 - 48112*a^7*b^12*c^3*d^16 + 213338*a^7*b^12*c^5*d^14 - 425832*a^7*b^12*c^7*d^12 + 434414*a^7*b^12*c^9*d^10 - 219064*a^7*b^12*c^11*d^8 + 50732*a^7*b^12*c^13*d^6 - 7220*a^7*b^12*c^15*d^4 + 364*a^7*b^12*c^17*d^2 + 20720*a^8*b^11*c^2*d^17 - 135520*a^8*b^11*c^4*d^15 + 364608*a^8*b^11*c^6*d^13 - 496336*a^8*b^11*c^8*d^11 + 343832*a^8*b^11*c^10*d^9 - 111220*a^8*b^11*c^12*d^7 + 17956*a^8*b^11*c^14*d^5 - 1376*a^8*b^11*c^16*d^3 + 58925*a^9*b^10*c^3*d^16 - 235152*a^9*b^10*c^5*d^14 + 434414*a^9*b^10*c^7*d^12 - 401788*a^9*b^10*c^9*d^10 + 172673*a^9*b^10*c^11*d^8 - 31940*a^9*b^10*c^13*d^6 + 3244*a^9*b^10*c^15*d^4 - 18788*a^10*b^9*c^2*d^17 + 114144*a^10*b^9*c^4*d^15 - 281736*a^10*b^9*c^6*d^13 + 343832*a^10*b^9*c^8*d^11 - 197840*a^10*b^9*c^10*d^9 + 45940*a^10*b^9*c^12*d^7 - 4760*a^10*b^9*c^14*d^5 - 36732*a^11*b^8*c^3*d^16 + 130428*a^11*b^8*c^5*d^14 - 219064*a^11*b^8*c^7*d^12 + 172673*a^11*b^8*c^9*d^10 - 52480*a^11*b^8*c^11*d^8 + 4580*a^11*b^8*c^13*d^6 + 7392*a^12*b^7*c^2*d^17 - 44168*a^12*b^7*c^4*d^15 + 103104*a^12*b^7*c^6*d^13 - 111220*a^12*b^7*c^8*d^11 + 45940*a^12*b^7*c^10*d^9 - 4000*a^12*b^7*c^12*d^7 + 9736*a^13*b^6*c^3*d^16 - 31908*a^13*b^6*c^5*d^14 + 50732*a^13*b^6*c^7*d^12 - 31940*a^13*b^6*c^9*d^10 + 4580*a^13*b^6*c^11*d^8 - 520*a^14*b^5*c^2*d^17 + 5696*a^14*b^5*c^4*d^15 - 16860*a^14*b^5*c^6*d^13 + 17956*a^14*b^5*c^8*d^11 - 4760*a^14*b^5*c^10*d^9 - 760*a^15*b^4*c^3*d^16 + 3966*a^15*b^4*c^5*d^14 - 7220*a^15*b^4*c^7*d^12 + 3244*a^15*b^4*c^9*d^10 - 24*a^16*b^3*c^2*d^17 - 332*a^16*b^3*c^4*d^15 + 1660*a^16*b^3*c^6*d^13 - 1376*a^16*b^3*c^8*d^11 - 44*a^17*b^2*c^3*d^16 - 140*a^17*b^2*c^5*d^14 + 364*a^17*b^2*c^7*d^12))/(a^20*d^20 + b^20*c^20 - 4*a^2*b^18*c^20 + 6*a^4*b^16*c^20 - 4*a^6*b^14*c^20 + a^8*b^12*c^20 + a^12*b^8*d^20 - 4*a^14*b^6*d^20 + 6*a^16*b^4*d^20 - 4*a^18*b^2*d^20 - 4*a^20*c^2*d^18 + 6*a^20*c^4*d^16 - 4*a^20*c^6*d^14 + a^20*c^8*d^12 + b^20*c^12*d^8 - 4*b^20*c^14*d^6 + 6*b^20*c^16*d^4 - 4*b^20*c^18*d^2 - 12*a*b^19*c^11*d^9 + 48*a*b^19*c^13*d^7 - 72*a*b^19*c^15*d^5 + 48*a*b^19*c^17*d^3 + 48*a^3*b^17*c^19*d - 72*a^5*b^15*c^19*d + 48*a^7*b^13*c^19*d - 12*a^9*b^11*c^19*d - 12*a^11*b^9*c*d^19 + 48*a^13*b^7*c*d^19 - 72*a^15*b^5*c*d^19 + 48*a^17*b^3*c*d^19 + 48*a^19*b*c^3*d^17 - 72*a^19*b*c^5*d^15 + 48*a^19*b*c^7*d^13 - 12*a^19*b*c^9*d^11 + 66*a^2*b^18*c^10*d^10 - 268*a^2*b^18*c^12*d^8 + 412*a^2*b^18*c^14*d^6 - 288*a^2*b^18*c^16*d^4 + 82*a^2*b^18*c^18*d^2 - 220*a^3*b^17*c^9*d^11 + 928*a^3*b^17*c^11*d^9 - 1512*a^3*b^17*c^13*d^7 + 1168*a^3*b^17*c^15*d^5 - 412*a^3*b^17*c^17*d^3 + 495*a^4*b^16*c^8*d^12 - 2244*a^4*b^16*c^10*d^10 + 4032*a^4*b^16*c^12*d^8 - 3588*a^4*b^16*c^14*d^6 + 1587*a^4*b^16*c^16*d^4 - 288*a^4*b^16*c^18*d^2 - 792*a^5*b^15*c^7*d^13 + 4048*a^5*b^15*c^9*d^11 - 8344*a^5*b^15*c^11*d^9 + 8736*a^5*b^15*c^13*d^7 - 4744*a^5*b^15*c^15*d^5 + 1168*a^5*b^15*c^17*d^3 + 924*a^6*b^14*c^6*d^14 - 5676*a^6*b^14*c^8*d^12 + 13860*a^6*b^14*c^10*d^10 - 17164*a^6*b^14*c^12*d^8 + 11236*a^6*b^14*c^14*d^6 - 3588*a^6*b^14*c^16*d^4 + 412*a^6*b^14*c^18*d^2 - 792*a^7*b^13*c^5*d^15 + 6336*a^7*b^13*c^7*d^13 - 18744*a^7*b^13*c^9*d^11 + 27504*a^7*b^13*c^11*d^9 - 21576*a^7*b^13*c^13*d^7 + 8736*a^7*b^13*c^15*d^5 - 1512*a^7*b^13*c^17*d^3 + 495*a^8*b^12*c^4*d^16 - 5676*a^8*b^12*c^6*d^14 + 20724*a^8*b^12*c^8*d^12 - 36300*a^8*b^12*c^10*d^10 + 34156*a^8*b^12*c^12*d^8 - 