1,1,256,121,14.237523,"\text{Not used}","int(sin(e + f*x)^3*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)),x)","\frac{a^2\,c\,\left(15\,e-30\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-384\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-170\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+1140\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-640\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-1140\,{\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+170\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+30\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+15\,f\,x+90\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(e+f\,x\right)+225\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(e+f\,x\right)+300\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(e+f\,x\right)+225\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(e+f\,x\right)+90\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(e+f\,x\right)+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(e+f\,x\right)-64\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*(15*e - 30*tan(e/2 + (f*x)/2) - 384*tan(e/2 + (f*x)/2)^2 - 170*tan(e/2 + (f*x)/2)^3 + 1140*tan(e/2 + (f*x)/2)^5 - 640*tan(e/2 + (f*x)/2)^6 - 1140*tan(e/2 + (f*x)/2)^7 - 960*tan(e/2 + (f*x)/2)^8 + 170*tan(e/2 + (f*x)/2)^9 + 30*tan(e/2 + (f*x)/2)^11 + 15*f*x + 90*tan(e/2 + (f*x)/2)^2*(e + f*x) + 225*tan(e/2 + (f*x)/2)^4*(e + f*x) + 300*tan(e/2 + (f*x)/2)^6*(e + f*x) + 225*tan(e/2 + (f*x)/2)^8*(e + f*x) + 90*tan(e/2 + (f*x)/2)^10*(e + f*x) + 15*tan(e/2 + (f*x)/2)^12*(e + f*x) - 64))/(240*f*(tan(e/2 + (f*x)/2)^2 + 1)^6)","B"
2,1,212,96,14.183181,"\text{Not used}","int(sin(e + f*x)^2*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)),x)","\frac{a^2\,c\,\left(15\,e-30\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-160\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+180\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+160\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-480\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-180\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+30\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+15\,f\,x+75\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(e+f\,x\right)+150\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(e+f\,x\right)+150\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(e+f\,x\right)+75\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(e+f\,x\right)+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(e+f\,x\right)-32\right)}{120\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(a^2*c*(15*e - 30*tan(e/2 + (f*x)/2) - 160*tan(e/2 + (f*x)/2)^2 + 180*tan(e/2 + (f*x)/2)^3 + 160*tan(e/2 + (f*x)/2)^4 - 480*tan(e/2 + (f*x)/2)^6 - 180*tan(e/2 + (f*x)/2)^7 + 30*tan(e/2 + (f*x)/2)^9 + 15*f*x + 75*tan(e/2 + (f*x)/2)^2*(e + f*x) + 150*tan(e/2 + (f*x)/2)^4*(e + f*x) + 150*tan(e/2 + (f*x)/2)^6*(e + f*x) + 75*tan(e/2 + (f*x)/2)^8*(e + f*x) + 15*tan(e/2 + (f*x)/2)^10*(e + f*x) - 32))/(120*f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
3,1,250,77,14.122706,"\text{Not used}","int(sin(e + f*x)*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)),x)","\frac{a^2\,c\,x}{8}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^2\,c\,\left(3\,e+3\,f\,x\right)}{6}-\frac{a^2\,c\,\left(12\,e+12\,f\,x-16\right)}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{a^2\,c\,\left(3\,e+3\,f\,x\right)}{6}-\frac{a^2\,c\,\left(12\,e+12\,f\,x-48\right)}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^2\,c\,\left(3\,e+3\,f\,x\right)}{4}-\frac{a^2\,c\,\left(18\,e+18\,f\,x-48\right)}{24}\right)+\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}-\frac{7\,a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{4}+\frac{7\,a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{4}-\frac{a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{4}+\frac{a^2\,c\,\left(3\,e+3\,f\,x\right)}{24}-\frac{a^2\,c\,\left(3\,e+3\,f\,x-16\right)}{24}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(a^2*c*x)/8 - (tan(e/2 + (f*x)/2)^2*((a^2*c*(3*e + 3*f*x))/6 - (a^2*c*(12*e + 12*f*x - 16))/24) + tan(e/2 + (f*x)/2)^6*((a^2*c*(3*e + 3*f*x))/6 - (a^2*c*(12*e + 12*f*x - 48))/24) + tan(e/2 + (f*x)/2)^4*((a^2*c*(3*e + 3*f*x))/4 - (a^2*c*(18*e + 18*f*x - 48))/24) + (a^2*c*tan(e/2 + (f*x)/2))/4 - (7*a^2*c*tan(e/2 + (f*x)/2)^3)/4 + (7*a^2*c*tan(e/2 + (f*x)/2)^5)/4 - (a^2*c*tan(e/2 + (f*x)/2)^7)/4 + (a^2*c*(3*e + 3*f*x))/24 - (a^2*c*(3*e + 3*f*x - 16))/24)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^4)","B"
4,1,125,52,14.301085,"\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"
5,1,88,63,12.892281,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x),x)","\frac{a^2\,c\,\left(\cos\left(e+f\,x\right)+\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)+\frac{\sin\left(2\,e+2\,f\,x\right)}{4}+\mathrm{atan}\left(\frac{\sqrt{5}\,\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{5\,\cos\left(\frac{e}{2}+\mathrm{atan}\left(\frac{1}{2}\right)+\frac{f\,x}{2}\right)}\right)\right)}{f}","Not used",1,"(a^2*c*(cos(e + f*x) + log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)) + sin(2*e + 2*f*x)/4 + atan((5^(1/2)*(cos(e/2 + (f*x)/2) + 2*sin(e/2 + (f*x)/2)))/(5*cos(e/2 + atan(1/2) + (f*x)/2)))))/f","B"
6,1,110,53,12.393947,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x)^2,x)","\frac{a^2\,c\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{2\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}\right)+\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\right)}{f}-\frac{a^2\,c\,\left(\cos\left(e+f\,x\right)-\frac{\sin\left(2\,e+2\,f\,x\right)}{2}\right)}{f\,\sin\left(e+f\,x\right)}","Not used",1,"(a^2*c*(2*atan((2^(1/2)*(cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2)))/(2*cos(e/2 - pi/4 + (f*x)/2))) + log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2))))/f - (a^2*c*(cos(e + f*x) - sin(2*e + 2*f*x)/2))/(f*sin(e + f*x))","B"
7,1,163,64,12.262075,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x)^3,x)","\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,f}-\frac{a^2\,c\,\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{2\,a^2\,c\,\mathrm{atan}\left(\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f}-\frac{a^2\,c\,\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{2\,f}-\frac{a^2\,c\,{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}+\frac{a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}","Not used",1,"(a^2*c*tan(e/2 + (f*x)/2))/(2*f) - (a^2*c*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(2*f) - (2*a^2*c*atan((2*cos(e/2 + (f*x)/2) + sin(e/2 + (f*x)/2))/(cos(e/2 + (f*x)/2) - 2*sin(e/2 + (f*x)/2))))/f - (a^2*c*cot(e/2 + (f*x)/2))/(2*f) - (a^2*c*cot(e/2 + (f*x)/2)^2)/(8*f) + (a^2*c*tan(e/2 + (f*x)/2)^2)/(8*f)","B"
8,1,132,61,12.222760,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x)^4,x)","\frac{a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2}{8\,f}-\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-c\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+c\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{c\,a^2}{3}\right)}{8\,f}+\frac{a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24\,f}-\frac{a^2\,c\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{2\,f}","Not used",1,"(a^2*c*tan(e/2 + (f*x)/2)^2)/(8*f) - (a^2*c*tan(e/2 + (f*x)/2))/(8*f) - (cot(e/2 + (f*x)/2)^3*((a^2*c)/3 + a^2*c*tan(e/2 + (f*x)/2) - a^2*c*tan(e/2 + (f*x)/2)^2))/(8*f) + (a^2*c*tan(e/2 + (f*x)/2)^3)/(24*f) - (a^2*c*log(tan(e/2 + (f*x)/2)))/(2*f)","B"
9,1,133,86,12.184482,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x)^5,x)","\frac{a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{24\,f}-\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8\,f}-\frac{{\mathrm{cot}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(-2\,c\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\frac{2\,c\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{3}+\frac{c\,a^2}{4}\right)}{16\,f}+\frac{a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{64\,f}-\frac{a^2\,c\,\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{8\,f}","Not used",1,"(a^2*c*tan(e/2 + (f*x)/2)^3)/(24*f) - (a^2*c*tan(e/2 + (f*x)/2))/(8*f) - (cot(e/2 + (f*x)/2)^4*((a^2*c)/4 + (2*a^2*c*tan(e/2 + (f*x)/2))/3 - 2*a^2*c*tan(e/2 + (f*x)/2)^3))/(16*f) + (a^2*c*tan(e/2 + (f*x)/2)^4)/(64*f) - (a^2*c*log(tan(e/2 + (f*x)/2)))/(8*f)","B"