17164*a^8*b^12*c^14*d^6 + 4032*a^8*b^12*c^16*d^4 - 268*a^8*b^12*c^18*d^2 - 220*a^9*b^11*c^3*d^17 + 4048*a^9*b^11*c^5*d^15 - 18744*a^9*b^11*c^7*d^13 + 39776*a^9*b^11*c^9*d^11 - 44936*a^9*b^11*c^11*d^9 + 27504*a^9*b^11*c^13*d^7 - 8344*a^9*b^11*c^15*d^5 + 928*a^9*b^11*c^17*d^3 + 66*a^10*b^10*c^2*d^18 - 2244*a^10*b^10*c^4*d^16 + 13860*a^10*b^10*c^6*d^14 - 36300*a^10*b^10*c^8*d^12 + 49236*a^10*b^10*c^10*d^10 - 36300*a^10*b^10*c^12*d^8 + 13860*a^10*b^10*c^14*d^6 - 2244*a^10*b^10*c^16*d^4 + 66*a^10*b^10*c^18*d^2 + 928*a^11*b^9*c^3*d^17 - 8344*a^11*b^9*c^5*d^15 + 27504*a^11*b^9*c^7*d^13 - 44936*a^11*b^9*c^9*d^11 + 39776*a^11*b^9*c^11*d^9 - 18744*a^11*b^9*c^13*d^7 + 4048*a^11*b^9*c^15*d^5 - 220*a^11*b^9*c^17*d^3 - 268*a^12*b^8*c^2*d^18 + 4032*a^12*b^8*c^4*d^16 - 17164*a^12*b^8*c^6*d^14 + 34156*a^12*b^8*c^8*d^12 - 36300*a^12*b^8*c^10*d^10 + 20724*a^12*b^8*c^12*d^8 - 5676*a^12*b^8*c^14*d^6 + 495*a^12*b^8*c^16*d^4 - 1512*a^13*b^7*c^3*d^17 + 8736*a^13*b^7*c^5*d^15 - 21576*a^13*b^7*c^7*d^13 + 27504*a^13*b^7*c^9*d^11 - 18744*a^13*b^7*c^11*d^9 + 6336*a^13*b^7*c^13*d^7 - 792*a^13*b^7*c^15*d^5 + 412*a^14*b^6*c^2*d^18 - 3588*a^14*b^6*c^4*d^16 + 11236*a^14*b^6*c^6*d^14 - 17164*a^14*b^6*c^8*d^12 + 13860*a^14*b^6*c^10*d^10 - 5676*a^14*b^6*c^12*d^8 + 924*a^14*b^6*c^14*d^6 + 1168*a^15*b^5*c^3*d^17 - 4744*a^15*b^5*c^5*d^15 + 8736*a^15*b^5*c^7*d^13 - 8344*a^15*b^5*c^9*d^11 + 4048*a^15*b^5*c^11*d^9 - 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33825*a^6*b^24*c^26*d^4 - 1950*a^6*b^24*c^28*d^2 - 77520*a^7*b^23*c^13*d^17 + 465120*a^7*b^23*c^15*d^15 - 1174200*a^7*b^23*c^17*d^13 + 1607600*a^7*b^23*c^19*d^11 - 1277800*a^7*b^23*c^21*d^9 + 581120*a^7*b^23*c^23*d^7 - 136520*a^7*b^23*c^25*d^5 + 12400*a^7*b^23*c^27*d^3 + 125970*a^8*b^22*c^12*d^18 - 823650*a^8*b^22*c^14*d^16 + 2277150*a^8*b^22*c^16*d^14 - 3441850*a^8*b^22*c^18*d^12 + 3061855*a^8*b^22*c^20*d^10 - 1598495*a^8*b^22*c^22*d^8 + 455100*a^8*b^22*c^24*d^6 - 58000*a^8*b^22*c^26*d^4 + 1925*a^8*b^22*c^28*d^2 - 167960*a^9*b^21*c^11*d^19 + 1227400*a^9*b^21*c^13*d^17 - 3772640*a^9*b^21*c^15*d^15 + 6342200*a^9*b^21*c^17*d^13 - 6323300*a^9*b^21*c^19*d^11 + 3770860*a^9*b^21*c^21*d^9 - 1277800*a^9*b^21*c^23*d^7 + 213040*a^9*b^21*c^25*d^5 - 11900*a^9*b^21*c^27*d^3 + 184756*a^10*b^20*c^10*d^20 - 1553630*a^10*b^20*c^12*d^18 + 5384410*a^10*b^20*c^14*d^16 - 10132510*a^10*b^20*c^16*d^14 + 11341480*a^10*b^20*c^18*d^12 - 7699257*a^10*b^20*c^20*d^10 + 3061855*a^10*b^20*c^22*d^8 - 639360*a^10*b^20*c^24*d^6 + 53210*a^10*b^20*c^26*d^4 - 955*a^10*b^20*c^28*d^2 - 167960*a^11*b^19*c^9*d^21 + 1679600*a^11*b^19*c^11*d^19 - 6653800*a^11*b^19*c^13*d^17 + 14108640*a^11*b^19*c^15*d^15 - 17770700*a^11*b^19*c^17*d^13 + 13697880*a^11*b^19*c^19*d^11 - 6323300*a^11*b^19*c^21*d^9 + 1607600*a^11*b^19*c^23*d^7 - 183740*a^11*b^19*c^25*d^5 + 5800*a^11*b^19*c^27*d^3 + 125970*a^12*b^18*c^8*d^22 - 1553630*a^12*b^18*c^10*d^20 + 7138300*a^12*b^18*c^12*d^18 - 17183600*a^12*b^18*c^14*d^16 + 24426875*a^12*b^18*c^16*d^14 - 21339185*a^12*b^18*c^18*d^12 + 11341480*a^12*b^18*c^20*d^10 - 3441850*a^12*b^18*c^22*d^8 + 510625*a^12*b^18*c^24*d^6 - 25175*a^12*b^18*c^26*d^4 + 190*a^12*b^18*c^28*d^2 - 77520*a^13*b^17*c^7*d^23 + 1227400*a^13*b^17*c^9*d^21 - 6653800*a^13*b^17*c^11*d^19 + 18346400*a^13*b^17*c^13*d^17 - 29535120*a^13*b^17*c^15*d^15 + 29213260*a^13*b^17*c^17*d^13 - 17770700*a^13*b^17*c^19*d^11 + 6342200*a^13*b^17*c^21*d^9 - 1174200*a^13*b^17*c^23*d^7 + 83220*a^13*b^17*c^25*d^5 - 1140*a^13*b^17*c^27*d^3 + 38760*a^14*b^16*c^6*d^24 - 823650*a^14*b^16*c^8*d^22 + 5384410*a^14*b^16*c^10*d^20 - 17183600*a^14*b^16*c^12*d^18 + 31460200*a^14*b^16*c^14*d^16 - 35234455*a^14*b^16*c^16*d^14 + 24426875*a^14*b^16*c^18*d^12 - 10132510*a^14*b^16*c^20*d^10 + 2277150*a^14*b^16*c^22*d^8 - 218025*a^14*b^16*c^24*d^6 + 4845*a^14*b^16*c^26*d^4 - 15504*a^15*b^15*c^5*d^25 + 465120*a^15*b^15*c^7*d^23 - 3772640*a^15*b^15*c^9*d^21 + 14108640*a^15*b^15*c^11*d^19 - 29535120*a^15*b^15*c^13*d^17 + 37499008*a^15*b^15*c^15*d^15 - 29535120*a^15*b^15*c^17*d^13 + 14108640*a^15*b^15*c^19*d^11 - 3772640*a^15*b^15*c^21*d^9 + 465120*a^15*b^15*c^23*d^7 - 15504*a^15*b^15*c^25*d^5 + 4845*a^16*b^14*c^4*d^26 - 218025*a^16*b^14*c^6*d^24 + 2277150*a^16*b^14*c^8*d^22 - 10132510*a^16*b^14*c^10*d^20 + 24426875*a^16*b^14*c^12*d^18 - 35234455*a^16*b^14*c^14*d^16 + 31460200*a^16*b^14*c^16*d^14 - 17183600*a^16*b^14*c^18*d^12 + 5384410*a^16*b^14*c^20*d^10 - 823650*a^16*b^14*c^22*d^8 + 38760*a^16*b^14*c^24*d^6 - 1140*a^17*b^13*c^3*d^27 + 83220*a^17*b^13*c^5*d^25 - 1174200*a^17*b^13*c^7*d^23 + 6342200*a^17*b^13*c^9*d^21 - 17770700*a^17*b^13*c^11*d^19 + 29213260*a^17*b^13*c^13*d^17 - 29535120*a^17*b^13*c^15*d^15 + 18346400*a^17*b^13*c^17*d^13 - 6653800*a^17*b^13*c^19*d^11 + 1227400*a^17*b^13*c^21*d^9 - 77520*a^17*b^13*c^23*d^7 + 190*a^18*b^12*c^2*d^28 - 25175*a^18*b^12*c^4*d^26 + 510625*a^18*b^12*c^6*d^24 - 3441850*a^18*b^12*c^8*d^22 + 11341480*a^18*b^12*c^10*d^20 - 21339185*a^18*b^12*c^12*d^18 + 24426875*a^18*b^12*c^14*d^16 - 17183600*a^18*b^12*c^16*d^14 + 7138300*a^18*b^12*c^18*d^12 - 1553630*a^18*b^12*c^20*d^10 + 125970*a^18*b^12*c^22*d^8 + 5800*a^19*b^11*c^3*d^27 - 183740*a^19*b^11*c^5*d^25 + 1607600*a^19*b^11*c^7*d^23 - 6323300*a^19*b^11*c^9*d^21 + 13697880*a^19*b^11*c^11*d^19 - 17770700*a^19*b^11*c^13*d^17 + 14108640*a^19*b^11*c^15*d^15 - 6653800*a^19*b^11*c^17*d^13 + 1679600*a^19*b^11*c^19*d^11 - 167960*a^19*b^11*c^21*d^9 - 955*a^20*b^10*c^2*d^28 + 53210*a^20*b^10*c^4*d^26 - 639360*a^20*b^10*c^6*d^24 + 3061855*a^20*b^10*c^8*d^22 - 7699257*a^20*b^10*c^10*d^20 + 11341480*a^20*b^10*c^12*d^18 - 10132510*a^20*b^10*c^14*d^16 + 5384410*a^20*b^10*c^16*d^14 - 1553630*a^20*b^10*c^18*d^12 + 184756*a^20*b^10*c^20*d^10 - 11900*a^21*b^9*c^3*d^27 + 213040*a^21*b^9*c^5*d^25 - 1277800*a^21*b^9*c^7*d^23 + 3770860*a^21*b^9*c^9*d^21 - 6323300*a^21*b^9*c^11*d^19 + 6342200*a^21*b^9*c^13*d^17 - 3772640*a^21*b^9*c^15*d^15 + 1227400*a^21*b^9*c^17*d^13 - 167960*a^21*b^9*c^19*d^11 + 1925*a^22*b^8*c^2*d^28 - 58000*a^22*b^8*c^4*d^26 + 455100*a^22*b^8*c^6*d^24 - 1598495*a^22*b^8*c^8*d^22 + 3061855*a^22*b^8*c^10*d^20 - 3441850*a^22*b^8*c^12*d^18 + 2277150*a^22*b^8*c^14*d^16 - 823650*a^22*b^8*c^16*d^14 + 125970*a^22*b^8*c^18*d^12 + 12400*a^23*b^7*c^3*d^27 - 136520*a^23*b^7*c^5*d^25 + 581120*a^23*b^7*c^7*d^23 - 1277800*a^23*b^7*c^9*d^21 + 1607600*a^23*b^7*c^11*d^19 - 1174200*a^23*b^7*c^13*d^17 + 465120*a^23*b^7*c^15*d^15 - 77520*a^23*b^7*c^17*d^13 - 1950*a^24*b^6*c^2*d^28 + 33825*a^24*b^6*c^4*d^26 - 178985*a^24*b^6*c^6*d^24 + 455100*a^24*b^6*c^8*d^22 - 639360*a^24*b^6*c^10*d^20 + 510625*a^24*b^6*c^12*d^18 - 218025*a^24*b^6*c^14*d^16 + 38760*a^24*b^6*c^16*d^14 - 6700*a^25*b^5*c^3*d^27 + 46004*a^25*b^5*c^5*d^25 - 136520*a^25*b^5*c^7*d^23 + 213040*a^25*b^5*c^9*d^21 - 183740*a^25*b^5*c^11*d^19 + 83220*a^25*b^5*c^13*d^17 - 15504*a^25*b^5*c^15*d^15 + 1000*a^26*b^4*c^2*d^28 - 9695*a^26*b^4*c^4*d^26 + 33825*a^26*b^4*c^6*d^24 - 58000*a^26*b^4*c^8*d^22 + 53210*a^26*b^4*c^10*d^20 - 25175*a^26*b^4*c^12*d^18 + 4845*a^26*b^4*c^14*d^16 + 1640*a^27*b^3*c^3*d^27 - 6700*a^27*b^3*c^5*d^25 + 12400*a^27*b^3*c^7*d^23 - 11900*a^27*b^3*c^9*d^21 + 5800*a^27*b^3*c^11*d^19 - 1140*a^27*b^3*c^13*d^17 - 215*a^28*b^2*c^2*d^28 + 1000*a^28*b^2*c^4*d^26 - 1950*a^28*b^2*c^6*d^24 + 1925*a^28*b^2*c^8*d^22 - 955*a^28*b^2*c^10*d^20 + 190*a^28*b^2*c^12*d^18 + 20*a*b^29*c^29*d + 20*a^29*b*c*d^29)))^(1/2)*2i)/f","B"
723,0,-1,298,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2),x)","\int \left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2), x)","F"
724,0,-1,235,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2),x)","\int \left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2), x)","F"
725,0,-1,181,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2),x)","\int \left(a+b\,\sin\left(e+f\,x\right)\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2), x)","F"
726,1,176,140,8.579877,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(1/2),x)","\frac{b\,\left(2\,c\,\mathrm{F}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|\frac{2\,d}{c+d}\right)-2\,\left(c+d\right)\,\mathrm{E}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|\frac{2\,d}{c+d}\right)\right)\,\sqrt{{\cos\left(e+f\,x\right)}^2}\,\sqrt{\frac{c+d\,\sin\left(e+f\,x\right)}{c+d}}}{d\,f\,\cos\left(e+f\,x\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}-\frac{2\,a\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|\frac{2\,d}{c+d}\right)\,\sqrt{\frac{c+d\,\sin\left(e+f\,x\right)}{c+d}}}{f\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}","Not used",1,"(b*(2*c*ellipticF(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), (2*d)/(c + d)) - 2*(c + d)*ellipticE(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), (2*d)/(c + d)))*(cos(e + f*x)^2)^(1/2)*((c + d*sin(e + f*x))/(c + d))^(1/2))/(d*f*cos(e + f*x)*(c + d*sin(e + f*x))^(1/2)) - (2*a*ellipticF(pi/4 - e/2 - (f*x)/2, (2*d)/(c + d))*((c + d*sin(e + f*x))/(c + d))^(1/2))/(f*(c + d*sin(e + f*x))^(1/2))","B"
727,0,-1,195,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{a+b\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(3/2), x)","F"
728,0,-1,285,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{a+b\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(5/2), x)","F"
729,0,-1,369,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(7/2),x)","\int \frac{a+b\,\sin\left(e+f\,x\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))/(c + d*sin(e + f*x))^(7/2), x)","F"
730,0,-1,451,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2), x)","F"
731,0,-1,347,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2), x)","F"
732,0,-1,254,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2), x)","F"
733,0,-1,203,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(1/2), x)","F"
734,0,-1,228,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(3/2), x)","F"
735,0,-1,329,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(5/2), x)","F"