10,1,244,105,12.369356,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x)^6,x)","-\frac{a^2\,c\,\left(6\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-6\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-15\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+15\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-10\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+60\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-60\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+120\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}{960\,f\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}","Not used",1,"-(a^2*c*(6*cos(e/2 + (f*x)/2)^10 - 6*sin(e/2 + (f*x)/2)^10 - 15*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^9 + 15*cos(e/2 + (f*x)/2)^9*sin(e/2 + (f*x)/2) - 10*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^8 + 60*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2)^6 - 60*cos(e/2 + (f*x)/2)^6*sin(e/2 + (f*x)/2)^4 + 10*cos(e/2 + (f*x)/2)^8*sin(e/2 + (f*x)/2)^2 + 120*cos(e/2 + (f*x)/2)^5*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2))*sin(e/2 + (f*x)/2)^5))/(960*f*cos(e/2 + (f*x)/2)^5*sin(e/2 + (f*x)/2)^5)","B"
11,1,340,130,12.541641,"\text{Not used}","int(((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)))/sin(e + f*x)^7,x)","-\frac{a^2\,c\,\left(5\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}-12\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+12\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-15\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}-20\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+15\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+120\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7-120\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-15\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+20\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+15\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+120\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\ln\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\right)}{1920\,f\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6}","Not used",1,"-(a^2*c*(5*cos(e/2 + (f*x)/2)^12 - 5*sin(e/2 + (f*x)/2)^12 - 12*cos(e/2 + (f*x)/2)*sin(e/2 + (f*x)/2)^11 + 12*cos(e/2 + (f*x)/2)^11*sin(e/2 + (f*x)/2) - 15*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2)^10 - 20*cos(e/2 + (f*x)/2)^3*sin(e/2 + (f*x)/2)^9 + 15*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2)^8 + 120*cos(e/2 + (f*x)/2)^5*sin(e/2 + (f*x)/2)^7 - 120*cos(e/2 + (f*x)/2)^7*sin(e/2 + (f*x)/2)^5 - 15*cos(e/2 + (f*x)/2)^8*sin(e/2 + (f*x)/2)^4 + 20*cos(e/2 + (f*x)/2)^9*sin(e/2 + (f*x)/2)^3 + 15*cos(e/2 + (f*x)/2)^10*sin(e/2 + (f*x)/2)^2 + 120*cos(e/2 + (f*x)/2)^6*log(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2))*sin(e/2 + (f*x)/2)^6))/(1920*f*cos(e/2 + (f*x)/2)^6*sin(e/2 + (f*x)/2)^6)","B"
12,0,-1,128,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)*(c - c*sin(c + d*x)),x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+a\,\sin\left(c+d\,x\right)\right)}^{3/2}\,\left(c-c\,\sin\left(c+d\,x\right)\right) \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a*sin(c + d*x))^(3/2)*(c - c*sin(c + d*x)), x)","F"
13,0,-1,69,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c - c*sin(e + f*x))),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sin\left(e+f\,x\right)\,\left(c-c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((a + a*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c - c*sin(e + f*x))), x)","F"
14,0,-1,120,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c-c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))), x)","F"
15,0,-1,103,0.000000,"\text{Not used}","int(((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x)), x)","F"
16,1,52,43,12.939061,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/((g*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))),x)","\frac{2\,\sin\left(2\,e+2\,f\,x\right)\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}}{c\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)\,\sqrt{g\,\sin\left(e+f\,x\right)}}","Not used",1,"(2*sin(2*e + 2*f*x)*(a*(sin(e + f*x) + 1))^(1/2))/(c*f*(cos(2*e + 2*f*x) + 1)*(g*sin(e + f*x))^(1/2))","B"
17,0,-1,114,0.000000,"\text{Not used}","int((g*sin(e + f*x))^(1/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c-c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*sin(e + f*x))^(1/2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))), x)","F"
18,0,-1,118,0.000000,"\text{Not used}","int(1/((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c-c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))), x)","F"
19,0,-1,46,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/sin(e + f*x),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\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))/sin(e + f*x), x)","F"
20,0,-1,102,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\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)/(sin(e + f*x)*(c - c*sin(e + f*x))^(1/2)), x)","F"
21,0,-1,100,0.000000,"\text{Not used}","int((c - c*sin(e + f*x))^(1/2)/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\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)/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)), x)","F"
22,0,-1,46,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\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/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
23,0,-1,105,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c + d*sin(e + f*x))),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\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)/(sin(e + f*x)*(c + d*sin(e + f*x))), x)","F"
24,0,-1,165,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\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/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
25,0,-1,149,0.000000,"\text{Not used}","int(((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x)), x)","F"
26,0,-1,83,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/((g*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sqrt{g\,\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)/((g*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
27,0,-1,166,0.000000,"\text{Not used}","int((g*sin(e + f*x))^(1/2)/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}}{\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((g*sin(e + f*x))^(1/2)/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
28,0,-1,168,0.000000,"\text{Not used}","int(1/((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\sin\left(e+f\,x\right)}\,\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/((g*sin(e + f*x))^(1/2)*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
29,0,-1,238,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c + c*sin(e + f*x))),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{\sin\left(e+f\,x\right)\,\left(c+c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c + c*sin(e + f*x))), x)","F"
30,0,-1,246,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\left(c+c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))), x)","F"
31,0,-1,267,0.000000,"\text{Not used}","int(((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+b\,\sin\left(e+f\,x\right)}}{c+c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2))/(c + c*sin(e + f*x)), x)","F"
32,0,-1,116,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/((g*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{\sqrt{g\,\sin\left(e+f\,x\right)}\,\left(c+c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/((g*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))), x)","F"