736,0,-1,460,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^2/(c + d*sin(e + f*x))^(7/2), x)","F"
737,0,-1,642,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(5/2), x)","F"
738,0,-1,496,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2), x)","F"
739,0,-1,375,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2), x)","F"
740,0,-1,302,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(1/2), x)","F"
741,0,-1,361,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(3/2), x)","F"
742,0,-1,391,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(5/2), x)","F"
743,0,-1,532,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(7/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(7/2), x)","F"
744,0,-1,716,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(9/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^3/(c + d*sin(e + f*x))^(9/2), x)","F"
745,0,-1,296,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x)),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x)), x)","F"
746,0,-1,229,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x)),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x)), x)","F"
747,0,-1,153,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x)),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x)), x)","F"
748,0,-1,75,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\left(a+b\,\sin\left(e+f\,x\right)\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)), x)","F"
749,0,-1,220,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{\left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2)), x)","F"
750,0,-1,399,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{\left(a+b\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(5/2)), x)","F"
751,0,-1,534,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(7/2)/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(7/2)/(a + b*sin(e + f*x))^2, x)","F"
752,0,-1,390,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^2, x)","F"
753,0,-1,351,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^2, x)","F"
754,0,-1,307,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^2,x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^2, x)","F"
755,0,-1,325,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(1/2)), x)","F"
756,0,-1,449,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(3/2)), x)","F"
757,0,-1,661,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))^(5/2)), x)","F"
758,0,-1,816,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(9/2)/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(9/2)/(a + b*sin(e + f*x))^3, x)","F"
759,0,-1,605,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(7/2)/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(7/2)/(a + b*sin(e + f*x))^3, x)","F"
760,0,-1,549,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^3, x)","F"
761,0,-1,472,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^3, x)","F"
762,0,-1,487,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^3,x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^3, x)","F"
763,0,-1,503,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(1/2)), x)","F"
764,0,-1,682,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^3*(c + d*sin(e + f*x))^(3/2)), x)","F"
765,0,-1,888,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2),x)","\int \sqrt{a+b\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2), x)","F"