33,0,-1,252,0.000000,"\text{Not used}","int((g*sin(e + f*x))^(1/2)/((a + b*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}}{\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\left(c+c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*sin(e + f*x))^(1/2)/((a + b*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))), x)","F"
34,0,-1,256,0.000000,"\text{Not used}","int(1/((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\left(c+c\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2)*(c + c*sin(e + f*x))), x)","F"
35,0,-1,123,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2))/sin(e + f*x),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}{\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))/sin(e + f*x), x)","F"
36,0,-1,61,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\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)/(sin(e + f*x)*(c + d*sin(e + f*x))^(1/2)), x)","F"
37,0,-1,140,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{\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)/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)), x)","F"
38,0,-1,140,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\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/(sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
39,1,23933,181,27.406599,"\text{Not used}","int(sin(e + f*x)^2/((a + b*sin(e + f*x))^2*(c + d*sin(e + f*x))),x)","-\frac{\frac{2\,a^2}{\left(a^2-b^2\right)\,\left(a\,d-b\,c\right)}+\frac{2\,a\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\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{c^2\,\mathrm{atan}\left(\frac{\frac{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{c^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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{c^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(a^5\,b\,c^5+d\,a^4\,b^2\,c^4-2\,a^3\,b^3\,c^5\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(2\,a^6\,c^5+4\,a^5\,b\,c^4\,d-6\,a^4\,b^2\,c^5+2\,a^4\,b^2\,c^3\,d^2-6\,a^3\,b^3\,c^4\,d+4\,a^2\,b^4\,c^5\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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{c^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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{c^2\,\sqrt{d^2-c^2}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{c^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{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{a\,\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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{a\,\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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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(a^5\,b\,c^5+d\,a^4\,b^2\,c^4-2\,a^3\,b^3\,c^5\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(2\,a^6\,c^5+4\,a^5\,b\,c^4\,d-6\,a^4\,b^2\,c^5+2\,a^4\,b^2\,c^3\,d^2-6\,a^3\,b^3\,c^4\,d+4\,a^2\,b^4\,c^5\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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{a\,\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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^8\,c^4\,d^2+2\,a^7\,b\,c^3\,d^3-a^6\,b^2\,c^6-6\,a^6\,b^2\,c^4\,d^2+a^6\,b^2\,c^2\,d^4+2\,a^5\,b^3\,c^5\,d-5\,a^5\,b^3\,c^3\,d^3+2\,a^4\,b^4\,c^6+8\,a^4\,b^4\,c^4\,d^2-3\,a^3\,b^5\,c^5\,d-a^2\,b^6\,c^6\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^8\,c^5\,d+2\,a^8\,c^3\,d^3+2\,a^7\,b\,c^6-4\,a^7\,b\,c^4\,d^2+4\,a^7\,b\,c^2\,d^4+10\,a^6\,b^2\,c^5\,d-13\,a^6\,b^2\,c^3\,d^3+2\,a^6\,b^2\,c\,d^5-8\,a^5\,b^3\,c^6+13\,a^5\,b^3\,c^4\,d^2-10\,a^5\,b^3\,c^2\,d^4-13\,a^4\,b^4\,c^5\,d+16\,a^4\,b^4\,c^3\,d^3+9\,a^3\,b^5\,c^6-8\,a^3\,b^5\,c^4\,d^2+2\,a^2\,b^6\,c^5\,d-2\,a\,b^7\,c^6\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{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(a^{10}\,c^2\,d^5-4\,a^9\,b\,c^3\,d^4+a^9\,b\,c\,d^6+6\,a^8\,b^2\,c^4\,d^3-6\,a^8\,b^2\,c^2\,d^5-4\,a^7\,b^3\,c^5\,d^2+13\,a^7\,b^3\,c^3\,d^4-a^7\,b^3\,c\,d^6+a^6\,b^4\,c^6\,d-12\,a^6\,b^4\,c^4\,d^3+5\,a^6\,b^4\,c^2\,d^5+3\,a^5\,b^5\,c^5\,d^2-9\,a^5\,b^5\,c^3\,d^4+2\,a^4\,b^6\,c^6\,d+6\,a^4\,b^6\