766,0,-1,784,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2),x)","\int \sqrt{a+b\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2), x)","F"
767,0,-1,628,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2),x)","\int \sqrt{a+b\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2), x)","F"
768,0,-1,198,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(1/2), x)","F"
769,0,-1,409,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(3/2), x)","F"
770,0,-1,489,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/(c + d*sin(e + f*x))^(5/2), x)","F"
771,0,-1,1080,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2), x)","F"
772,0,-1,870,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2), x)","F"
773,0,-1,740,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2), x)","F"
774,0,-1,644,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(1/2), x)","F"
775,0,-1,600,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(3/2), x)","F"
776,0,-1,497,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(3/2)/(c + d*sin(e + f*x))^(5/2), x)","F"
777,0,-1,1295,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2), x)","F"
778,0,-1,1071,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2), x)","F"
779,0,-1,894,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2), x)","F"
780,0,-1,745,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(1/2), x)","F"
781,0,-1,780,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(3/2), x)","F"
782,0,-1,737,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(5/2)/(c + d*sin(e + f*x))^(5/2), x)","F"
783,0,-1,772,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{a+b\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^(1/2), x)","F"
784,0,-1,644,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^(1/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+b\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^(1/2), x)","F"
785,0,-1,198,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^(1/2),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{\sqrt{a+b\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^(1/2), x)","F"
786,0,-1,192,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
787,0,-1,405,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{\sqrt{a+b\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
788,0,-1,521,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{\sqrt{a+b\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
789,0,-1,822,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^(3/2), x)","F"
790,0,-1,600,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^(3/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^(3/2), x)","F"
791,0,-1,409,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^(3/2),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^(3/2), x)","F"
792,0,-1,405,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
793,0,-1,495,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
794,0,-1,681,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
795,0,-1,736,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(5/2)/(a + b*sin(e + f*x))^(5/2), x)","F"
796,0,-1,497,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^(5/2),x)","\int \frac{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(3/2)/(a + b*sin(e + f*x))^(5/2), x)","F"
797,0,-1,489,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^(5/2),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(a + b*sin(e + f*x))^(5/2), x)","F"
798,0,-1,516,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
799,0,-1,688,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
800,0,-1,941,0.000000,"\text{Not used}","int(1/((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{1}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
801,0,-1,28,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",0,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
802,0,-1,311,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^2,x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^2, x)","F"
803,0,-1,229,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x)),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x)), x)","F"
804,0,-1,104,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m,x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((a + b*sin(e + f*x))^m, x)","F"
805,0,-1,28,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x)),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x)), x)","F"
806,0,-1,28,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^2,x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^2, x)","F"
807,0,-1,28,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^3,x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^3, x)","F"
808,0,-1,30,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(5/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(5/2), x)","F"
809,0,-1,30,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2), x)","F"
810,0,-1,30,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2), x)","F"
811,0,-1,30,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^(1/2), x)","F"
812,0,-1,30,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^(3/2), x)","F"
813,0,-1,30,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",0,"int((a + b*sin(e + f*x))^m/(c + d*sin(e + f*x))^(5/2), x)","F"
814,0,-1,272,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n*(a + a*sin(e + f*x))^3,x)","\int {\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((d/sin(e + f*x))^n*(a + a*sin(e + f*x))^3, x)","F"
815,0,-1,203,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n*(a + a*sin(e + f*x))^2,x)","\int {\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((d/sin(e + f*x))^n*(a + a*sin(e + f*x))^2, x)","F"
816,0,-1,149,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n*(a + a*sin(e + f*x)),x)","\int {\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n\,\left(a+a\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((d/sin(e + f*x))^n*(a + a*sin(e + f*x)), x)","F"
817,0,-1,171,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n/(a + a*sin(e + f*x)),x)","\int \frac{{\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((d/sin(e + f*x))^n/(a + a*sin(e + f*x)), x)","F"
818,0,-1,231,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((d/sin(e + f*x))^n/(a + a*sin(e + f*x))^2, x)","F"
819,0,-1,113,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x))^m,x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x))^m, x)","F"