,c^4\,d^3-a^3\,b^7\,c^7+a^3\,b^7\,c^5\,d^2-3\,a^2\,b^8\,c^6\,d+a\,b^9\,c^7\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^3\,d^4-8\,a^9\,b\,c^4\,d^3+2\,a^9\,b\,c^2\,d^5+12\,a^8\,b^2\,c^5\,d^2-14\,a^8\,b^2\,c^3\,d^4+2\,a^8\,b^2\,c\,d^6-8\,a^7\,b^3\,c^6\,d+36\,a^7\,b^3\,c^4\,d^3-12\,a^7\,b^3\,c^2\,d^5+2\,a^6\,b^4\,c^7-44\,a^6\,b^4\,c^5\,d^2+32\,a^6\,b^4\,c^3\,d^4-2\,a^6\,b^4\,c\,d^6+26\,a^5\,b^5\,c^6\,d-48\,a^5\,b^5\,c^4\,d^3+10\,a^5\,b^5\,c^2\,d^5-6\,a^4\,b^6\,c^7+42\,a^4\,b^6\,c^5\,d^2-20\,a^4\,b^6\,c^3\,d^4-20\,a^3\,b^7\,c^6\,d+20\,a^3\,b^7\,c^4\,d^3+4\,a^2\,b^8\,c^7-10\,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{a\,\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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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(c\,a^2+d\,a\,b-2\,c\,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,"- ((2*a^2)/((a^2 - b^2)*(a*d - b*c)) + (2*a*b*tan(e/2 + (f*x)/2))/((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)) - (c^2*atan(((c^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) + (c^2*(d^2 - c^2)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) + (c^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) + (c^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) - (c^2*(d^2 - c^2)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) - (c^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*(a^5*b*c^5 - 2*a^3*b^3*c^5 + a^4*b^2*c^4*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) + (64*tan(e/2 + (f*x)/2)*(2*a^6*c^5 + 4*a^2*b^4*c^5 - 6*a^4*b^2*c^5 - 6*a^3*b^3*c^4*d + 2*a^4*b^2*c^3*d^2 + 4*a^5*b*c^4*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) + (c^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) + (c^2*(d^2 - c^2)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) + (c^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) - (c^2*(d^2 - c^2)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) - (c^2*(d^2 - c^2)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) - (c^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)) - (a*atan(((a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) + (a*((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)*(a^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d)*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) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) - (a*((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)*(a^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d)*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*(a^5*b*c^5 - 2*a^3*b^3*c^5 + a^4*b^2*c^4*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) + (64*tan(e/2 + (f*x)/2)*(2*a^6*c^5 + 4*a^2*b^4*c^5 - 6*a^4*b^2*c^5 - 6*a^3*b^3*c^4*d + 2*a^4*b^2*c^3*d^2 + 4*a^5*b*c^4*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) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) + (a*((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)*(a^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d))/(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*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(2*a^4*b^4*c^6 - a^2*b^6*c^6 - a^6*b^2*c^6 + a^8*c^4*d^2 - 3*a^3*b^5*c^5*d + 2*a^5*b^3*c^5*d + 2*a^7*b*c^3*d^3 + 8*a^4*b^4*c^4*d^2 - 5*a^5*b^3*c^3*d^3 + a^6*b^2*c^2*d^4 - 6*a^6*b^2*c^4*d^2))/(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^7*b*c^6 - 2*a*b^7*c^6 - 2*a^8*c^5*d + 9*a^3*b^5*c^6 - 8*a^5*b^3*c^6 + 2*a^8*c^3*d^3 + 2*a^2*b^6*c^5*d - 13*a^4*b^4*c^5*d + 2*a^6*b^2*c*d^5 + 10*a^6*b^2*c^5*d + 4*a^7*b*c^2*d^4 - 4*a^7*b*c^4*d^2 - 8*a^3*b^5*c^4*d^2 + 16*a^4*b^4*c^3*d^3 - 10*a^5*b^3*c^2*d^4 + 13*a^5*b^3*c^4*d^2 - 13*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) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(a*b^9*c^7 - a^3*b^7*c^7 + a^10*c^2*d^5 - 3*a^2*b^8*c^6*d + 2*a^4*b^6*c^6*d + a^6*b^4*c^6*d - a^7*b^3*c*d^6 - 4*a^9*b*c^3*d^4 + a^3*b^7*c^5*d^2 + 6*a^4*b^6*c^4*d^3 - 9*a^5*b^5*c^3*d^4 + 3*a^5*b^5*c^5*d^2 + 5*a^6*b^4*c^2*d^5 - 12*a^6*b^4*c^4*d^3 + 13*a^7*b^3*c^3*d^4 - 4*a^7*b^3*c^5*d^2 - 6*a^8*b^2*c^2*d^5 + 6*a^8*b^2*c^4*d^3 + 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)*(4*a^2*b^8*c^7 - 6*a^4*b^6*c^7 + 2*a^6*b^4*c^7 + 2*a^10*c^3*d^4 - 20*a^3*b^7*c^6*d + 26*a^5*b^5*c^6*d - 2*a^6*b^4*c*d^6 - 8*a^7*b^3*c^6*d + 2*a^8*b^2*c*d^6 + 2*a^9*b*c^2*d^5 - 8*a^9*b*c^4*d^3 - 10*a^2*b^8*c^5*d^2 + 20*a^3*b^7*c^4*d^3 - 20*a^4*b^6*c^3*d^4 + 42*a^4*b^6*c^5*d^2 + 10*a^5*b^5*c^2*d^5 - 48*a^5*b^5*c^4*d^3 + 32*a^6*b^4*c^3*d^4 - 44*a^6*b^4*c^5*d^2 - 12*a^7*b^3*c^2*d^5 + 36*a^7*b^3*c^4*d^3 - 14*a^8*b^2*c^3*d^4 + 12*a^8*b^2*c^5*d^2 + 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) - (a*((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)*(a^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d))/(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^2*c - 2*b^2*c + a*b*d))/(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)*(a^2*c - 2*b^2*c + a*b*d)*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"
40,0,-1,154,0.000000,"\text{Not used}","int((c + d*sin(e + f*x))^(1/2)/(sin(e + f*x)*(a + b*sin(e + f*x))),x)","\int \frac{\sqrt{c+d\,\sin\left(e+f\,x\right)}}{\sin\left(e+f\,x\right)\,\left(a+b\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((c + d*sin(e + f*x))^(1/2)/(sin(e + f*x)*(a + b*sin(e + f*x))), x)","F"
41,0,-1,146,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{1}{\sin\left(e+f\,x\right)\,\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/(sin(e + f*x)*(a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)), x)","F"
42,0,-1,254,0.000000,"\text{Not used}","int(((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+b\,\sin\left(e+f\,x\right)}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x)), x)","F"
43,0,-1,250,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/((g*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{\sqrt{g\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((a + b*sin(e + f*x))^(1/2)/((g*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
44,0,-1,114,0.000000,"\text{Not used}","int((g*sin(e + f*x))^(1/2)/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}}{\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((g*sin(e + f*x))^(1/2)/((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
45,0,-1,246,0.000000,"\text{Not used}","int(1/((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{1}{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((g*sin(e + f*x))^(1/2)*(a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
46,0,-1,254,0.000000,"\text{Not used}","int(((g*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((g*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x)), x)","F"
47,0,-1,114,0.000000,"\text{Not used}","int((g*sin(e + f*x))^(1/2)/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{g\,\sin\left(e+f\,x\right)}}{\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((g*sin(e + f*x))^(1/2)/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2)), x)","F"
48,0,-1,391,0.000000,"\text{Not used}","int(((a + b*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^(1/2))/sin(e + f*x),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}\,\sqrt{c+d\,\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)*(c + d*sin(e + f*x))^(1/2))/sin(e + f*x), x)","F"
49,0,-1,198,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^(1/2)/(sin(e + f*x)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{\sqrt{a+b\,\sin\left(e+f\,x\right)}}{\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)/(sin(e + f*x)*(c + d*sin(e + f*x))^(1/2)), x)","F"
50,0,-1,398,0.000000,"\text{Not used}","int(1/(sin(e + f*x)*(a + b*sin(e + f*x))^(1/2)*(c + d*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)}\,\sqrt{c+d\,\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)*(c + d*sin(e + f*x))^(1/2)), x)","F"
51,0,-1,157,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))^p*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int {\left(A+B\,\sin\left(e+f\,x\right)\right)}^p\,{\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 + B*sin(e + f*x))^p*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"