820,0,-1,299,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x))^3,x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x))^3, x)","F"
821,0,-1,222,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x))^2,x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x))^2, x)","F"
822,0,-1,163,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x)),x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,\left(a+a\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + a*sin(e + f*x)), x)","F"
823,0,-1,189,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n/(a + a*sin(e + f*x)),x)","\int \frac{{\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n/(a + a*sin(e + f*x)), x)","F"
824,0,-1,288,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n/(a + a*sin(e + f*x))^2, x)","F"
825,0,-1,298,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n*(a + b*sin(e + f*x))^3,x)","\int {\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((d/sin(e + f*x))^n*(a + b*sin(e + f*x))^3, x)","F"
826,0,-1,213,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n*(a + b*sin(e + f*x))^2,x)","\int {\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((d/sin(e + f*x))^n*(a + b*sin(e + f*x))^2, x)","F"
827,0,-1,149,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n*(a + b*sin(e + f*x)),x)","\int {\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n\,\left(a+b\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((d/sin(e + f*x))^n*(a + b*sin(e + f*x)), x)","F"
828,0,-1,204,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n/(a + b*sin(e + f*x)),x)","\int \frac{{\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((d/sin(e + f*x))^n/(a + b*sin(e + f*x)), x)","F"
829,0,-1,321,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((d/sin(e + f*x))^n/(a + b*sin(e + f*x))^2, x)","F"
830,0,-1,432,0.000000,"\text{Not used}","int((d/sin(e + f*x))^n/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(\frac{d}{\sin\left(e+f\,x\right)}\right)}^n}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((d/sin(e + f*x))^n/(a + b*sin(e + f*x))^3, x)","F"
831,0,-1,56,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x))^m,x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",0,"int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x))^m, x)","F"
832,0,-1,323,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x))^3,x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x))^3, x)","F"
833,0,-1,231,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x))^2,x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x))^2, x)","F"
834,0,-1,163,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x)),x)","\int {\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n\,\left(a+b\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n*(a + b*sin(e + f*x)), x)","F"
835,0,-1,204,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n/(a + b*sin(e + f*x)),x)","\int \frac{{\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n/(a + b*sin(e + f*x)), x)","F"
836,0,-1,322,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n/(a + b*sin(e + f*x))^2, x)","F"
837,0,-1,428,0.000000,"\text{Not used}","int((c*(d*sin(e + f*x))^p)^n/(a + b*sin(e + f*x))^3,x)","\int \frac{{\left(c\,{\left(d\,\sin\left(e+f\,x\right)\right)}^p\right)}^n}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((c*(d*sin(e + f*x))^p)^n/(a + b*sin(e + f*x))^3, x)","F"